# The Prime Focus Spectrograph Galaxy Evolution Survey

Jenny E. Greene  Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA  Rachel Bezanson  Department of Physics and
Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA  Masami Ouchi
Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha,
Kashiwa, Chiba 277-8582, Japan  Kavli IPMU (WPI), The University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan  John Silverman  Kavli IPMU
(WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583,
Japan  Department of Astronomy, School of Science, The University of Tokyo,
7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan  Stéphane Arnouts  Aix Marseille
University, CNRS, CNES, LAM, Marseille, France  Andy D. Goulding  Department
of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Meng Gu  Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA  James E. Gunn  Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  Yuichi Harikane  Institute for
Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,
Chiba 277-8582, Japan  Timothy Heckman  Johns Hopkins University  Benjamin
Horowitz  Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA  Sean D. Johnson  University of Michigan  Daichi
Kashino  Institute for Advanced Research, Nagoya University, Nagoya 464-8601,
Japan  Division of Particle and Astrophysical Science, Graduate School of
Science, Nagoya University, Nagoya 464-8602, Japan  Khee-Gan Lee  Kavli IPMU
(WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583,
Japan  Joel Leja  Department of Astronomy & Astrophysics, The Pennsylvania
State University, University Park, PA 16802, USA  Institute for Computational
& Data Sciences, The Pennsylvania State University, University Park, PA, USA
Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA  Yen-Ting Lin  Institute of Astronomy and
Astrophysics, Academia Sinica  Danilo Marchesini  Tufts University  Yoshiki
Matsuoka  Research Center for Space and Cosmic Evolution, Ehime University
Kentaro Nagamine Theoretical Astrophysics, Department of Earth & Space
Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama,
Toyonaka, Osaka 560-0043, Japan  Kavli IPMU (WPI), The University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan  Department of Physics &
Astronomy, University of Nevada, Las Vegas, 4505 S. Maryland Pkwy, Las Vegas,
NV 89154-4002, USA  Yoshiaki Ono  Institute for Cosmic Ray Research, The
University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582, Japan  Alan
Pearl  Department of Physics and Astronomy, University of Pittsburgh,
Pittsburgh, PA 15260, USA  Takatoshi Shibuya  Kitami Institute of Technology,
165 Koen-cho, Kitami, Hokkaido 090-8507, Japan  Michael A. Strauss  Department
of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Allison L. Strom  Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA  Yuma Sugahara  National Astronomical Observatory of
Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Waseda Research Institute
for Science and Engineering, Faculty of Science and Engineering, Waseda
University, 3-4-1, Okubo, Shinjuku, Tokyo 169-8555, Japan  Laurence Tresse
Aix Marseille University, CNRS, CNES, LAM, Marseille, France  Kiyoto Yabe
Kavli IPMU (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba
277-8583, Japan  Takuji Yamashita  National Astronomical Observatory of Japan,
2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Masayuki Akiyama  Astronomical
Institute, Tohoku University  Metin Ata  Kavli IPMU (WPI), The University of
Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan  Gabriel M. Azevedo
Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Av.
Bento Gonçalves, 9500, Porto Alegre, RS, Brazil  Chian-Chou Chen  Academia
Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Sec. 4,
Roosevelt Road, Taipei 10617, Taiwan  Ana L. Chies-Santos  Instituto de
Física, Universidade Federal do Rio Grande do Sul (UFRGS), Av. Bento
Gonçalves, 9500, Porto Alegre, RS, Brazil  Richard S Ellis  University College
London  ChangHoon Hahn  Department of Astrophysical Sciences, Princeton
University, Princeton, NJ 08544, USA  Gabriel Roberto Hauschild Roier
Universidade Federal do Rio Grande do Sul  Kohei Ichikawa  Tohoku University
Kei Ito  Department of Astronomy, School of Science, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan  Linhua Jiang  Kavli Institute
for Astronomy and Astrophysics, Peking University, Beijing 100871, China  Y.P.
Jing  Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao
Tong University, Shanghai, 200240, People’s Republic of China  Taiki Kawamuro
Extreme Natural Phenomena RIKEN Hakubi Research Team, Cluster for Pioneering
Research, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan  Chiaki Kobayashi
Centre for Astrophysics Research, Department of Physics, Astronomy and
Mathematics, University of Hertfordshire, Hatfield, AL10 9AB, UK  Katarina
Kraljic  Aix Marseille University, CNRS, CNES, LAM, Marseille, France  Vincent
Le Brun  Aix Marseille University, CNRS, CNES, LAM, Marseille, France  Xin Liu
Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W.
Green Street, Urbana, IL 61801, USA; National Center for Supercomputing
Applications, 1205 W. Clark Street, Urbana, IL 61801, USA  Peter Melchior
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA  Claudia L. Mendes de Oliveira  Departamento de Astronomia,
Instituto de Astronomia, Geofísica e Ciências Atmosféricas da USP, Cidade
Universitária, 05508-900, São Paulo, SP, Brazil  Rogério Monteiro-Oliveira
Academia Sinica, Institute of Astronomy and Astrophysics, 11F of AS/NTU
Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Rd, Taipei 10617,
Taiwan, R.O.C.  Tohru Nagao  Ehime University  Masato Onodera  Subaru
Telescope, National Astronomical Observatory of Japan, National Institutes of
Natural Sciences (NINS), 650 North A’ohoku Place, Hilo, HI 96720, USA  Roderik
A. Overzier  Observatório Nacional/MCTI, Rua General José Cristino, 77, São
Cristóvão, Rio de Janeiro, RJ 20921-400, Brazil  David Schiminovich
Department of Astronomy, Colunbia University  Malte Schramm  Planetary
Exploration Research Center, Chiba Institute of Technology, Tsudanuma,
Narashino, Chiba 275-0016, Japan  Rhythm Shimakawa  National Astronomical
Observatory of Japan  Laerte Sodré  Departamento dAstronomia, IAG,
Universidade de São Paulo  Thaisa Storchi-Bergmann  Instituto de Fisica -
Universidade Federal do Rio Grande do Sul, RS, Brazil  Tomoko L. Suzuki  Kavli
IPMU (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba
277-8583, Japan  Masayuki Tanaka  National Astronomical Observatory of Japan,
2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Yoshiki Toba  National
Astronomical Observatory of Japan  Hideki Umehata  Nagoya University  Jiaqi
Wang  Department of Astronomy, School of Physics and Astronomy, and Shanghai
Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong
University, Shanghai 200240, China  Charlotte Welker  Johns Hopkins University
Katherine Whitaker  University of Massachusetts Amherst  Kun Xu  Department of
Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University,
Shanghai, 200240, People’s Republic of China  Yongquan Xue  CAS Key Laboratory
for Research in Galaxies and Cosmology, Department of Astronomy, University of
Science and Technology of China, Hefei 230026, China  Xiaohu Yang  Department
of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University,
Shanghai 200240, China  Ying Zu  Department of Astronomy, School of Physics
and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

###### Abstract

We present the Prime Focus Spectrograph (PFS) Galaxy Evolution pillar of the
360-night PFS Subaru Strategic Program. This 130-night program will capitalize
on the wide wavelength coverage and massive multiplexing capabilities of PFS
to study the evolution of typical galaxies from cosmic dawn to the present.
From Lyman $\alpha$ emitters at $z\sim 7$ to probe reionization, drop-outs at
$z\sim 3$ to map the inter-galactic medium in absorption, and a continuum-
selected sample at $z\sim 1.5$, we will chart the physics of galaxy evolution
within the evolving cosmic web. This article is dedicated to the memory of
Olivier Le Fevre, who was an early advocate for the construction of PFS, and a
key early member of the Galaxy Evolution Working Group.

footnote

##  1 Introduction

Figure 1: Number of spectra in each subset of the PFS GE survey (top) and a
representative light cone to demonstrate the key redshift regimes it will
probe (middle). Pop-out panels depict the recovery of cosmic structures from
the PFS SSP (top panels: truth, bottom panels: recovered) at $\langle
z\rangle=1.1,2.4$ and 6.6. The top left panel shows reionization bubbles in
the HI 21cm brightness temperature distribution from Kubota & Done (2019),
while the bottom panel shows the LAE distribution observed by PFS
spectroscopy, which is anti-correlated with the ionized bubbles in this
particular model. The top middle and right panels show the simulated density
fields from the Horizon AGN simulation at $\langle z\rangle=2.4$ and $\langle
z\rangle=1.1$, while bottom middle and right show the reconstructed density
from the PFS galaxy redshift distribution and IGM absorption data using the
ARGO (Ata et al., 2015) and TARDIS (Horowitz et al., 2019a) algorithms,
respectively.

The evolution of galaxies is inextricably linked to the cosmic web (Somerville
& Davé, 2015). After inflation, the primordial density fluctuations grow via
gravitational instability, increasing the density contrast in the dark matter,
and eventually forming a cosmic web of sheets, filaments, and nodes containing
virialized dark matter halos. Baryons flow with the dark matter on large
scales, and some are incorporated into the halos. Unlike dark matter, baryons
can lose energy by radiation, and sink deeper into the potential well. In the
simplest picture, this inflow is halted by centrifugal forces and the baryons
form a disk (Mo et al., 1998; Burkert et al., 2016). Stars form within the
central regions of these disks, as do the seeds of supermassive black holes.
Galaxies continue to grow over billions of years, primarily through continuing
accretion of gas from the web, and secondarily through mergers with other dark
matter haloes and their baryonic contents (e.g., Vogelsberger et al., 2014).

In this standard Cold Dark Matter paradigm, the formation and evolution of
galaxies are driven both by the collapse, growth, and assembly of dark matter
halos in which galaxies reside, and by complex baryonic physics. In
particular, feedback from massive stars and supermassive black holes play a
critical role (e.g., Croton et al., 2006). The large-scale environment, on a
variety of scales, may also impact both the dark matter accretion history and
baryonic processes in complex ways (e.g., Cooper et al., 2008; Peng et al.,
2010; Kovač et al., 2014). To fully map the connection between large-scale
structure and galaxy evolution, we need to explore a large range of scales,
from kpc to tens of Mpc, and redshifts from $z=1$ to 6, which can be mapped
with a dense spectroscopic survey covering more than 10 deg2 in order to cover
transverse scales of $\gtrsim 100$ Mpc.

This is the primary objective of the Galaxy Evolution Survey planned for the
Prime Focus Spectrograph, as we describe below. The paper will proceed as
follows. In §3 we lay out the main science questions that drive the survey
design, while in §4, we describe the samples required to answer these
questions. §5 presents the available photometry to select these samples and §6
describes the sensitivity assumptions and mock galaxy catalogs that we use for
planning. Finally, in §7 we justify the survey design by presenting the
deliverables that we have extracted from our mock spectra. Throughout this
document we use the AB magnitude system unless specified otherwise.

Figure 2: (Left) The combined spectral resolution and statistical samples
produced by the PFS GE survey components would lie in unprecedented parameter
space at $z\gtrsim 1$ (compilation adapted from Förster Schreiber & Wuyts
2020). (Right) The dense sampling and large volume probed by the PFS sample
will extend maps of the cosmic web beyond the local Universe. Our high
sampling reaches smaller average inter-galaxy separations than previous high
redshift surveys.

##  2 Half a Million Spectra Covering 6 Gyrs of Cosmic Evolution

Outstanding questions about the physics of galaxy formation cannot be answered
without a large spectroscopic survey at $z>1$. Spectra provide a rich suite of
diagnostics of the fundamental properties of galaxies and their environments.
The sample must be large to map out the distributions of, and causal
connections between, these properties, and to chart their evolution in
redshift. In order to optimally measure the galaxy properties, the spectral
resolution must be matched to the internal velocity dispersions of galaxies,
and the signal-to-noise ratio must be sufficient to measure the key spectral
diagnostics. To connect the properties of galaxies to the large-scale cosmic
web, the spectroscopic survey must have sufficient spatial sampling over a
wide enough area to average over cosmic variance and span environments at
density extremes.

Table 1: Galaxy samples and depths

Type | Redshift | Selection | Exp. Time | # of spectra
---|---|---|---|---
| range |  | (hrs) | (${\times}10^{3}$)
Continuum | $0.7-2$ | $y,J{<}22.8$ | 2, 12 | $261,\,14$
IGM | $2.1-3.5$ |  $y{<}24.3$,$g{<}24.7$ | 6, 12 | $30.3,\,14$
LBG | $3.5-7$ | $y{<}24.5$ | 6 | 22
LAE | $2.2,\,5.7,\,6.6$ |  L${}_{\rm Ly\alpha}{>}3{\times}10^{42}$ erg s-1 | $3,\,6,\,12$ | $7.4,\,4.5,\,2.8$
AGN-GE | $0.5-6.0$ | various (see text) | $1-5$ | 4.2

Note. — Shortened target table, including the main science targets, their
redshift ranges, the main selection criteria (in AB mags), exposure times, and
expected number of spectra. “Continuum” refers to the $0.7{<}z{<}1.7$ survey;
“IGM” is the inter-galactic medium tomography More details are given in §3
below.

The Subaru Prime Focus Spectrograph (PFS), currently under construction for
the 8.2m Subaru Telescope on Maunakea, Hawai’i, is specifically designed to
make these goals feasible. With 2394 fibers covering a 1.25 deg2 field-of-view
and wide wavelength coverage spanning the ultraviolet to the near-infrared
($0.38-1.25\mu$m), the PFS is uniquely positioned in the coming decade to
probe the evolution of typical Milky Way-like galaxies from the epoch of
reionization at $z\sim 7$ to the present. The PFS Galaxy Evolution (GE) survey
will target complementary sub-samples, each designed to fully leverage the
instrumental capabilities and capture the physical properties of galaxies at
critical moments in cosmic history (see Table 1 and Figure 1). The GE survey
will leverage deep imaging from the Hyper Suprime-Cam Subaru Strategic Program
(HSC-SSP; Aihara et al. 2018) Deep fields, as described in detail in §5. The
PFS Galaxy Evolution survey will be one pillar of a proposed 360-night Subaru
Strategic Program for PFS (PFS-SSP) following commissioning. Together, the
three pillars – Cosmology, Galactic Archeology, and Galaxy Evolution – will
focus on Cosmic Evolution and The Dark Sector; the Galaxy Evolution pillar is
a critical component that focuses on tying evolution in dark matter halos with
galaxies (Takada et al., 2014).

The PFS Galaxy Evolution survey represents a dramatic improvement in sample
size, spectral resolution, and density of targeting over previous
spectroscopic surveys of the critical epoch of galaxy formation ($z{>}1$).
Previous studies have been limited to lower redshifts [e.g., DEEP-2 (Newman et
al., 2013), zCOSMOS (Lilly et al., 2007), VVDS (Le Fèvre et al., 2005), LEGA-C
(van der Wel et al., 2016)] or at higher-z to much smaller, biased samples
[e.g., KBSS (Steidel et al., 2014a), MOSDEF (Kriek et al., 2015), and FMOS-
COSMOS (Silverman et al., 2015)] or low spectral resolution (e.g., 3D-HST,
Momcheva et al. 2016) (Fig. 2). Our survey is also highly complementary to the
other upcoming massively multiplexed spectroscopic survey studying the
properties of $z=1-6$ galaxies, MOONRISE (Maiolino et al., 2020). VLT/MOONS
will cover the rest-frame optical lines to $z\approx 2$, allowing for better
characterization of inter-stellar medium (ISM) physics at cosmic noon. PFS
will have more than twice the number of fiber-hours ($\sim$1.3 million versus
500,000 for the MOONRISE XSwitch strategy) and blue coverage. These together
allow us to perform an inter-galactic medium (IGM) tomography survey,
characterizing the cosmic web and the IGM at cosmic noon, go deep on
continuum-selected galaxies at $z\approx 1.5$, and probe Lyman $\alpha$
(Ly$\alpha$) emission in galaxies at $z\gtrsim 2$. Finally, our high spectral
resolution and broad wavelength coverage will also be complementary to the
Euclid (Laureijs et al., 2011) and Roman Space Telescope (Spergel et al.,
2015) grism surveys.

We will study the peak epoch of star formation using continuum-selected
galaxies with $J{<}22.8$, which will capture $\sim$90% of the
$M_{*}~{}{\gtrsim}~{}3{\times}10^{10}$ ${\rm M}_{\odot}$ population. This Main
sample of 300,000 galaxies will have a ${\sim}70\%$ average completeness and
thus include multiple galaxies in groups down to $M_{\rm halo}{\sim}10^{13.5}$
${\rm M}_{\odot}$. Exposure times of 2-hr integrations will provide a high
spectroscopic redshift completeness. We will integrate for 8-12 hrs on an
additional 14,000 galaxies (the “Deep” sample) to measure stellar ages,
chemical abundance ratios, stellar velocity dispersions, and faint emission
lines such as [O III]$\,\lambda\,4363$.

The overarching connection of galaxies to large-scale structures will be
extended out to $z{\sim}6$. In particular, the distribution of neutral
hydrogen in the cosmic web at $z{=}2.1{-}2.5$ will be mapped at a co-moving
scale of $\sim$4 Mpc through an IGM tomographic experiment based on the
detection of Ly$\alpha$ absorption seen in the spectra of background galaxies
at $2.5{<}z{<}3.5$. From $3.5{<}z{<}7$, we will target Lyman Break Galaxies
(LBGs) to $y{<}24.5$, which will provide a powerful sample for studying the
early formation of galaxies and their clustering strength. These will be
complemented at the furthest distances with a sample of $\sim$15k Ly$\alpha$
Emitters (LAE) at $6{<}z{<}7$ selected from the Subaru/HSC narrow-band imaging
to probe the formation of young galaxies at cosmic dawn.

Together, these samples will allow us to jointly address two main themes from
$z\sim 1$ to the epoch of reionization. On the largest scale, we will map the
cosmic web through the distribution of galaxies (§3.1 and §3.2). On smaller
scales, we will measure the evolution of the properties of the stars and gas
in galaxies to elucidate the underlying physical processes driving their
formation and growth (§3.3).

Table 2: Large Scale Structure

Component of the Web | Expected Number
---|---
$M_{\rm halo}>10^{13}\,M_{\odot}$ | 2200
$M_{\rm halo}>10^{13.5}\,M_{\odot}$ | 450
$M_{\rm halo}>10^{14}\,M_{\odot}$ | 35
Voids ($z{<}2$, $r>7$ cMpc) | 132,000
Voids ($z{<}2$, $r>20$ cMpc) | 3,000
Voids ($z>2$, $r>7$ cMpc) | 1000
Protoclusters ($2{<}z{<}6$) | 100

Note. — Top three rows quantify the number of massive halos that we expect
above this limit in the PFS volume. Next three lines quantify the number of
voids with the given redshift and size limits. The final entry is the expected
number of protoclusters.

##  3 Galaxies within the Cosmic Web

The growth of structure drives the evolution of dark matter halos and the flow
of gas between and into galaxies, and therefore is the fundamental process
behind the formation and evolution of galaxies themselves. On the largest
scales, we have strong theoretical reasons to believe that galaxies evolving
in voids will have different star formation histories and angular momentum
distributions from those in filaments or nodes. We know that the orientation
of filaments does impact the spins of galaxies (e.g., Kereš et al., 2005;
Pichon et al., 2011; Zhang et al., 2013), and possibly their star formation
histories (e.g., Kraljic et al., 2018a), while mergers which take place along
filaments can change the galaxy angular momentum and may lead to quenching
(e.g., Dubois et al., 2014). Large galaxy redshift surveys like VIPERS and
zCOSMOS at $z\approx 0.7$ are just starting to detect these effects (Malavasi
et al., 2017; Laigle et al., 2018). Prior to PFS it was not possible for a
single survey to test this at earlier times with simultaneously (a) wide
enough area to probe the rarest overdensities and overcome cosmic variance and
(b) dense enough sampling to trace the large-scale structure on ${\sim}1{-}3$
Mpc scales. Thanks to our unprecedented multiplexing and wavelength coverage,
we will perform the redshift survey needed to make a high-fidelity map of the
large-scale structure in the distant Universe and situate the galaxy
properties within that context.

###  3.1 Charting the Evolving Cosmic Web

PFS will substantially expand on existing surveys both in sky volume and
object density, mapping galaxies and gas at three critical epochs. We show the
key targets for cosmic web reconstruction in Figure 1. With the Main and Deep
samples at $z\sim 1.1$ we will test the role of the cosmic web in regulating
star formation at cosmic noon (right). At $z\sim 2.4$, we will use IGM
tomography to produce the most detailed and largest-scale maps of the
intergalactic medium that fuels galaxies at the peak epoch of star formation
(center). Finally, the program will use LAEs at $z=6-7$ to map the
reionization of the Universe (left). Together, these three regions will
provide a representative picture of the galaxy-environment relationship over
cosmic time.

We will spectroscopically identify unprecedented numbers of groups,
(proto)clusters, and voids of a range of sizes (see Table 2) to facilitate
unprecedented tests of environmental effects on galaxy evolution at early
times (see more details in §7.9.1). We will explore the role of galaxy
overdensity in driving star formation histories and quenching as a function of
mass and redshift (e.g. Peng et al., 2010; Wang et al., 2018; Lemaux et al.,
2022). Deviations between galaxy environment and the associated HI absorption
will highlight the growth of the warm-hot intergalactic medium (Cen et al.,
2005) and intracluster medium (Kooistra et al., 2022).

###  3.2 Statistically connecting Galaxies to the Cosmic Web

At $5.5{<}z{<}7$, spanning the epoch of reionization, we will map the galaxy-
cosmic web connection by measuring the spatial cross-power spectrum between
the ionizing galaxies, detected by PFS as LAEs, and the H I gas in the cosmic
web detected in redshifted 21 cm emission by the SKA1 array (Key Science
Project observations start in 2024; Fig. 3). Models predict that on small
scales (single ionized bubbles), one-halo clustering introduces a positive
correlation. Beyond a bubble radius, an anti-correlation will result if
reionization proceeds from regions of high to low density. The amplitude of
the signal, the spatial scale at the correlations become negative (the cross-
power spectrum transition), and the overall shape of the cross-power spectrum,
all constrain the reionization history of the Universe (e.g., Sobacchi et al.,
2016).

With the PFS LAE spectroscopic data, we will calculate the cross-power
spectrum of the spatial distribution of the LAEs and redshifted Hi 21-cm radio
emission using the data from the SKA-1 at $z\sim 6-7$ (Hasegawa et al. 2016),
aiming at the first detection of the epoch of reionization 21-cm emission and
the identification of the cross-power spectrum transition at the $3-5\sigma$
levels. The radiation transfer models of Kubota & Done (2018) demonstrate that
the PFS LAEs and the 21-cm data will allow us to detect the cross-power
spectrum turnover (Fig. 3), which cannot be accomplished with only HSC
imaging, due to the redshift uncertainty of LAEs. The PFS measurements for the
spatial distribution of LAEs will reveal the cross-power spectrum turnover
scale ($k\sim 0.2$ Mpc-1) with the accuracy of $\delta k=0.1$ and the overall
shape of the cross-correlation, which determine the reionization history and
ionized bubble topology, respectively.

Figure 3: Spatial distribution of LAEs and imprint on reionization: The
absolute cross-power spectrum of brightness temperature between LAEs and 21cm
emission at $z=6.6$ ($|\Delta^{2}_{\rm 21gal}|$) is shown as a function of the
wavenumber $k$. The red solid line indicates the expected signal predicted by
numerical simulations tailored for the PFS survey (Kubota & Done, 2018). The
red dotted line is the same as the red solid line, but indicates the negative
signal, and the cross-power spectrum turnover is found at $k\sim 0.2$ Mpc-1.
The grey shade represents the variance in the PFS survey field. The black and
blue dotted lines denote the sensitivity of LAE observations accomplished by
the HSC SSP survey alone and the combination of HSC+PFS observations,
respectively.

At cosmic noon, the IGM tomography sample will not only trace the cosmic web,
but also give us new insight into the state of the gas in and around galaxies.
A critical component of our program is the measurement of foreground galaxy
redshifts (i.e., 25k continuum-selected galaxies, 9.2k LAEs, and 1.3k AGN)
that lie within the H I web. With this sample, we will use galaxy
morphological features identified through HSC (and later Roman) imaging to
constrain possible intrinsic alignments with respect to the cosmic web traced
by the HI tomography (Krolewski et al., 2017). We will also measure the 3D
cross-correlation between the galaxies and HI absorption to constrain the
underlying bias (and hence halo mass) of the galaxies as a function of stellar
mass, star-formation rate, metallicity, and other properties. Cross-
correlations can also be extended to metals reflecting the velocity field near
galaxies, allowing the study to extend down to CGM scales in conjunction with
detailed hydrodynamical simulations (Turner et al., 2017; Nagamine et al.,
2021).

With PFS, we can robustly measure the evolution of the stellar mass function
and the distribution of specific star-formation rates as a function of the
local mean over-density, to extend known trends between quenching and
environment at $z{<}1$. There are tantalizing clues that the sign of the
morphology–density relation may change at higher redshift, with strong star
formation occurring in protocluster cores at $z\gtrsim 2$ (e.g. Wang et al.,
2016). We will also test whether the 3D location in the web (e.g. distance
from the nearest filament) plays an additional role in affecting galaxy
properties over a range of epochs (Laigle et al., 2018).

On $\sim$Mpc scales, the connection between galaxies and their host dark
matter halos has provided a compelling framework to understand the overall
efficiency of galaxy formation (e.g. Wechsler & Tinker, 2018). The most basic
measure of this relation is the stellar mass-to-halo mass (SMHM) relation
(e.g., Yang et al., 2012), which captures the overall efficiency of star
formation over the entire history of the Universe (e.g. Behroozi et al., 2013;
Yang et al., 2013). This relation is often derived using two-point statistics
to compare the biased clustering of galaxies at a given stellar mass to
compute the average masses of host dark matter haloes (Figure 4a). The default
analytic models used to describe the “galaxy-halo connection” rely on
deterministic mappings (including scatter) between $M_{halo}$ and $M_{\star}$
(e.g., Berlind & Weinberg, 2002; Yang et al., 2003), but increasing evidence
suggests that additional secondary factors, such as relative halo assembly
history, are important in driving the timing and efficiency of galaxy
formation. Empirically, this “assembly bias” manifests as stronger clustering
of older (or less-star-forming) galaxies at fixed stellar mass (Fig. 4b)
(e.g., Gao & White, 2007). No other photometric or spectroscopic survey at
$z>1$ would have the necessary statistics, accurate 3D positions, stellar
masses, star formation rates, and halo masses derived from clustering
measurements and halo occupation distribution models (e.g., Durkalec et al.,
2015; Kashino et al., 2017a) to measure the SMHM relation and test for the
importance of assembly bias in understanding the galaxy-halo connection in the
early Universe.

Figure 4: The expected projected clustering signal of continuum-selected
galaxies as measured from the PFS mock (Pearl et al., 2022), with errors
characteristic of the planned continuum-selected ($z{<}2$) sample volumes
after subdividing on stellar mass and specific star formation rate, without
(top) and with (bottom) assembly bias to show that the PFS Survey will allow
unprecedented clustering measurements, versus e.g., the FMOS survey (gray)
that can only measure clustering above a mass threshold (Kashino et al.,
2017b). Two-point correlation functions of spectroscopic samples of galaxies
provide a robust statistical measurement of host dark matter halo mass, thus
constraining the SMHM relation; PFS will constrain this relation from
$0.7\lesssim z\lesssim 4.5$. Furthermore, we will test models of the overall
efficiency of galaxy formation, as well as the existence of assembly bias in
the mapping from galaxy stellar mass to halo mass.

Finding clusters, voids, and filaments from $0.7{{<}}z{{<}}3$ demands the
following survey design parameters: (a) area $>$10 deg2 to probe $>1$ Gpc3
cosmic volumes and cover the largest overdensities, (b) sampling ${>}70\%$ to
get multiple galaxies in groups to 1013.5 ${\rm M}_{\odot}$, and (c) IGM
background targets to i$=$24.7 mag to sample the IGM with 3 Mpc resolution.

###  3.3 The Evolution of Internal Galaxy Properties:
From Statistics to Physics

To fully understand the drivers of galaxy evolution, we need to simultaneously
determine both what is flowing into galaxies (accretion of gas, dark matter,
and galaxies) and the galactic winds driven by star formation and black holes.
We need an accurate accounting of the star formation and chemical evolution
histories of galaxies at each epoch.

Our survey will have unprecedented wavelength coverage for half a million
galaxies from $0.7\lesssim z\lesssim 6$, which will allow us to quantify the
strength and prevalence of neutral outflows (§3.3.1), identify and study the
properties of active galactic nuclei that may also drive outflows, and situate
all of these physical properties within the evolving cosmic web. We can then
match the gas flows with the star formation histories of individual galaxies
(§3.3.2) and chemical abundances (§3.3.3).

####  3.3.1 Gas Flows

Most galaxies grow primarily through the accretion of gas from the cosmic web.
This inflow fuels new star formation and black hole growth, which in turn can
drive outflows that may change the dynamical and thermal state of the
inflowing gas. This cycle likely plays a key role in the self-regulation (and
quenching) of star formation and black hole growth. PFS will chart the
evolution of intergalactic gas on large scales, starting from reionization (as
probed by LAEs) through the metallicity and spatial distribution of the IGM at
$z{\sim}2$ with the IGM tomography experiment.

With PFS, feedback from both massive stars and AGN can be characterized by
measuring the incidence rate and outflow velocities of warm ionized gas as
traced by blue-shifted inter- stellar absorption-lines. This will require
stacking to achieve the necessary S/N, but the PFS sample size is so large
that the stacking can be done in many bins in the 4-D space of redshift,
stellar mass, star formation rate (SFR), and AGN luminosity. This will enable
direct tests of competing feedback models: momentum-driven (e.g. Murray et
al., 2005) vs. energy-driven winds (e.g. Chevalier & Clegg, 1985), that
predict how outflow velocities should depend on these quantities.

Figure 5: Demonstration that PFS spectra will recover star formation histories
over the key epoch of cosmic noon. In (d) we show that star formation
histories inferred from local galaxy spectra (red and blue lines) fail to
capture the basic rise-and-fall of the history of star formation (black), and
particularly diverge at cosmic noon (adapted from Leja et al., 2019). On the
other hand, PFS spectroscopy demonstrated in (a) from the Deep sample will
directly probe (${\lesssim}2$Gyr) star formation histories at this crucial
epoch, capturing both higher order moments (e.g. quenching, bursts) for
individual galaxies and the average star formation history of the galaxy
population to high precision. Specifically, in (b) we show models (red and
blue lines) representing non-parametric reconstructions that manage to recover
the main features of the input star formation histories, including a galaxy
with a recent burst hidden under a fresh phase of star formation (top) and a
galaxy which quenches slowly and gradually over several Gyr (bottom). Finally,
in (d) we see that [Fe/H] and, crucially, nonsolar abundances captured via
[Mg/Fe] are recovered within the uncertainties as well.

The interface where the inflow meets feedback is the circum-galactic medium
(CGM), a region with a scale of roughly the virial radius, and which contains
a baryonic mass comparable to the stellar component (Tumlinson et al., 2017).
PFS will probe the CGM around the $z{\sim}1$ continuum-selected sample using
the Ly$\alpha$ tomography sample as backlights, reaching expected equivalent
widths of 0.3 Å within 200 kpc impact parameters for 100-galaxy stacks. The
galaxy sample from the PFS cosmology survey will also be probed by SDSS
quasars as backlights, reaching 0.10 Å equivalent widths in stacks in bins of
redshift and impact parameter. At the same time, as described in the next two
sections, we will have access to the detailed star formation and chemical
enrichment histories of the target galaxies to connect with their CGM
reservoirs and larger scale environments.

####  3.3.2 Charting Detailed Star Formation Histories

The bulk of star formation over cosmic time occurs in galaxies on the “Star
Forming Main Sequence” (e.g., Noeske et al., 2007), a correlation between SFR
and $M_{\ast}$ that evolves strongly towards higher SFR with increasing
redshift (e.g., Speagle et al., 2014). While this evolution can be largely
understood as tracing the overall cosmic rate of accretion and merging, the
processes that lead to a relatively small dispersion in the relation at a
given redshift are poorly understood. Additional populations lie above and
below this relation; starburst galaxies are responsible for $\sim$10% of the
global star formation and a population of quenched galaxies dominate at the
highest masses today.

With the PFS dataset, the distribution of galaxies along and across the main
sequence, and the fraction of star-forming, starburst, quenching, and quenched
galaxies will be determined as a function of redshift. For the subset with
deep (12 hour) exposures, the continuum spectra will hold critical information
to describe higher-order moments of the star formation histories of galaxies,
where photometric measurements are fundamentally limited by the adopted priors
(e.g. Carnall et al., 2019), leading to the power of PFS to reconstruct real
star-formation histories at cosmic noon (Figure 5). In particular, we can
expect to reconstruct reliable star-formation histories and recover reliable
abundance ratios, for individual galaxies at $0.7{<}z{<}1.7$, particularly
from the Deep spectra (see also §7.3). Thus, we will begin to quantify the
extent of ongoing star formation, the importance of rejuvenation, and time the
quenching for $>$10,000 galaxies between $0.7{<}z{<}2$.

There is good evidence that the quenching process has evolved significantly
between $z\sim 0$ and 1 (Behroozi & Silk, 2018). As described in Sec. 7.10,
PFS will provide a detailed mapping between environmental metrics on scales
from individual dark matter halos to large scales (e.g., filaments and voids)
and galaxy star formation histories. We will also explore the role of active
galactic nuclei (AGN) in halting star formation. The main sample of AGN will
be drawn directly from the galaxy sample using a variety of strong-line
criteria (e.g., Baldwin et al., 1981a; Juneau et al., 2011), making it
straightforward to quantify incidence rates in the 3D parameter space of
stellar mass, SFR, and redshift (Kauffmann et al., 2004; Silverman et al.,
2009). This sample will be supplemented by AGN selected by a diverse set of
multi-wavelength criteria, designed to fully probe the population of AGN at
these redshifts.

####  3.3.3 Chemical Evolution

The chemical abundances of galaxies provide powerful constraints on their
prior star-formation histories and on the roles of inflows of low-metallicity
gas and outflows of high-metallicity gas (Tremonti et al., 2004; Maiolino &
Mannucci, 2019). Historically, the state-of-the-art for studying chemical
abundances of galaxy populations has been the measurement of the correlation
between galaxy stellar mass and metallicity (Garnett, 2002; Erb, 2008;
Finlator & Davé, 2008). With PFS, the statistical characterization of the
stellar mass–gas-phase metallicity relation at $z{\sim}0.7-1.7$ will for the
first time be comparable to the analysis that has been possible for almost two
decades at $z\sim 0$ using SDSS, while at the same time PFS Deep spectra could
provide the first stellar mass–stellar metallicity relation beyond the local
universe (Gallazzi et al., 2005; Kirby et al., 2013). This represents a
significant advance over what is currently possible with smaller and more
heterogeneously-selected samples at intermediate redshifts ($z{<}1$; e.g.,
Lamareille et al., 2009; Zahid et al., 2011). Because of the dramatic changes
in galaxies’ star formation histories during this period, completing a
detailed, robust census of enrichment as a function of galaxy properties will
serve as an important benchmark for theoretical predictions.

In addition to single element abundances like O/H or Fe/H, PFS will also
enable the determination of stellar and gas-phase abundance ratios such as
O/Fe, N/O, and C/O with sufficient S/N. Iron abundances can be determined from
stellar continua in deep individual spectra or in spectral stacks, or by
inferring the shape of the dominant ionizing radiation field from an ensemble
of emission lines. Both N and C are primarily measured using emission lines in
individual galaxy spectra: the [N II]$\lambda\lambda 6549,83$ doublet can only
be observed with PFS at $z\lesssim 0.9$, but beyond $z>1$ the C
III]$\lambda\lambda 1907,9$ doublet will probe gas density in higher-
ionization gas. The ratio of stellar $\alpha$ abundances to Fe that we can
recover from the Deep spectra (Fig. 5) probe the most recent episode of star
formation, distinguishing between contributions of Type Ia supernovae from
low-mass stars with that of Type II from high-mass stars. C and N are mainly
formed in low- and intermediate-mass stars, respectively, tracing different
timescales from core-collapse and Type Ia supernovae (note that the timescale
of C production is comparable to SNIa; Vincenzo et al., 2019). With PFS, this
analysis can be performed with stacked deep spectra in bins of stellar mass,
SFR and, uniquely, with redshift.

We foremost rely on the wide wavelength coverage and high spectral resolution
of PFS to model detailed galaxy physics from our spectra. We require deep
integrations (12 hrs) to unlock detailed star formation histories for
individual or small ensembles of galaxies, as well as to detect the weak
emission lines ([O III]4363, C III]) that are required to model the chemical
enrichment history of the gas. Likewise, deep integrations are required to
reach high target density (and thus faint targets) to map the metallicity of
the CGM.

##  4 Galaxy Samples

Left: Spectral S/N achieved as a function of apparent magnitude for different
components of the survey, based on the simulator described in §6. Different
samples are evaluated at different observed wavelengths, as indicated. LBGs at
$z\approx 4$ are shown per resolution element. Right: Example mock PFS spectra
with the integration times as indicated. We show a typical galaxy spectrum
observed for two (top) and 12 (second) hours (§4.3). We also show the
Ly$\alpha$ region of a $z=3.145$ star-forming galaxy (third), from which we
will measure the Ly$\alpha$ absorption from gas at $z\sim 2.1-2.5$ (§4.2). At
the bottom we show two example LAEs (§4.1).

We summarize the main samples here, along with key science drivers motivating
the area and sampling choices. We note that the number of required fiber hours
(FH), the product of the exposure time per object by the number of spectra, is
meaningful unit in which to compare time investments rather than nights, since
we will be interleaving programs with different target selections throughout
for efficiency.

###  4.1 Lyman $\alpha$ emitters

We will target a total of 12k LAEs at $z\sim 2$ and $6-7$ with $L\gtrsim
L_{*}$ selected from the Subaru/HSC narrowband (NB) imaging data (Ouchi et
al., 2018; Shibuya et al., 2018a, b; Konno et al., 2018). Shibuya et al.
(2018b) have obtained spectroscopic confirmation of $z=5.7$ and $6.6$ LAEs
with $\simeq 1-1.5$ hr integrations using Subaru/FOCAS and Magellan/LDSS3,
while subsequent near-IR (NIR) spectroscopy with Subaru/nuMOIRCS and
Keck/MOSFIRE show detections of associated UV nebular lines.

We use numerical simulations of LAEs whose spectra with Ly$\alpha$ emission
are determined by radiative transfer calculations that are tuned to reproduce
observed LAE samples in a partially neutral IGM (Inoue et al., 2020a). Based
on simulations of the PFS spectra (§7.5), we set the on-source PFS integration
time to 6 (12) hours, allowing us to detect Ly$\alpha$ at $z\sim 6-7$ down to
$\log L_{\rm Ly\alpha}/[{\rm erg\ s^{-1}}]>42.7$ $(42.5-42.7)$ at the $\gtrsim
5\sigma$ level.

Furthermore, we consider the detectability of strong UV nebular lines,
observed ratios of nebular UV lines (Stark et al., 2015a, b; Sobral et al.,
2015; Stark et al., 2017) for sources with $\log L_{\rm Ly\alpha}/[{\rm erg\
s^{-1}}]>43.0$. We set the on-source PFS integration time to 3 hours for
$z\sim 2$ LAEs with $\log L_{\rm Ly\alpha}/[{\rm erg\ s^{-1}}]>42.5$. Assuming
the average Ly$\alpha$ to [Oii] line ratio of Erb et al. (2016), we expect to
detect [Oii] lines in those $z\sim 2$ LAEs with a luminosity $\log L_{\rm
Ly\alpha}/[{\rm erg\ s^{-1}}]>43.0$. In total, we request 68k FH (Table 3).

###  4.2 Drop-out galaxies ($2{<}z{<}7$)

The primary drivers of the survey design at $z>2$ are (1) the tomographic
mapping of diffuse HI gas as traced by Ly$\alpha$ absorption, (2) the spatial
correlation between HI gas and galaxies, and (3) the two-point projected
correlation function in multiple bins of redshift and spatial scale. These
will be met by targeting 54k galaxies spread over the 12.3 square degrees of
the PFS GE program. Targets will be selected from the HSC Deep layer using
five broad-band filters ($grizy$) and CLAUDS $u$-band imaging (Sawicki et al.,
2019). The $y$-band limit (24.3 or 24.5; see Table 3) ensures a high degree of
success ($\sim 70\%$) with measuring spectroscopic redshifts while an
additional $g$-band selection is required to probe the foreground IGM for
galaxies at $2.5{<}z{<}3.5$ (see below). Exposure times are nominally 6 or 12
hours, in order to provide the S/N that is required by the IGM tomography
program. In total, this sample requires 395k FH of observing time.

This spectroscopic sample will provide accurate redshifts to build upon the
remarkable LBG samples available from the HSC Deep and Ultradeep layers.
Harikane et al. (2022) have used 4.1 million LBGs at $2{<}z{<}7$ to construct
their rest-UV luminosity functions and angular correlation functions which
demonstrate the rise of the AGN population at high luminosities
($M_{UV}\lesssim-23$). Thus, the PFS-SSP will enable studies of the connection
between massive galaxies, supermassive black holes, and environment in the
early universe for the first time with sufficient statistical accuracy.

####  4.2.1 Area, Sampling, Depth for IGM Tomography

The primary requirement for the Hi Ly$\alpha$ tomographic mapping is the
reconstruction of the 3D gas distribution using background separations of
$\langle d_{\perp}\rangle\approx 4$ cMpc. Lee et al. (2014a) have demonstrated
that 8–10m optical telescopes can effectively provide spectra (S/N $\geq$ 2
per resolution element of $\sim 2.5$Å) in a reasonable amount of time of the
required density of sight lines. Based on simulations (see Figure 8 in Lee et
al., 2014a) and previous observations (Lee et al., 2014b), we estimate that
observing 18.3k galaxies with $2.5{<}z{<}3.5$ and $g{<}$24.7 would yield the
required density of sight lines ($\sim$1600 deg-2), that are separated by
$\langle d_{\perp}\rangle\approx 2.5h^{-1}\,\mathrm{Mpc}$ , to produce
reconstructed maps at an effective map S/N$\approx$3 per
$2.5h^{-1}\,\mathrm{Mpc}$ side-length volume element. In practice, we divide
the sample into bright and faint components, splitting at $g=24.2$, with
different exposure times. If we were to limit ourselves to the bright objects,
the sight line separation would increase to $3.7h^{-1}\,\mathrm{Mpc}$.

The exposure times for the bright and faint components are set by the $g$-band
limiting magnitudes of 24.2 (texp=6 hrs) and 24.7 (texp=12 hrs). These
exposure times are required to reach at least S/N=2 per 1.8Å resolution
element, evaluated at around 4200Å in the observed frame. Additional
continuum-selected targets provide a redshift-space distribution of galaxies
in the same cosmic volume as the HI map, and allow us to investigate the
HI–galaxy correlation. In total, the HI tomography component of the survey
requires 287k FH including the foreground galaxies at $2.1{<}z{<}2.5$.

Figure 6:  Distribution of galaxy mass for the $J$-band magnitude limit in
COSMOS at $1{<}z{<}1.5$ (quiescent in solid red; star-forming in solid blue)
relative to a $K-$band selected sample (dotted). Employing a $J-$band
selection results in a 90% mass-complete sample of galaxies of all colors to
$M^{*}\sim 3\times 10^{10}$ ${\rm M}_{\odot}$, and a representative sample of
both active and quiescent galaxies to below $L^{*}(M^{*}\sim 10^{10}$ ${\rm
M}_{\odot}$).

###  4.3 Continuum-selected galaxies ($z{<}2$)

The “Main” $z{<}2$ sample is designed to map the large-scale structure, with
galaxies observed for a total of 2 hours. We will also select a “Deep”
subsample, which will be observed for 12 hours in total. The selection and
main science goals of these samples are described below.

Main sample: We will select targets with $0.7{<}z{<}1.7$ using a photometric
redshift (photo-$z$) selection (§5.4), with a magnitude limit of $y=22.5$ over
the full redshift range and $J=22.8$ mag for $z>1$ galaxies (see Table 3).
These two magnitude limits provide roughly constant stellar mass sensitivity
down to $M_{*}\approx 3\times 10^{10}$ ${\rm M}_{\odot}$ (90% completeness).
Our $y$\- or $J$-selection falls redward of the 4000Å break over our full
redshift range, and thus is sensitive to stellar mass as well as star
formation (see example spectra in Figure 4, right). Thus, we will chart the
evolution of typical galaxies over this entire epoch, with 326k FH.

Deep sample: We will spend an additional 144k FH on a deep spectroscopic
component, targeting galaxies chosen from among the primary sample with
measured redshifts. We will study 14,000 galaxies with $J{<}22.5$ spread
throughout the survey areas, split evenly between quiescent and star-forming
galaxies (and thus not mass-representative).

####  4.3.1 Area, Sampling, Depth

Our area is set by our desire to sample cluster-mass halos. In 11 PFS
pointings (corresponding to $\sim$ 12.3 deg2 after accounting for overlapping
fields) we will cover a comoving volume of $\sim 0.1$ Gpc3. We can recover the
galaxy number density in $\delta M_{\ast}=0.5$ dex and $\delta z=0.4$ bins to
better than 0.03 dex for stellar mass ${<}10^{11}~{}M_{\odot}$ (e.g., Moster
et al., 2011), such that we will not be cosmic-variance limited. In the
deliverables section (§7), we show that this area includes $\sim 35$ halos
with $M_{h}>10^{14}$ ${\rm M}_{\odot}$.

As described in detail in §7.9, our high sampling (with mean inter-galaxy
spacing between 7 and 10 Mpc) will allow us to measure clustering at scales of
$0.1~{}h^{-1}\mathrm{comoving~{}Mpc}$, reaching the virial radius of $\sim
10^{12}$ ${\rm M}_{\odot}$ halos (Figure 6, right). Kraljic et al. (2018b) and
Malavasi et al. (2017) have reconstructed the cosmic web in lower redshift
surveys with a similar range of inter-galaxy spacings.

The depth of the Main sample is chosen to achieve redshift success for the
majority of targets (see §7). The Deep sample will require 12 hour
integrations. With this depth, we will be able to measure reliable stellar
velocity dispersions and star formation histories in the spectra of individual
galaxies, and abundance ratios from the stellar continuum in stacks of 20-30
objects (§7). We will also measure weak emission lines such as [Ne III] and C
III] in individual galaxies extending to $1\sigma$ below the star forming main
sequence, allowing us to determine ionization parameter and gas-phase
enrichment and abundance ratios. We will use measurements of the full suite of
emission lines in the spectra of individual Deep galaxies to calibrate the use
of the strong lines ([O II], [O III], H$\beta$) that will be commonly detected
in the Main sample spectra. We can then stack individual Main sample galaxies
in bins of stellar mass and star formation rate to determine nebular
properties as a function of stellar mass and star formation rate (e.g., Strom
et al., 2022, Figure 6). Our sample will be large enough to identify 20-30
galaxies in each of 10 redshift bins ($\delta z=0.1$), 3-5 stellar mass bins
and four bins in environment, as quantified by the distance to the nearest
filament (§7.9). This sampling therefore allows us to study trends in each of
these quantities separately.

In summary, our Main sample will comprise $\sim 230,000$ restframe-optical
continuum-selected galaxies down to $M^{*}\approx 3\times 10^{10}$ ${\rm
M}_{\odot}$ at $0.7{<}z{<}1.7$, and integration times of 2 hours. It will cost
550k FH. This will be complemented by Deep spectra for 14,000 galaxies with
integration times of 12 hours. Finally, we will supplement this with spectra
of 8000 AGN selected using a variety of multi-wavelength techniques as
described in the following subsection.

Table 3: Full Target Table

Redshift | Selection | Exp. Time | Targets | Sampling | # of | Fiber
---|---|---|---|---|---|---
range |  | (hrs) | PFS FOV | rate (%) | spectra ($10^{3}$) | khrs
Continuum-selected |  |  |  |  |  |
$\lesssim 1$ | $i{<}23$ | 2 | 6100 | 40 | 24 | 48
$0.7-1$ |  $y{<}22.5$ \+ $z_{\rm ph}$ | 2 | 11900 | 50 | 58 | 116
$1-2$ | $y>22.5+z_{\rm ph}$ | 2 | 11800 | 70 | 81 | 162
| \+ $J{<}22.8$ |  |  |  |  |
$0.7-2$ |  $y{<}22.8$ \+ $z_{\rm ph}$ | 12 | 1220 | … | 12 | 144
Tomography |  |  |  |  |  |
$2.1-2.5$ |  $y{<}24.3$ \+ $z_{\rm ph}$ | 6 | 8300 | 22 | 18 | 108
$2.5-3.5$ |  $y{<}24.3$ \+ $z_{\rm ph}$ | 6 | 770 | 90 | 6.8 | 41
| \+ $g{<}24.2$ |  |  |  |  |
$2.5-3.5$ |  $y{<}24.3$ \+ $z_{\rm ph}$ | 12 | 1800 | 65 | 11.5 | 138
| +$24.2{<}g{<}24.7$ |  |  |  |  |
LAE |  |  |  |  |  |
$3.5-7$ |  $y{<}24.5$ \+ $z_{\rm ph}$ | 6 | 2500 | 74 | 18 | 108
2.2 | log L${}_{Ly\alpha}>42.5$ | 3 | 770 | 80 | 6.0 | 18
5.7, 6.6 | log L${}_{Ly\alpha}>42.7$ | 6 | 470 | 80 | 3.7 | 22
5.7, 6.6 | log LLyα=42.5-42.7 | 12 | 290 | 80 | 2.3 | 28

Note. — Details of target selection. The first four entries summarize the
continuum-selected ($0.7{<}z{<}$ 1.7) sample, including the Main (2 hr) and
Deep (12 hr) components. The next three rows outline details of the IGM
tomography sample, and the final four rows focus on the very high redshift
drop-outs and LAEs. We include the color selection, exposure times, number of
targets in the 1.3 deg2 field of view, the fraction of that population that we
aim to target, the resulting total number of spectra and cost to the survey in
fiber hours.

###  4.4 Active Galactic Nuclei

The discovery of a tight correlation between supermassive black hole (SMBH)
masses ($M_{\rm BH}$) and the host galaxy properties, e.g., bulge masses, has
transformed our understanding on the role of SMBHs in the process of galaxy
evolution (e.g., Kormendy & Ho, 2013). While this correlation may be due
partly to frequent galaxy mergers in the hierarchical structure formation,
recent studies indicate that baryon physics within individual galaxies or dark
matter halos plays a fundamental role (e.g., Heckman & Best, 2014). In
particular, energy feedback from active galactic nuclei (AGNs) may have a
significant impact on the evolution of galaxies. It is critical to know when,
where, and how SMBHs have formed, evolved, and finally settled in the present-
day universe, and what is the consequence of the AGN activity which
accompanies SMBH growth in the heart of galaxies.

The intrinsic SED varies from one AGN to another, depending on $M_{\rm BH}$,
mass accretion efficiency (Eddington ratio $\lambda_{\rm Edd}$), and other
factors. Dust extinction further adds to the variety of observed SEDs. Indeed,
AGNs selected at different wavelengths are known to possess systematically
different properties (e.g., Hickox et al., 2009). In order to obtain a full
census of SMBHs and their impact on the host galaxies, it is therefore
imperative to observe various sub-populations of AGNs selected in multiple
complementary ways. The PFS-GE sample described above and the [O II] emitters
targeted in the PFS-Cosmology survey will include numerous obscured AGNs,
which we can identify with strong emission from the narrow line region, e.g.,
[O III] $\lambda$4959, 5007 and [N II] $\lambda$6548, 6583 lines (e.g.,
Baldwin et al., 1981b). This section describes a strategy to target other
classes of AGNs, exploiting existing multi-wavelength imaging data.

####  4.4.1 AGN selection

We select AGN targets from both the rich multi-wavelength data available in
the 12.3-deg2 Galaxy Evolution fields (§5), from X-ray to radio frequencies,
and the wide $\sim$1000-deg2 area of the PFS Cosmology field to look for more
luminous and rare AGNs. All the targets are selected from accurate HSC
photometry. The targeting strategy of each sub-population is detailed below,
and is summarized in Table 4. A total of 53k FHs are planned for AGN science.
We note that the AGN candidates presented here may partially overlap with
galaxies meeting the selection criteria of the galaxy evolution (this
document) or Cosmology targeting, so the fiber numbers listed in the table may
not simply add to the numbers planned in the two main surveys.

A major part of our sample consists of candidate broad-line (BL) AGNs across
the whole range of redshifts observable with the HSC imaging, out to $z>6$.
The target selection rests on all the available color information in the CFHT
$u$ through Spitzer 4.5-$\mu$m bands. We will establish a statistically robust
sample of 3,000 BL AGNs at $0.5{<}z{<}4$, and target all 15,000 quasar
candidates at $z>4$ that were imaged by HSC and are feasible to detect with
PFS. We will put high priority on the targets within 1 arcmin of bright SDSS
quasars at $z\sim 3$ in the GE field, which will allow us to probe the CGM/IGM
around the targets via absorption of the background quasar spectra (e.g.,
Prochaska et al., 2013) in an unprecedented number of sightlines.

We will also observe 2,000 X-ray sources, in order to probe the obscured and
possibly the most active phase of SMBH and galaxy assembly history (e.g.,
Blecha et al., 2018). The target selection rests on public XMM-Newton and
Chandra deep images as well as the all-sky eROSITA survey data, putting higher
priority on objects with $z_{\rm phot}>1$. We will further target dusty AGNs;
1,500 WISE sources with $f_{22{\mu}m}>3$ mJy in the Cosmology field lacking
SDSS spectra, and 1,000 JCMT/SCUBA-2 sub-mm sources with $f_{870{\mu}m}>5$ mJy
that have ALMA counterparts in the HSC Deep fields (Stach et al., 2018;
Simpson et al., 2020), both expected to include a significant fraction of AGNs
(e.g., Brand et al., 2006; Sacchi et al., 2009; Toba et al., 2015; Danielson
et al., 2017). We also aim to capture SMBHs at both the beginning and end of
their most active phase. Once they have become sufficiently massive, SMBHs are
often observed to produce large-scale ratio jets (e.g., McLure & Jarvis, 2004)
and may be found in over-dense regions (e.g., Miley & De Breuck, 2008). We
will observe 2,000 candidate radio AGNs obtained by cross-matching the HSC and
the FIRST survey catalogs. At the other extreme, black holes before
experiencing significant growth may be identified as intermediate-mass black
holes (IMBHs) with $M_{\rm BH}\lesssim 10^{4-5}M_{\odot}$ in the local
universe (e.g., Greene et al., 2020). We will look for IMBHs by targeting 300
candidate low-luminosity AGNs, identified via time variability in HSC Deep
fields (Kimura et al., 2020).

Finally, we aim to observe 1,100 lensed quasar and galaxy candidates in the
PFS Cosmology field. Confirmed systems will offer a wide range of
astrophysical and cosmological applications (e.g., Oguri et al., 2006),
including measurements of the mass structures of the foreground lenses,
mapping the host galaxies of the magnified background quasars, and
determination of the Hubble constant. The candidates were selected from the
HSC imaging, and are expected to include $\sim$100 lensed quasars as well as
$\sim$900 lensed galaxies (Sonnenfeld et al., 2018; Jaelani et al., 2020),
including $\sim$300 galaxy-scale and $\sim$600 group-to-cluster scale lenses.

Table 4: AGN target selection and observing strategy

Targets | Selection |  $N_{\rm AGN}^{\rm total}$ |  $N_{\rm AGN}$ |  $N_{\rm fiber}$ |  $T_{\rm exp}$ |  $N_{\rm fiber}T_{\rm exp}$
---|---|---|---|---|---|---
Galaxy Evolution |  |  |  |  |  |
BL candidates ($z{<}4$) | CFHT $u$ – Spitzer colors | 5,700 | 3,000 | 6,000 (0.5) | 1 – 4 | 15,000
BL candidates ($z>4$) | HSC – Spitzer colors | 500 | 500 | 1,000 (0.5) | 4 – 5 | 4,500
X-ray sources |  Chandra, XMM-Newton | 10,000 | 2,000 | 2,000 (1.0) | 4 – 5 | 9,000
Sub-mm galaxies | SCUBA-2 w/ ALMA counterparts | 300 | 300 | 1,000 (0.3) | 5 | 5,000
Radio galaxies | FIRST | 200 | 200 | 300 (0.7) | 3 | 900
IMBH candidates | HSC flux variability | 30 | 30 | 300 (0.1) | 2 | 600
Total |  |  | 6,030 | 10,600 |  | 35,000
Cosmology |  |  |  |  |  |
BL candidates ($z>4$) | HSC colors | 15,000 | 15,000 | 30,000 (0.5) | 0.5 | 15,000
X-ray sources | eROSITA | 1,700 | 1,700 | 1,700 (1.0) | 0.5 | 850
Mid-IR sources | WISE 22 $\mu$m | 1,000 | 1,000 | 1,500 (0.7) | 0.5 | 750
Radio galaxies | FIRST | 20,000 | 1,500 | 1,700 (0.9) | 0.5 | 850
Lensed quasar candidates | HSC shapes | 100 | 100 | 1,100 (0.1) | 0.5 | 550
Total |  |  | 19,300 | 36,000 |  | 18,000

Note. — Columns are: Target; Selection method; Total number of AGNs expected
over the entire survey field; Number of AGNs we aim to observe; Number of
requested fibers (the number in parenthesis represents the expected success
rate of AGN identification, i.e., $N_{\rm AGN}$/$N_{\rm fiber}$); Exposure
time (hr); Requested fiber hours.

##  5 Photometry for target selection and parameter estimation

Each component of the survey relies on multi-wavelength imaging for selection.
In this section, we review the available photometry and depths, along with the
photometric redshift precision that can be achieved with this photometry. The
basis of the survey are the HSC Deep fields, and specifically the $\sim 12.3$
deg2 with complementary NIR imaging (required to selected the Continuum
sample, whose 4000Å or Balmer breaks falls in the $J-$band at $z\approx 2$).
The HSC-Deep fields that already contain $J-$band photometry down to $\sim
23.7$ mag or better are XMM-LSS, DEEP2-3, and E-COSMOS. These fields already
have Spitzer 3.6 and 4.5$\micron$ IRAC data to a similar depths of $\sim 23.5$
mag, which is useful in constraining the stellar masses of our galaxies. The
CFHT Large Area $U-$band Deep Survey (CLAUDS) project has obtained 20 deg2 of
$u-$band data to $u=27$ mag ($5\sigma)$ with sub-arcsec seeing in the HSC Deep
Fields which, when combined with the $JK$+IRAC CH1+2 photometry, will allow
excellent determination of photo-$z$ (§5.4). These fields also have a range of
other multiwavelength data, including X-rays, far-IR/sub-mm, and radio, which
all contribute to constraining the accretion activity of the central
supermassive black holes across different levels of dust obscuration and
accretion rates.

PFS pointings comprising our survey (red) superimposed on multi-wavelength
data available in each field, illustrating how we have selected optimized
pointings to maximize multi-wavelength overlap. Different colors identify
different data. Green: HSC+CLAUDS; Orange: Spitzer; Purple: NIR
(VISTA+WIRCAM+UKIDSS); Blue:X-ray (Chandra+XMM); Black: Herschel. Grey: the
coverage for each survey band, such that the darkest regions have the most
overlapping multi-wavelength coverage. Red: PFS. Note that EN1 is not part of
the PFS survey area, but may be used for target exploration.

We summarize the 12.3 deg2 area with the PFS pointings overlaid in Figure 5.
We chose the pointings to optimize overlap with multi-wavelength data-sets
(summarized below) and in particular overlap with $J-$band imaging, which is
crucial for our success.

###  5.1 HSC Deep

The four fields of the HSC-SSP (Aihara et al., 2018) Deep layer cover $32$
deg2 with five broad-band filters ($grizy$) and a suite of narrow-band filters
plus a wealth of ancillary data, making them ideal deep fields for studying
galaxy evolution over a broad range of galaxy mass, redshift and environment.
These fields (XMM-LSS, E-COSMOS, ELAIS-N1, and DEEP2-3) reach a depth of $\sim
26.5$ mag ($5\sigma$ point sources), and contain the HSC UltraDeep layer with
two separate 1.75 square degree fields: COSMOS and the Subaru/XMM-Newton Deep
Survey (SXDS) that reach a depth of $i\sim$ 28 mag. It is also worth noting
the rich array of science enabled by the HSC Deep data has many synergies with
the science goals outlined here, including weak lensing (e.g., Huang et al.,
2020; Luo et al., 2022).

Deep HSC narrow-band (NB) imaging provides large samples of line-emitting
galaxies up to $z\sim 7$ (e.g., Shibuya et al., 2018a). The HSC-SSP includes
NB images centered at 387, 816 and 921 nm over most of the HSC Deep area that
are effective at detecting galaxies with strong emission lines (Hayashi et
al., 2020) including H$\alpha$, [OIII]$\lambda$5007 ($z=0.840,0.939$),
[OII]$\lambda 3727$ ($z=0.92,1.19,1.47,1.70$), and Ly$\alpha$
($z=2.18,5.73,6.58$). The program “Cosmic HydrOgen Reionization Unveiled with
Subaru” (CHORUS; Inoue et al. 2020b) supplements these with additional filters
at 387, 527, 718 and 973 nm in the HSC UD-COSMOS field at 5$\sigma$ depths
$\sim$26 (see Table 2 in Inoue et al. 2020b). Of interest for the PFS survey,
CHORUS extends the samples of LAEs to redshifts of 3.33, 4.90 and 6.99.

###  5.2 Near-IR Imaging

At the beginning of the HSC survey (ca. 2014), the majority of the HSC deep
fields lacked NIR data of comparable depth to the optical data from the HSC.
To remedy this, a team from the University of Arizona started the Dunes2
survey (PIs: E. Egami and X. Fan) in 2015, using UKIRT to survey the flanking
fields of the E-COSMOS, DEEP2-3, and part of the ELAIS-N1, to $J\approx 23.5$
and $K\approx 23.2$ (E. Egami et al. in prep.).

Even with this effort, both the depth and area covered are still insufficient
for carrying out a robust target selection of the PFS GE $z=0.7-1.7$
component. Another survey called DeepCos, using both UKIRT and CFHT, aims to
bring the depth uniformly to $J=23.7$ over 12.3 deg2 (in E-COSMOS, DEEP2-3,
and XMM-LSS) and was initiated and coordinated by Y.-T. Lin (ASIAA).111With
significant contributions from W.-H. Wang (ASIAA), M. Ouchi (The University of
Tokyo/NAOJ), Z. Cai and C. Li (Tsinghua University), and A. Goulding
(Princeton). Upon the completion of this survey (in 2023) we will have
sufficient NIR coverage for targeting.

###  5.3 Spitzer IRAC

Spitzer IRAC 3.6 $\mu$m and 4.5 $\mu$m coverage with good uniformity and
5$\sigma$ depth of 23.7 (23.3) magnitude for 3.6 $\mu$m (4.5 $\mu$m) exists
for the vast majority of the HSC-Deep fields. This coverage is primarily
thanks to the SERVS (Mauduit et al., 2012) and Spitzer DeepDrill surveys (Lacy
et al., 2021) as well as a dedicated $\approx$500hr Spitzer GO14 program
(SHIRAZ; PI: A. Sajina) to complete the IRAC coverage of the HSC-Deep fields.
This program is completed, the data are reduced and mosaics are nearing
publication (Annunziatella et al. 2022, AJ submitted). Specifically, we have
re-reduced all archival data for consistency and our mosaics for E-COSMOS,
ELAIS-N1 and DEEP2-3 incorporate both the new and archival data for a total of
$\approx$17 deg2.

IRAC data are critical for extending the wavelength coverage and thus
improving photo-$z$ and stellar population parameter estimates (see e.g.,
Muzzin et al., 2009a, §5.4), and by extension, our target selection. We note
that the above depth is measured from the IRAC catalog. However, work is in
progress on multi-band forced-photometry using shorter wavelength and higher-
resolution data (such as HSC $z$ or $y$) as priors. Based on our experience
(e.g. Nyland et al., 2017), using such priors allow us to reach at least 0.5
magnitudes deeper (e.g., $\approx$24.2 magnitude at 3.6 $\mu$m). As described
by Nyland et al. (2017), this is because we can mitigate blends and because
the prior positional knowledge allows us to glean spectral information from
the IRAC data even when the detection is $<5\sigma$ without the prior
positional information. At these depths, we should be able to reach galaxies
with stellar mass $\approx$109M⊙ at $z=1.0$ and $\approx$1011M⊙ at $z=5$.

###  5.4 Photometric redshifts and calibration

The PFS Galaxy Evolution targeting will rely on CLAUDS+HSC+NIR photometry. The
CLAUDS team has performed uniform $ugrizyJHK$ photometry in the XMM-LSS and
COSMOS fields, using near-infrared data from the Visible and Infrared Survey
Telescope for Astronomy (VISTA) Deep Extragalactic Observations (VIDEO) survey
(Jarvis et al., 2013) in XMM-LSS and from UltraVISTA (McCracken et al., 2012)
in COSMOS. Using the CLAUDS+HSC+NIR data at the nominal depth in the COSMOS
and XMM-LSS fields, we directly test the photo-$z$ accuracy. We compare our
preliminary HSC photo-$z$ with objects that have spectroscopic redshifts and
obtain encouraging results. We achieve excellent redshift success, with
$\sigma_{\Delta z/(1+z)}{<}0.03$ [0.04] with NIR [no NIR] and low
contamination fraction 4% [5%] below $z{<}2.5$, where we will use photo-$z$
selection. These tests are explored in detail in Deprez et al. (2022,
submitted).

###  5.5 Science Commissioning

In the first year of the SSP survey, we will spend $\sim 10$ nights on science
commissioning. Specifically, we will relax our color cuts and take a
representative set of spectra down to our magnitude limit of $J=22.8$ mag, in
order to (a) calibrate our photometric redshifts with a more representative
sample in color space and then (b) refine our color selection accordingly. We
will do this testing in the fourth HSC-Deep field, ELAIS-N1 (Figure 5) and
then use the results from this field to define the precise definition of the
main survey design. These calculations will be done in combination with our
mock universe simulation (§6).

Figure 7:  Comparison of the emission-line strengths in simulated PFS galaxy
spectra and real galaxies observed at $z=0.5-1$ and $z=2.0-2.5$. This
comparison ensures that our simulated spectra exhibit representative emission
line strength distributions. Left: Simulated [O II] emission line luminosity
versus stellar mass with the mock galaxy spectra at $z=0.5-1.0$ and $2.0-2.5$
shown in blue and red respectively. The solid line marks the running median
and dashed line marks $1\sigma$ scatter as a function of stellar mass. Right:
Same as the left panel but with [O II] luminosity versus SFR. In both panels,
galaxies at $z=0.5-1.0$ from LEGA-C and at $z=2.0-2.5$ from KBSS-MOSFIRE are
shown as red and blue points respectively.

##  6 Mock PFS Surveys

In order to perform end-to-end simulations of the survey, we need a mock
galaxy catalog that (a) has realistic spectral features and realistic PFS-like
noise on a per-galaxy basis and (b) that tells us about the relative positions
of galaxies, both physically and in projection. To accomplish this goal, we
build a mock catalog as described in the following two sections.

We generated a mock catalog of galaxies of similar volume to the planned
survey using data from the UniverseMachine DR1 (Behroozi et al., 2019). The
UniverseMachine is an empirical model which has been calibrated to statistics
of galaxy populations over $0{<}z{<}10$. This model places a galaxy at the
center of each halo from the Bolshoi-Planck cosmological $N$-body simulation
(Klypin et al., 2016), and assigns SFRs to track the accumulation of stellar
mass following the dark matter assembly for each galaxy. From the
UniverseMachine models, we constructed light cones over a randomized viewing
angle and origin inside of the periodic cube, with volumes matched to the PFS
survey specification (see details in Pearl et al., 2022).

At $z>2$, we use abundance matching to ensure we match the number density of
sources. At lower redshifts, $z{<}2$, we need to adapt the mapping between
mass and light in the default UniverseMachine catalogs to match our sample
properties. Specifically, we assigned fluxes in several filters to each mock
galaxy in the light cone at $z{<}2$, calibrated to UltraVISTA photometry in
the COSMOS field (Muzzin et al., 2013). This photometry is assigned onto the
physical properties as a multivariate mapping from the specific star formation
rate to the mass-to-light ratio in each observed-frame filter. To perform this
mapping, we trained a random forest on UltraVISTA sources, using the SFR
inferred from UV photometric bands and stellar mass derived from SED fitting.
These SEDs were fit by the spectral fitting code Fitting and Assessment of
Synthetic Templates (FAST Kriek et al., 2009), using the Chabrier (2003)
initial mass function, an exponentially declining star formation history, and
the Bruzual & Charlot (2003) stellar library. For each galaxy in the sample,
our mock survey contains a precise spectroscopic redshift, position on the
sky, and multiwavelength photometry. Because of its empirical calibration, the
mock provides excellent agreement with the color, redshift, and mass
distributions of galaxies in the real $0.7{<}z{<}1.7$ Universe (Pearl et al.,
2022). This mock facilitates a number of targeting and fiber assignment tests
as well as predictions for the survey performance.

###  6.1 PFS Simulator

Our model for the throughput of the spectrograph includes the quantum
efficiency of the chips, light losses at the fiber due to seeing, losses in
the fiber and fiber coupling, reflectivity of the Subaru primary mirror and
transmission of the corrector, throughput of the camera and collimator
(including vignetting) and dichroics as a function of wavelength, the grating
transmission, and the atmospheric transparency. The details of the instrument
throughput and the expected performance are summarized for the
public222https://pfs.ipmu.jp/research/parameters.html. The spectral simulator
models the two-dimensional distribution of source and sky photons on the chip,
then collapses along the spatial dimension to produce simulated one-
dimensional spectra and the corresponding error arrays. The noise calculation
includes shot noise from the source, sky emission lines, and sky continuum, as
well as read noise, dark current, and thermal background. Furthermore, an
additional noise of 1% of the sky background is added as a possible systematic
sky subtraction error. In the spectral simulation, we assume that the moon
phase is dark, the seeing is FWHM=0.8 arcsec, and the effective radius of
galaxies is 0.3 arcsec.

In order to guide the PFS survey design and ensure that the spectral quality
is sufficient for our science goals, we produced a large mock catalog of
galaxy spectra to run through the PFS spectral simulator. As a starting point,
we took the COSMOS+UltraVISTA photometric galaxy catalog (Muzzin et al., 2013)
described above and applied redshift and magnitude limits corresponding to the
different survey components. We then adopted the best-fit star-formation
history from COSMOS+UltraVISTA and produced a mock stellar spectrum for each
galaxy using the model of Bruzual & Charlot (2003).

While this produces a reasonable distribution of galaxy spectra tied to the
photometric redshifts and magnitudes of real galaxies, we must also include
emission lines and ISM absorption features. Furthermore, the spectral models
have insufficient spectral resolution in the NUV and FUV. To overcome these
limitations, we performed the following post-processing to produce the PFS
mock spectra.

  1. 1.

In the near-UV, the simple stellar population models have low resolution so we
take continuum-normalized NUV spectra from SDSS-BOSS stacks and insert them
onto the low-resolution simple stellar population model continuum. This
inserts realistic NUV ISM absorption and emission lines such as Mg II, Fe II,
Fe II*, etc. We created $6$ different NUV stacks using SDSS objects at
different redshifts and with different SFRs and adopted the stack that best-
matches the redshift and star formation rate of the corresponding
COSMOS$+$UltraVISTA galaxies.

  2. 2.

In the FUV, we follow the same approach except using stacks from the KBSS-
MOSFIRE survey (Steidel et al., 2014b) in mass bins so that real correlations
between Ly$\alpha$ strength, ISM absorption strengths, and mass are present in
our simulation. The KBSS-MOSFIRE galaxies have redshifts measured from non-
resonant, rest-frame optical emission lines ensuring (a) that redshift
uncertainty does not degrade the effective resolution of the stacked spectra
and (b) that the objects have realistic offsets between ISM absorption
velocities ($v_{\rm out}$) and the galaxy systemic velocities.

  3. 3.

The strong optical emission line are set based on Valentino et al. (2017),
which are calibrated at $z\approx 1.5$. In detail, the [O II] and H$\alpha$
emission are set based on the model SFR while the [O III] and other line
ratios are set based on correlations with stellar mass. Dust extinction is
included based on the SED and a nominal gas/stellar extinction ratio. We test
the emission-line strengths as a function of mass and SFR at both $z\approx
0.8$ and $z\approx 2.2$ by comparing with observed scalings from LEGA-C and
KBSS (Figure 7) and find reasonable agreement.

  4. 4.

In addition, we perform an independent set of simulations with the optical
line strengths set based on the UV SFR and low-$z$ metallicity-line ratio
relations from Kewley & Dopita (2002) and Maiolino et al. (2008). These mocks
represent a worst-case scenario because the expected emission line strengths
are lower when using the low-$z$ relations.

  5. 5.

For a small set of the galaxies, we also add higher ionization emission lines
such as [Ne V] and higher [O III]/H$\beta$ ratios as expected from obscured
AGN based on observed line strengths from (Yuan et al., 2016).

  6. 6.

For galaxies at $z\gtrsim 2$, IGM absorption from the H I Ly$\alpha$ forest
significantly impacts the FUV spectra of galaxies. To accurately include these
Ly$\alpha$ forest lines, for each $z>2$ galaxy we identified a quasar with a
similar redshift from the SQUAD database (Murphy et al., 2019) and multiplied
the mock galaxy spectrum by the continuum normalized UVES spectrum of the
quasar after degrading the UVES spectral resolution to match PFS.

  7. 7.

We create an additional set of LAE spectra specifically to explore recovery of
LAE line shapes. We use numerical simulations of LAEs whose spectra with
Ly$\alpha$ emission are determined by radiative transfer calculations that
reproduce the HSC LAE samples in the partly neutral IGM (Inoue et al., 2018).

##  7 Deliverables

We summarize here our target fidelity in key observables. We start with
redshifts, and we will demonstrate redshift fidelity of $\Delta
z/(1+z){<}5\times 10^{-4}$. We focus on the redshift fidelity of LAEs
specifically. This level of redshift success is assumed in the recovery tests
that follow. We show that with PFS data, we will quantify stellar masses to
$\sim 0.2$ dex, star formation rates of a few $M_{\odot}$ per year, gas-phase
metallicities to ${<}0.25$ dex, and outflow velocities (in stacks) to a few
percent. For the Deep $0.7{<}z{<}1.7$ sample, we will determine stellar and
gas velocity dispersions for the Deep galaxy sample to $\sim 15\%$ and star
formation histories to 20% for star-forming galaxies and even very low
specific star-formation rates to within a factor of two. In the AGN samples,
we expect to achieve black hole masses and Eddington ratios in broad-line AGN
to 0.2 dex.

###  7.1 Redshift fidelity

Figure 8: The median (points), interquartile range (smaller errorbars) and
range including 90% of the points (larger errorbars), of the difference
between true and inferred redshift for a sample of simulated GE galaxies
(§7.1). Results are shown as a function both of galaxy magnitude and [OII]
emission-line strength. The vast majority of galaxies have redshifts
determined to within $|\Delta z|=10^{-3}$.

The galaxy redshifts will be measured with a code called “Algorithms for
Massive Automatic Z Evaluation and Determination” (AMAZED; Schmitt et al.,
2019), which has been used extensively for ground-based multi-object surveys
such as the VIMOS VLT Deep Survey (Le Fèvre et al., 2005), and will be used to
analyze data from the Euclid survey (Laureijs et al., 2011). AMAZED models
galaxies as a superposition of continuum, emission lines, stellar and
interstellar absorption lines, and including a model for the Ly$\alpha$ forest
as a function of redshift. These models are fit to the data by minimizing
$\chi^{2}$, resulting in an estimate of the redshift and its uncertainty, as
well as emission-line and absorption-line parameters. We have tested this
approach extensively on simulated PFS spectra and we have found that 90% of
the simulated galaxy sample with $z{<}2.1$ have measured redshifts with
$\Delta z/(1+z){<}5\times 10^{-4}$, and 98% have errors less than $10^{-3}$
(Figure 8).

We also investigate the accuracy of the Ly$\alpha$ redshift and FWHM
determinations using the mocks described in §6. We find that the $1\sigma$
scatter of the redshift differences between the inputs and mock PFS LAE
spectrum measurements $\delta z$ is within $\delta z=0.0003$ down to our
luminosity limit of $\log L_{\rm Ly\alpha}/[{\rm erg\ s^{-1}}]=42.5$. The
right panel of Figure 7.1 shows the FWHM measurements of the mock LAE spectra.
The FWHM differences between the inputs and mock PFS spectrum measurements
$\delta FWHM=40$ km s-1. We assume a contamination rate of 10% in the
photometric LAE sample revealed by previous spectroscopic studies with
Suprime-Cam and HSC (Ouchi et al., 2010; Shibuya et al., 2018a), and adopt a
success rate of 90% in deriving our PFS feasibility results.

(a) Simulation results with mock PFS LAE spectra to determine the accuracy of
the LAE redshifts as a function of Ly$\alpha$ luminosity ($\log L_{\rm
Ly\alpha}$) for LAEs at $z=6-7$. The LAE redshift determination accuracies are
represented with ($z_{\rm out}^{\rm Ly\alpha}-z_{\rm in}^{\rm
Ly\alpha})/(1+z_{\rm in}^{\rm(Ly\alpha})\equiv\delta z/(1+z_{\rm in}^{\rm
Ly\alpha}$), where $z_{\rm in}^{\rm Ly\alpha}$ ($z_{\rm out}^{\rm Ly\alpha}$)
is the redshift of the input spectra (the measurements with the mock PFS LAE
spectra). The black circles are the individual LAEs, while the red circles and
the errors indicate the average values and the $1\sigma$ scatters. (b) Same as
(a), but for FWHM measurements. Here the Ly$\alpha$ FWHM determination
accuracies are similarly shown with ($FWHM_{\rm out}^{\rm Ly\alpha}-FWHM_{\rm
in}^{\rm Ly\alpha})/FWHM_{\rm in}^{\rm Ly\alpha}\equiv\delta FWHM/FWHM_{\rm
in}^{\rm Ly\alpha}$, where $FWHM_{\rm in}^{\rm Ly\alpha}$ ($FWHM_{\rm
out}^{\rm Ly\alpha}$) is the FWHM of the input spectra (the measurement with
the mock PFS LAE spectra).

###  7.2 Stellar Mass

For galaxies with $z{<}2$, fitting the spectral continuum provides significant
information about the star formation history. With a combination of PFS
spectra and $JK$+_Spitzer_ photometry, we can achieve a scatter of $\sim$0.2
dex in stellar mass, comparable to the systematics in stellar population
modeling (Figure 9, right) and demonstrably better than typical values based
on photometric data alone (e.g, 0.3 dex scatter in stellar mass and 0.4 dex
scatter in stellar age; Muzzin et al., 2009b).

For galaxies at higher redshifts ($z>2$), the spectra probe only the rest-
frame UV, thus the stellar mass estimates are solely based on broad-band
photometry, in particular the NIR+_Spitzer_ photometry, combined with accurate
spectroscopic redshifts from PFS that improve the stellar mass precision over
photometric redshifts. We use photometric data with similar depths to our
galaxies and redshift precision as set by the redshift simulations to find 95%
of the galaxies have stellar mass precision better than 0.2 dex (Figure 9).
This is substantially better than the photo-$z$ only case, in which a
significant tail of objects have unconstrained photo-$z$ at $z>2$. Note that
the redshift errors are systematics limited because of velocity shifts between
Ly$\alpha$, ISM absorption lines, and the systemic velocity of the galaxy
(Steidel et al., 2014a).

Figure 9:  Errors in $M_{*}$ as a function of redshift for both the $z<2$
continuum-selected (left panels) and the $2<z<4$ drop-out selection (right
panels). The top panels show the impact of random errors in the photometric
redshifts while the bottom panels show systematic errors. These errors compare
the best possible mass with the mass we will achieve in the survey. ”Best”
masses are derived using 50-band COSMOS photometry (from the GALEX UV to the
MIPS 24 micron Muzzin et al., 2013) and the best available redshift. “PFS”
masses come from the HSC-Deep photometry ($u,\,grizy,\,JK,\rm{CH12}$, §5) and
photometric redshifts derived using the HSC-Joint photometry. SED-modeling
assumptions were kept the same. The green curve shows the median in the
difference, and the blue/red curves shows the 5-95/15-85 percentile curves.
Even with the more limited photometry available to us, we will achieve
reliable masses for targeting and science.

###  7.3 Star Formation Rates

We will use our H$\alpha$ measurements out to $z\approx 0.9$ to calibrate star
formation rates based on [OII]+UV continuum luminosity to apply to the Main
sample. We will be sensitive to unreddened star-formation rates of a few
tenths of a solar mass per year at $z\sim 0.8$ (based directly on H$\alpha$)
and of a few solar masses per year at our median $z=1.5$, based on [OII]. At
$z\sim 1.5$, the unobscured star-formation rate is a few solar masses per year
for $L^{*}$ galaxies, a limit that we can readily reach (Whitaker et al.,
2017). Our effective star formation sensitivity will be a factor of a few
lower, given the typical $A_{V}\sim 1.8$ seen in emission-line galaxies at
$z\sim 1.5$ (Price et al., 2014; Martis et al., 2016).

At higher redshifts ($z\gtrsim 2$), unobscured star formation will be assessed
from the absolute UV magnitude ($M_{UV}$). The similarity of the IRX-$\beta$
relation for local and high-$z$ galaxies up to $z\sim 4$ (Fudamoto et al.,
2020) allows us to account for the obscured component to the SFR in cases for
which the UV slope ($\beta$) can be evaluated using both photometry and PFS
spectra.

###  7.4 Deep Spectra: Dynamics and Star Formation Histories

To evaluate our ability to recover higher-order dynamical information from the
Deep spectra, we generated 6, 12, and 20 hr integrations with the PFS
simulator, and evaluated our ability to recover the key spectral parameters of
stellar velocity dispersion and stellar ages. Figure 10 shows that with 12 hr
integrations, we will be able to recover stellar velocity dispersions and
stellar ages at our Deep magnitude limit.

For individual galaxies, ${<}15\%$ errors will allow us to derive dynamical
masses that are competitive with the stellar population masses. We will
achieve this level of precision down to $J=21.5$ mag. Previous studies, e.g.,
van der Wel et al. 2008, have explored the size-$\sigma_{*}$ evolution with
only 50 galaxies; with PFS and HSC imaging, we will be able to do this for
orders of magnitude more galaxies, and thus explore trends in dynamical mass
with star formation history and environment. We will also use these data to
calibrate a relation between $\sigma_{*}$ and gas line width $\sigma_{g}$, as
can be measured at the low redshift end of our sample using LEGA-C (Bezanson
et al., 2018). We will use this relation to estimate $\sigma_{*}$ for the Main
sample, so that we can stack quiescent galaxies in bins of inferred
$\sigma_{*}$ to measure stellar ages and abundance ratios.

We have performed detailed recovery tests of star formation history recovery
jointly constrained with simulated 12-hour PFS spectra and the available
photometry. The tests include full constraints on a wide range of galaxy
properties, including non-parametric input star formation histories with
sophisticated models of starbursts and quenching. These tests show that we can
recover the average age of a quenched galaxy at z=1.4 with $M_{*}=10^{11}$
${\rm M}_{\odot}$ to an accuracy of 4%, and determine the very low levels of
residual star formation in these systems (specific star formation rate $\sim
10^{-11}$ yr-1) to within a factor of two. Similarly, for a bursty star-
forming system, we determine the average age of the stars to within 15% and
the recent star formation rate to within 20%. A key challenge is the age and
strength of the burst: the recovery tests show we can infer the time and total
mass formed in the recent burst (0.3-1 Gyr in the past) to within a factor of
two thanks to the strong continuum constraints from PFS.

Figure 10:  Left: Recovery of stellar velocity dispersions from 12-hour
integrations for the Deep sample. Even at our Deep magnitude limit of $J=22.5$
mag, we will derive meaningful measurements of stellar velocity dispersions
for individual galaxies. Right: Similar test but for emission line widths. At
our detection limit we we still getting reasonable and unbiased line-width
measurements of gas emission lines. Recent results (Bezanson et al., 2018)
show that the gas velocity dispersion tracks the stellar velocity dispersion
without bias, and so we can use gas emission lines as a proxy for stellar
velocity dispersion for the main galaxy sample.

###  7.5 Gas-phase metallicities and ISM physics

The wide wavelength coverage of PFS will enable a variety of both restframe-UV
and restframe-optical emission line diagnostics of galaxies’ enrichment and
physical conditions, including gas density and ionization state. Specifically,
gas-phase metallicity (typically O/H) can be measured using the ratios of
“strong” rest-optical lines, including

$R_{23}=\log\left(\frac{[\textrm{O}\,\textsc{ii}]\lambda\lambda
3727,3729+[\textrm{O}\,\textsc{iii}]\lambda\lambda
4959,5007}{\textrm{H}\beta}\right),$ (1)

which will be observable in the spectra of galaxies at $z{<}1.5$. Figure 11
shows the uncertainty in O/H determined using $R_{23}$ for mock galaxies as a
function of SFR, based on the realistic emission-line catalog from the
simulation in Section 6. Accounting for measurement uncertainties in the
emission lines, we expect typical metallicity errors ${<}0.15$ dex (${<}0.25$
dex) for galaxies with $\log$(SFR/($M_{\odot}$ yr-1))$>0.5$ at $0.5{<}z{<}0.9$
($0.9{<}z{<}1.5$). For galaxies with $z\lesssim 0.9$, we will also be able to
measure nitrogen-to-oxygen abundance ratios (N/O) using the [N
II]$\lambda\lambda 6549,6583$ doublet. Nitrogen is thought to originate via
both primary (metallicity-independent) and secondary (metallicity-dependent)
production, with N/O increasing with increasing O/H in more chemically mature
galaxies (e.g., Vila-Costas & Edmunds, 1993). As a result, combining
measurements of N/O (and C/O, see below) with O/H can provide additional
insight into the chemical evolution of individual galaxies in the sample.

In addition to elemental abundances, gas density can be determined using the
[O II]$\lambda\lambda 3727,3729$ doublet for galaxies at $z\lesssim 2.35$. At
$z\lesssim 1.5$, [O II] measurements can be combined with measurements of [O
III]$\lambda 4969,5007$ to probe the ionization state of the gas, as well as
discriminate between predominately ionization-bounded and density-bounded
star-forming regions. Finally, classic restframe-optical diagnostics such as
the “BPT” diagrams (Baldwin et al., 1981b; Veilleux & Osterbrock, 1987) can be
used to identify contributions from different sources of ionizing radiation in
galaxies, including star formation, AGN (see § 7.7), and shocks.

Figure 11:  Measurement errors for R23-based gas-phase metallicities (gray
dots), estimated from the mock spectra, as a function of SFR. Solid lines show
90th, 50th, and 10th percentiles of the metallicity measurement errors from
top to bottom. Pixel noises on the mock spectra are carefully propagated into
emission line flux measurement errors and thus metallicity measurement errors.
Here we assume 2-hour integration with PFS.

At higher redshifts, restframe UV emission lines, including Ly$\alpha$ and
CIII]$\lambda 1909$ (e.g., Nakajima et al., 2018; Byler et al., 2018), will
allow us to measure other physical properties of high-$z$ galaxies in addition
to the metallicity (Faisst et al., 2016), such as the ionization state of the
ISM. These diagnostics will be particularly accessible in spectra having
higher S/N in the redshift regime $2{<}z{<}3.5$, given the chosen magnitude
limits and integration times. We expect 20 (5)% of the galaxies at
$z=2.5(5.1)$ to have CIII] emission detected ($>5\sigma$) while 10% of the
galaxies at $z=5.1$ will be detected at $>3\sigma$ (Le Fèvre et al., 2019).
Ly$\alpha$ profiles (Verhamme et al., 2015) encode information on the Hi
column density and dust distribution that can be assessed with PFS co-added
spectra having information on the systemic velocity.

###  7.6 Infall and Outflow

Over the full redshift range spanned by PFS ($0.7{<}z{<}7$), we will have both
the strong emission ([OII] at least) and interstellar absorption lines needed
to measure the velocity offsets in the interstellar lines. We will search for
gas outflow or inflow using the interstellar absorption lines Mg II and Fe II
in stacks of $\sim 100$ spectra.

With PFS, we will provide absorption line measurements such as Mgii2796, 2804,
Cii1335, and Siii. From simulations, we have found that it is possible to
recover reliable Mg II equivalent widths and outflow velocities from stacks of
100 galaxies for the entire redshift range for the main sample galaxies. We
insert Mg II blueshifts into our mock spectra to examine our ability to
recover outflow velocities in the face of redshift errors. We find that in
stacks of $\sim 100$ galaxies, we can reliably recover average outflow
velocities to 10% precision even with realistic redshift errors.

###  7.7 Accreting Black Hole Signatures

In the first place, we will uncover obscured and low-luminosity active
galaxies using emission-line diagnostics on the galaxies in our main
continuum-selected sample ($0.7<z<1.7$). This will allow us to study the
factors that may trigger accretion, as well as the impact of the AGN on their
hosts (e.g., Kauffmann et al., 2003). We will be able to measure H$\beta$, [O
III], H$\alpha$, and [N II] for all accreting black holes with $M_{\rm
BH}>10^{7}$ ${\rm M}_{\odot}$ and Eddington ratios ${>}0.05$ at $z{<}0.9$.
These lines can also be used to estimate the metallicity of the host galaxy.
We will supplement the above sample with luminous sub-populations of active
galaxies using multi-wavelength selection. We will measure the black hole mass
based on Mg II and/or H$\beta$, with ${<}$0.2 dex accuracy across $0{<}z{<}6$,
not including calibration uncertainty. This measurement will be combined with
the continuum luminosity to derive the bivariate distribution function of mass
and Eddington ratio, the most fundamental quantity to characterize black hole
evolution.

Figure 12: Top: Simulated PFS spectra of quasars with $M_{1450}=-23$ mag
placed at $z=0.5$ (black), 2.0 (blue), 4.0 (green), and 6.0 (red). The average
observing conditions and 1-hr on-source integration are assumed in the
simulations. Bottom: Simulated 30-min spectra of simulated cosmology quasars
placed at z = 4.0 and 6.0. As above, $M_{1450}=-23$ mag.

Detailed modeling of the emission lines will further allow us to measure key
physical quantities, such as $M_{\rm BH}$, $\lambda_{\rm Edd}$, and gas-phase
metallicity. The wide spectral coverage of PFS enables uniform measurements of
$M_{\rm BH}$ with Mg II $\lambda$2800 at $0.35{<}z{<}3.5$ and with C IV
$\lambda$1549 at $z>1.5$, and also provides a cross-calibration of the $M_{\rm
BH}$ estimates based on the different lines (see Figure 12). We will exploit
the statistical BL sample at $0{<}z{<}4$ to measure the fundamental, bivariate
distribution function of $M_{\rm BH}$ and $\lambda_{\rm Edd}$ with
unprecedented accuracy, down to $\sim$2 mag lower luminosity than previous
studies (e.g., Bongiorno et al., 2016). The sample at $z>4$ will be used to
measure the faint end of the quasar luminosity function (e.g., Ikeda et al.,
2011, 2012), as well as the auto-correlation function or cross-correlation
function with HSC photometric galaxies, which will provide insight into the
underlying dark matter halo mass distributions.

The central engines of the X-ray, mid-IR, and sub-mm targets are not
necessarily obscured, and thus will partially overlap with the BL sample. For
obscured objects, PFS will primarily measure emission lines from the narrow
line regions and/or the host galaxies, providing accurate redshifts, source
identification, and gas kinematics (after stacking if necessary). This is also
the case for radio AGNs (e.g., Yamashita et al., 2020). We will constrain
their statistical properties such as number density and clustering amplitudes,
which will then be compared to/merged with those of the BL sample, in order to
reveal the full picture of the cosmological assembly of SMBHs and the host
galaxies. This picture is further complemented by the identification of IMBHs
in the local universe; PFS spectra of the IMBH candidates will be examined to
find broad component in the emission lines, such as H$\alpha$ and H$\beta$,
which will then be used to estimate black hole masses.

Finally, for lensed quasar candidates, PFS spectroscopy will provide (i)
confirmation of the lensing nature and (ii) accurate redshifts of the
background sources and/or the foreground lenses. These pieces of information
are essential for most scientific studies exploiting the lensed systems, as
partially raised in the previous section.

###  7.8 IGM Tomography Recovery

The survey component at $2.2{<}z{<}3.5$ is primarily designed to reveal the
cosmic web at $2.2{<}z{<}2.6$. As such, the main deliverable is the recovery
of the underlying 3D matter density field within the targeted volume. Using
the forward modelling TARDIS-II algorithm applied jointly to mock Ly$\alpha$
forest absorption data and the foreground LBG sample, we find that the PFS GE
survey will be able to recover the smoothed density field (convolved by a
$2\,h^{-1}\,\mathrm{Mpc}$ Gaussian kernel) with a Pearson correlation
coefficient of $r_{\mathrm{pearson}}=0.72$ over logarithmic overdensity
voxels. The efficacy of this reconstruction can be seen in Figure 13, where
the 3D matter density field in a mock PFS sample is well-recovered over a
range of overdensities at $z\sim 2.3$.

Figure 13: Comparison of reconstructed dark matter density at $z\sim 2.5$ to
simulated dark matter density from the Ly$\alpha$ forest absorption together
with foreground galaxy positions in a PFS-like mock catalog. The Pearson
correlation coefficient between the reconstructed densities and true
underlying densities is $r_{\mathrm{pearson}}=0.72$. (Horowitz et al., 2021a).

Figure 14:  Light-cone output at $z\approx 2-3$, covering
$100\,cMpch^{-1},{\rm(height)}\times 1\,h^{-1}{\rm cGpc}\times 10\,cMpch^{-1}$
(depth) from the Osaka group’s cosmological simulation. Panels from top to
bottom show: projected gas overdensity, Hi overdensity, temperature,
metallicity, and galaxy distribution color-coded by the stellar mass,
respectively. In the bottom panel, one can see the effect of galaxy bias,
where more massive galaxies are more clustered in high-density regions.

####  7.8.1 Hydrodynamical simulations of the IGM

Apart from reconstructions of the cosmic web and matter density field in the
IGM tomography sample, one of the major science applications would be the
cross-correlation between the IGM absorption and foreground galaxies. The
interpretation of such cross-correlations, however, would require cosmological
hydrodynamical simulations. Fortunately, cosmological hydrodynamic simulations
have reached a level of sophistication over the past years that the formation
of large-scale structure and galaxy formation can be solved together from
high-redshift to the present day based on the gravitational instability
paradigm within a Cold Dark Matter model. Subgrid models for star formation
and feedback allow us to compute the cosmic star formation history and the
interaction between galaxies, CGM and IGM. To facilitate the IGM cross-
correlation measurements from PFS GE data, the Osaka group has developed
cosmological hydrodynamic simulations of a 100 cMpc/h box including the models
of star formation and supernova feedback (Shimizu et al., 2019; Oku et al.,
2022), and other box sizes are also being prepared. They created light-cone
outputs between $z=2-3$ (with evolving density fields and taking peculiar
velocities into account) to generate a mock dataset for IGM tomography that
was used in designing this survey (see the Appendix of Nagamine et al., 2021).
These simulations can be used to assess the impact of varying feedback models
on the IGM tomography and HI–galaxy cross-correlation.

###  7.9 Characterizing Groups and Clusters

With roughly ten times the area coverage as existing spectroscopic surveys at
comparable redshifts, we expect to detect a statistically meaningful number of
clusters with $M_{halo}>10^{14}$ ${\rm M}_{\odot}$, but also enough rich
groups to investigate how star formation proceeds in the group environment as
a function of their larger-scale environment. The area of the survey is chosen
to mitigate cosmic variance and to be large enough to probe rare rich
environments, while the sampling rate is high enough to identify individual
groups and filaments. Concretely, we expect to find $N_{\rm halo}\approx
2000,500,40$ halos with masses $M_{\rm halo}>10^{13},10^{13.5},10^{14}$ ${\rm
M}_{\odot}$, while we expect to find voids with projected sizes ranging from
$10-70$ Mpc (although the exact numbers depend on cosmology). We note that
there are no existing void catalogs at $1{<}z{<}1.5$, and we will not be able
to detect the large voids at all without $>10$ deg2 of coverage. We will also
detect unprecedented numbers of spectroscopically selected protoclusters at
$2{<}z{<}6$ (e.g. Tasca et al., 2017; Toshikawa et al., 2018; Higuchi et al.,
2019), allowing crucial systematic tests of cluster growth (Chiang et al.,
2013) and the onset of environmental effects on galaxy evolution at high
redshift (Shimakawa et al., 2018). With these new large-scale structure
measurements, we expect to uncover new trends. In terms of clustering, we will
be able to measure the bias $b_{\rm sub}$ with unprecedented subsamples in
$M^{*}$ and star-formation rate. We will determine whether, at fixed stellar
mass, quenched galaxies are preferentially found in denser environments. Going
beyond two-point functions, in simulations trends between galaxy specific star
formation rate and filament distance (at fixed local galaxy overdensity) are
found due to increased gas accretion within the filament.

The powerful new analysis tool of constrained simulations will also be brought
to bear on the protoclusters detected by PFS, allowing us to directly model
and trace their cosmic evolution in their full large-scale structure context,
as they evolve from their observed epochs $>10\,$Gyrs in the past into massive
galaxy clusters by our present day (e.g. Ata et al. 2022). This will allow us
to estimate the individual final masses and merger histories of these cosmic
superstructures with much better accuracy than feasible with generic
cosmological simulations.

####  7.9.1 Groups and protocluster candidates from the photometric redshift
data

To demonstrate the power of the CLAUDS+HSC photometry to identify proto-
cluster candidates, group and protocluster candidates were recently obtained
by Li et al. (2022) from 5.6 million galaxies with $i$-band magnitude $i{<}26$
within the redshift range ($0{<}z{<}6$)333Data are available at this link:
https://gax.sjtu.edu.cn/data/PFS.html. Here the groups were identified using
the extended halo-based group finder developed by Yang et al. (2021), which is
able to deal with galaxies via spectroscopic and photometric redshifts
simultaneously. A total of 2.2 million groups were identified, within which
400k groups have at least three member galaxies. By checking the galaxy number
distributions within a $5-7h^{-1}\,\mathrm{Mpc}$ projected separation and a
redshift difference $\Delta z\leq 0.1$ around those richest groups at redshift
$z>2$, we have obtained a list of 761, 343 and 43 protocluster candidates in
the redshift bins $2\leq z{<}3$, $3\leq z{<}4$ and $z\geq 4$, respectively.
These groups and protocluster candidates may suffer from the photometric
redshift errors, but PFS will be very effective at confirming them and
identifying the brightest cluster galaxy as well.

###  7.10 Mapping the Cosmic Web

In conjunction with HSC, PFS will be able to not only constrain the intrinsic
alignment of galaxy shapes with the underlying cosmic web but explore this
relationship as a function of redshift (see Figure 1 for examples of our
ability to reconstruct the cosmic web). To compare observed galaxy shapes with
the underlying cosmic web, we first reconstruct the three-dimensional matter
field from observed galaxy positions and/or Ly$\alpha$ absorption using either
a dynamical forward modelling approach (Horowitz et al., 2019b, 2021b) or a
Wiener filter (Pichon et al., 2001). In addition to these, we will also use
the galaxy groups to construct the matter field (Wang et al., 2012). From
these three-dimensional reconstructions we calculate the Hessian of the
inferred potential of the field, known as the deformation tensor. The
signature of the eigenvalues of this tensor can be used to classify the cosmic
structures (i.e., void, sheet, filament, node) and the eigenvectors can be
used to define their spatial orientation (Lee & White, 2016; Krolewski et al.,
2017). The principle spatial orientation of the underlying cosmic web can then
be correlated to the inferred shape and/or spin of the observed galaxies to
constrain the intrinsic alignment (Zhang et al., 2013, 2015). This analysis
can be performed both in the continuum-selected samples using galaxy-only
reconstruction and in the IGM tomography sample using joint galaxy-Ly$\alpha$
Forest reconstruction.

##  8 Summary

The PFS Galaxy Evolution Survey will change our view of galaxy evolution by
studying typical galaxies over most of cosmic time, from the epoch of
reionization until $z\sim 0.7$. The wide wavelength coverage provided by the
spectrograph will allow for detailed studies of star formation histories,
abundances and abundance ratios, the prevalence of outflows, and so much more,
while the high multiplexing capability means that we will have unprecedented
sampling with which to reconstruct the cosmic web. We have built a survey to
take advantage of these strengths, and to complement other upcoming work in
this decade.

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