# Search for extended Lyman-$\alpha$ emission around 9k quasars at z=2–3

Rhythm Shimakawa1
1National Astronomical Observatory of Japan (NAOJ), National Institutes of
Natural Sciences, Osawa, Mitaka, Tokyo 181-8588, Japan
E-mail<EMAIL_ADDRESS>Fellow

(Accepted 2022 June 6. Received 2022 June 6; in original form 2022 January 16)

###### Abstract

Enormous Ly$\alpha$ nebulae (ELANe) around quasars have provided unique
insights into the formation of massive galaxies and their associations with
super-massive black holes since their discovery. However, their detection
remains highly limited. This paper introduces a systematic search for extended
Ly$\alpha$ emission around 8683 quasars at $z=$ 2.34–3.00 using a simple but
very effective broad-band $gri$ selection based on the Third Public Data
Release of the Hyper Suprime-Cam Subaru Strategic Program. Although the broad-
band selection detects only bright Ly$\alpha$ emission ($\gtrsim 1\times
10^{-17}$ erg s-1cm-2arcsec-2) compared with narrow-band imaging and integral
field spectroscopy, we can apply this method to far more sources than such
common approaches. We first generated continuum $g$-band images without
contributions from Ly$\alpha$ emission for host and satellite galaxies using
$r$\- and $i$-bands. Then, we established Ly$\alpha$ maps by subtracting them
from observed $g$-band images with Ly$\alpha$ emissions. Consequently, we
discovered extended Ly$\alpha$ emission (with masked area $>40$ arcsec2) for 7
and 32 out of 366 and 8317 quasars in the Deep and Ultra-deep (35 deg2) and
Wide (890 deg2) layers, parts of which may be potential candidates of ELANe.
However, none of them seem to be equivalent to the largest ELANe ever found.
We detected higher fractions of quasars with large nebulae around more
luminous or radio-loud quasars, supporting previous results. Future
applications to the forthcoming big data from the Vera C. Rubin Observatory
will help us detect more promising candidates. The source catalogue and
obtained Ly$\alpha$ properties for all the quasar targets are accessible as
online material.

###### keywords:

galaxies: haloes – galaxies: high-redshift – intergalactic medium – quasars:
emission lines – quasars: general

††pubyear: 2022††pagerange: Search for extended Lyman-$\alpha$ emission around
9k quasars at z=2–3–A

##  1 Introduction

Extended Lyman-$\alpha$ (Ly$\alpha$) nebulae around luminous quasars in the
high-redshift universe provide spatial information about cool gas in the
circumgalactic medium (CGM) and the intergalactic medium (IGM) around quasars.
Hence, they have a key role in understanding gas feeding and feedback
mechanisms of massive galaxies and their connections to activities of super-
massive black holes (e.g., McCarthy et al. 1987; McCarthy 1993; van Ojik et
al. 1997; Villar-Martín 2007; Faucher-Giguère et al. 2010; Goerdt et al. 2010;
Tumlinson et al. 2017; Cantalupo 2017; Kimock et al. 2021, and references
therein). Multi-wavelength studies have also detected various emissions other
than Ly$\alpha$ from gaseous nebulae, e.g., rest-UV helium and metal lines
(McCarthy et al., 1990; Maxfield et al., 2002; Villar-Martín et al., 2003;
Prescott et al., 2015; Cai et al., 2017; Cantalupo et al., 2019; Guo et al.,
2020; Sanderson et al., 2021), H$\alpha$ line (Shimakawa et al., 2018; Leibler
et al., 2018), dust and molecular gas (Emonts et al. 2016, 2019; Li et al.
2021, but see Decarli et al. 2021). Previous studies from a wide range of
viewpoints spatially and kinetically uncovered ionisation structures by
mapping multi-phase gas components on a $\sim 100$ proper kpc (pkpc) scale,
and addressed causal relationships between extended Ly$\alpha$ emissions and
energy sources.

Highlights of recent research include discoveries of enormous Ly$\alpha$
nebulae (ELANe) around luminous radio-quiet quasars, defined as Ly$\alpha$
nebulosities with particularly high surface brightness spreading beyond
hundreds pkpc (Cantalupo et al., 2014; Hennawi et al., 2015; Cai et al., 2017;
Cai et al., 2018; Arrigoni Battaia et al., 2018). Such extreme cases extending
beyond the virial radius allocated an exclusive role as a probe of the
underlying large-scale structures at high spatial resolution (see also Erb et
al. 2011; Fumagalli et al. 2016; Umehata et al. 2019; Kikuta et al. 2019;
Daddi et al. 2021, 2022). Discoveries of ELANe also suggested that cool gas
components are more enriched over the IGM scale in and around massive haloes
at high redshifts than previously considered.

Such great progress is particularly brought by the advent of integral field
units (IFU), e.g., the Multi- Unit Spectroscopic Explorer on the Very Large
Telescope (VLT/MUSE; Bacon et al. 2010) and the Keck Cosmic Web Imager on the
Keck telescope (Keck/KCWI; Morrissey et al. 2012). The high-performance IFUs
enable intensive surveys of diffuse Ly$\alpha$ emission around 10 to 100 high-
redshift quasars (Borisova et al., 2016; Arrigoni Battaia et al., 2019; Cai et
al., 2019; Farina et al., 2019; Drake et al., 2019; Fossati et al., 2021) to
investigate the diversity of Ly$\alpha$ nebulosities depending on factors such
as dynamics, luminosity, redshift, and radio loudness. Front-line observations
also show that ELANe take a crucial role as a signpost of (metal-enriched)
inspiraling accretion occurring in proto-cluster haloes (Arrigoni Battaia et
al. 2018; see also Anglés-Alcázar et al. 2017; Brennan et al. 2018; Grand et
al. 2019). Such a new perspective provides unique insights into puzzling
questions to the gas feeding mechanism in massive haloes at high redshifts
(Kereš et al., 2005; Dekel et al., 2009; Suresh et al., 2019; Stern et al.,
2020), and star formation (Chen et al., 2021; Nowotka et al., 2022; Arrigoni
Battaia et al., 2021) and chemical enrichment of proto-clusters (Davé et al.,
2011; Shimakawa et al., 2015; Valentino et al., 2016; Vogelsberger et al.,
2018; Maiolino & Mannucci, 2019). Thus, increasing the number of ELAN samples
will help achieve consensus on wide-ranging gas feeding and feedback phenomena
in high-$z$ massive haloes, but it is challenging. Arrigoni Battaia et al.
(2019) have reported that ELANe are extremely rare among luminous quasars with
$-28.29\leq M_{1450}\leq-25.65$ ($\sim 1$ per cent), indicating that the
pruning of quasar samples is necessary to increase identifications of ELANe
within reasonable observational times.

Motivated by these results, this study performs a systematic search for the
extended Ly$\alpha$ emission associated with quasars at $z=$ 2–3 based on the
advanced wide-field imaging data delivered by the Hyper Suprime-Cam Subaru
Strategic Program on the 8.2 m Subaru Telescope (HSC-SSP; Aihara et al. 2018;
Miyazaki et al. 2018; Furusawa et al. 2018; Kawanomoto et al. 2018; Komiyama
et al. 2018). The HSC-SSP searches in the $grizy$ broad-bands approximately
3–4 mag deeper and with better-seeing size compared to the Sloan Digital Sky
Survey (SDSS, Gunn et al. 1998; Gunn et al. 2006; Doi et al. 2010) and the
Panoramic Survey Telescope and Rapid Response System (Pan-STARRS, Chambers et
al. 2016) but over $>10$ times smaller survey area, e.g., $5\sigma$ limiting
magnitude of $\gtrsim 26$ mag and seeing full-width-half-maximum (FWHM) of
$\sim 0.6$ arcsec in the $i$-band (see Aihara et al. 2022 for details).
Various studies have demonstrated the utility of the high-quality data from
the HSC-SSP, such as high-redshift galaxy and quasar surveys (Ono et al.,
2018; Matsuoka et al., 2016), cluster and void search (Oguri et al., 2018;
Shimakawa et al., 2021), and machine-learning-based explorations of peculiar
objects (Kojima et al., 2020; Tanaka et al., 2022). This paper adds another
chapter to such past achievements in the HSC-SSP. We aim to detect extended
Ly$\alpha$ emission around more quasars than ever before by using broad-band
data sets taken over a 1000 square degree field. Prescott et al. (2012, 2013)
performed a similar approach to the 9.4 deg2 Boötes field and confirmed that
it worked successfully. It allows us to prune quasars and, hence, select
prospective candidates of ELANe before more expensive narrow-band and IFU
observations. Moreover, we can investigate statistical trends of spatial
properties of Ly$\alpha$ emissions in response to various physical parameters
with unrivalled data sets, down to a sensitivity limit $\sim 10^{-17}$ erg
s-1cm-2arcsec-2, providing important insights into the relationship between
super-massive black holes and the extent of Ly$\alpha$ emission.

This work is based on the public data from the Third Public Data Release of
the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP PDR3; Aihara et al.
2022), covering approximately 1200–1300 deg2 out of the entire survey
footprint of 1400 deg2 in $grizy$ bands. Additionally, we adopt the final
Sloan Digital Sky Survey IV (SDSS-IV; Blanton et al. 2017) quasar catalogue
(DR16Q; Lyke et al. 2020) from Data Release 16 of the extended Baryon
Oscillation Spectroscopic Survey (eBOSS; Dawson et al. 2016). These two large
databases enable an intensive search for extended Ly$\alpha$ emission around
more than 9000 quasars at $z=$ 2–3 (section 2). Combined with the public
spec-$z$ sources at the similar redshift, we construct Ly$\alpha$ images of
the targets using the redshift-corrected broad-band $gri$ colours (section 3)
and investigate the extent of Ly$\alpha$ emission around the quasar samples
(section 4). We then discuss general trends of obtained Ly$\alpha$ properties
against luminosity, redshifts, and radio loudness of quasars (section 5). The
results and conclusions achieved by this work are organised by the last
section 6.

This research adopts the AB magnitude system (Oke & Gunn, 1983). Moreover, we
assume cosmological parameters of $\Omega_{M}=0.310$,
$\Omega_{\Lambda}=0.689$, and $H_{0}=67.7$ km s-1Mpc-1 in a flat Lambda cold
dark matter model, which are consistent with those from the Planck 2018 VI
results (Planck Collaboration et al., 2020).

##  2 SDSS quasars in HSC-SSP PDR3

This paper employs 8683 quasars at $z=$ 2.34–3.00 from the DR16Q catalogue
(Lyke et al., 2020) covered by the HSC-SSP PDR3 field (Aihara et al., 2022).
This section explains how and why we select these quasars as our targets.

We began with 119,219 quasars at the Ly$\alpha$ redshift (Z_LYA) = 2.34–3.00
with $|\Delta z|\equiv|\mathtt{Z\\_PIPE-Z\\_LYA}|<0.15$ and ZWARN_LYA = 0 in
the DR16Q catalogue. They are originally selected based on three data sets of
SDSS-IV/eBOSS (Myers et al., 2015), the Wide-field Infrared Survey Explorer
(Wright et al., 2010; Lang et al., 2016), and the Palomar Transient Factory
(Law et al., 2009; Rau et al., 2009) over 14,000 deg2, with a magnitude limit
of $g<22$ or $r<22$. Then, they are classified as quasars if their spectra
taken by the eBOSS spectrographs (Smee et al., 2013) are best matched to
quasar models through the BOSS spec1d pipeline (Bolton et al. 2012; see
section 2 and 3 in Lyke et al. 2020 for details). The reason why we select
quasars at $z=$ 2.34–3.00 is that their Ly$\alpha$ lines fall into the
$g$-band of Subaru/HSC (figure 1), which enables us to extract those extended
features around quasars using $gri$ broad-band colour selection (section 3).
In fact, the $g$-band filter can capture Ly$\alpha$ line up to $z\sim 3.5$;
however, we do not use quasars at $z>3$ because of heavy IGM absorption at
$\lesssim 1020$ Å penetrating the $g$-band. We will discuss this point in
section 3.

Figure 1:  Effective throughput of HSC broad-band filters ($grizy$). The cyan and pink filled regions depict example spectra of our target quasars at $z=2.34$ and $z=3.00$, respectively (arbitrary scale).  Table 1:  SDSS/eBOSS quasars adopted in this study. Here 290 duplicates are removed from the Wide layer sample.  Layer | Area (deg2) | Depth (min-max) [$g,r,i$] | N
---|---|---|---
DUD | 35 | [26.0-28.5, 25.7-28.1, 25.3-28.1] | 366
Wide | 890 | [25.8-27.1, 25.4-27.0, 25.2-26.8] | 8317

After that, we cross-matched the quasar samples with the HSC-SSP PDR3 sources
within a radius of 1 arcsec. The HSC-SSP PDR3 field consists of the Deep and
Ultra-deep (DUD) and Wide layers, respectively, covering 37 and 1332 deg2 in
278 nights of observation (Aihara et al., 2022). The HSC-SSP PDR3 gives us a
science-ready catalogue and coadd data, which were well reduced by the
dedicated pipeline (hscPipe version 8; Bosch et al. 2018). The survey area is
split on the database into approximately $1.7\times 1.7$ deg2 areas, termed
tracts, and further divided into approximately $12\times 12$ arcmin2 regions
called patches (Aihara et al., 2022). To remove the data taken under poor sky
conditions, we discarded patches with seeing FWHM $>1.0$ arcsec or relatively
shallow imaging depths in either of the $gri$ bands (see the limiting
magnitude range in table 1). This quality management reduced the survey area
to 35 and 890 deg2 in the DUD and Wide layers. Furthermore, we selected
quasars not affected by nearby bright stars ($G<18$ mag; Aihara et al. 2022)
and bad pixels in the $grizy$-band data of the HSC-SSP PDR3, by applying the
following criteria in the SQL query:

–

isprimary=True,

–

inputcount_flag_noinputs=False,

–

pixelflags_edge=False,

–

pixelflags_bad=False,

–

mask_brightstar_halo=False,

–

mask_brightstar_ghost=False,

–

mask_brightstar_blooming=False.

For details on these catalogue flags, refer to Coupon et al. (2018); Bosch et
al. (2018); Aihara et al. (2022).

Consequently, we were left with 366 and 8317 quasars at $z=$ 2.34–3.00 in the
DUD and Wide layers of 35 and 890 deg2, respectively (table 1). We here
removed 290 duplications in the Wide layer sample with those in the DUD layer.
We cut out $gri$ coadd images ($200\times 200$ pixel2 with a pixel scale of
0.168 arcsec) for selected quasars from the HSC-SSP database and conducted the
spatial $2\times 2$ binning to increase the signal-to-noise ratio, i.e., each
image adopted in this study has $100\times 100$ pixel2 with a pixel scale of
0.336 arcsec. Their identification numbers and sky coordinates from Aihara et
al. (2022), and pipeline and Ly$\alpha$ redshifts (Z_PIPE and Z_LYA from Lyke
et al. 2020) are summarised in table 2.

##  3 Broad-band selection

This section discusses the details of our broad-band selection to extract
extended Ly$\alpha$ emission associated with the quasar targets. The method is
conceptually the same as a well-known narrow-band technique. However, we
employ only the broad-band ($gri$) filters: (1) we construct a continuum
$g$-band image ($RI_{z}$) using the $r,i$-bands, and (2) subtract the
extrapolated $RI_{z}$ image from the observed $g$-band image ($G$), which has
both continuum + Ly$\alpha$ emission at $z=$ 2.34–3.00. Here, the subscript
$z$ means redshift not $z$-band. Prescott et al. (2012) also tested a similar
approach using $B,R$ bands over the 9.4 deg2 Boötes field. They then confirmed
that the methodology worked well by follow-up spectroscopic observations
(Prescott et al., 2013). We should note that this work fully ignores potential
contributions from rest-UV helium and metal lines (e.g., Cai et al. 2017; Guo
et al. 2020) to the broad-band images, which could cause over- or under-
estimates of Ly$\alpha$ emission at some level depending on the source
redshift.

Figure 2:  (a) Top panel shows comparisons between $g$-band magnitudes ($G$)
and extrapolated $g$-band ($RI$) magnitudes from $r,i$-bands
($RI=1.350R-0.338I$) for 4400 spec-$z$ sources at $z=$ 2.34–3.00 in the HSC-
SSP DUD layer. The SDSS/eBOSS quasars are not included here. The dashed line
depicts the identity line. (b) $G-RI$ versus spectroscopic redshifts. The
purple dots are 4400 spec-$z$ sources at $z=$ 2.34–3.00 and 5780 spec-$z$
samples at $z<2.34$ and $3.00<z$. The black dashed line is the best-fit line
($G-RI=0.422\ z-1.120$) for spec-$z$ sources at $z=$ 2.34–3.00. (c) Same as
the middle panel but for 154,416 spec-$z$ sources at $z=$ 0–5. The red dots
and vertical lines depict the median values and 68th percentiles at each
redshift bin. (d) Bottom panel shows the same as in (c), but with the object
masking through the SVMs classification (see text).

For extracting the extended Ly$\alpha$ emission, it is most important to
subtract the rest-frame ultra-violet continua of host galaxies and satellites.
At the same time, we do not consider quasars themselves because they can be
regarded as point sources. At first, an empirical extrapolation of the
$RI$-band images from the $r,i$-bands ($R,I$) is performed based on 4400
spec-$z$ sources at $z=$ 2.34–3.00 from 3D-HST (Brammer et al., 2012; Momcheva
et al., 2016), DEIMOS 10k sample (Hasinger et al., 2018), PRIMUS (Coil et al.,
2011; Cool et al., 2013), and VVDS (Le Fèvre et al., 2013),

$RI=1.350\ R-0.338\ I.$ (1)

The best-fit relation (figure 2) is obtained using a non-linear optimisation
and curve-fitting tool for Python, lmfit (Newville et al., 2014). We do not
incorporate the SDSS/eBOSS quasars into the spec-$z$ sample here. In practice,
Ly$\alpha$ emission of these spec-$z$ sources should also affect $g$-band
photometry. However, we assume that their average Ly$\alpha$ emission does not
significantly affect the fitting. We indeed confirm that the best-fit relation
well traces spec-$z$ sources at $z<2.3$, where there is no Ly$\alpha$
contribution to the $g$-band (figure 2). Besides, additional colour correction
has been applied to calibrate a small redshift ($z$) dependence as seen in
figure 2b,

$RI_{z}=RI-0.422\ z+1.120,$ (2)

where $RI_{z}$ is the obtained continuum image adopted in this work. We
matched seeing sizes of all the $gri$ imaging data to FWHM $=1$ arcsec of the
original sizes obtained from the adaptive moments of the PSF model
(sdssshape_psf_shape; see Aihara et al. 2022; Bernstein & Jarvis 2002) by
Gaussian smoothing. Seeing-matched radial profiles of surface flux densities
of quasars in the $g$-band and PSF in the $gri$-bands are presented in figure
3. Galactic extinctions were also corrected for the individual $gri$ images.
We show sample $G$, $RI_{z}$, and $G-RI_{z}$ images of a target quasar at
$z=2.35$ in figure 4, demonstrating that we can erase continuum sources in the
residual $G-RI_{z}$ map. The residual map is critical for this study to search
for extended Ly$\alpha$ emissions around the quasar sample as described in
section 4. However, we should note that some clear over- and under-
subtractions can be observed due to different colour-terms of foreground and
background sources, as discussed in detail below.

Figure 3:  Radial profiles of normalised $g$-band surface flux densities of
quasars at $z=$ 2.34–3.00 in the DUD layer (left) and the Wide layer (right).
The circles and colour-filled regions depict median values and 68th
percentiles, respectively. Seeing-matched PSFs (68th percentiles over each
survey layer) in the $gri$-bands are also shown by blue, red, and green lines,
which are mostly overlapped in each panel.  Figure 4:  Examples of $G$,
$RI_{z}$, and $G-RI_{z}$ images (a quasar at $z=2.85$). The image sizes are
$34\times 34$ arcsec2, where the seeing FWHM are matched to 1 arcsec. They are
stretched by hyperbolic sine with the same min-max values for the sake of
visibility (the colour-bar shows the pixel counts in the magnitude zero point
of 27 mag).

Figure 2 summarises the empirical extrapolations of $g$-band without
Ly$\alpha$ contributions. The derived relation (eq. 1) well extrapolates
$g$-band photometry of spec-$z$ sources from those in the $r,i$-bands with a
standard deviation of 0.22 mag, corresponding to $\sim 20$% errors in the
residual Ly$\alpha$ fluxes. The further redshift correction (eq. 2) marginally
improves the extrapolation. We observed an increase of scatter of $G-RI$ at
$z>3$, likely caused by significant contributions of Ly$\alpha$ and Ly$\beta$
forests. Given such an increasing scatter at $z>3$, we did not adopt quasars
at $z=$ 3.0–3.5, although their Ly$\alpha$ lines fell into the $g$-band data.
Figure 4c shows the $G-RI$ distributions in a wider redshift range ($z=$ 0–5),
where we employed spec-$z$ sources from GAMA DR3 (Baldry et al., 2018) and
SDSS DR15 (Aguado et al., 2019).111Although the data release paper (Aihara et
al., 2022) refers to different versions in GAMA (DR2) and SDSS (DR16), release
versions cited here are the right versions. Increasing colour scatter can be
found at $z<1.5$ and $z>3$, requiring us to be aware of irrelevant neighbours,
especially outliers in the foreground. Otherwise, we may overestimate an area
of extended Ly$\alpha$ emission.

To minimise such contaminants from the foreground and background neighbours,
we masked outlier candidates at $z<2.34$, $3.00<z$ based on the $grizy$
magnitudes (cmodel; Abazajian et al. 2004; Bosch et al. 2018) with support
vector machines (SVMs; Boser et al. 1992; Cortes & Vapnik 1995). We employed
Scikit-learn (version 0.24.2; Pedregosa et al. 2011) to implement the SVMs
classification with Radial Basis Function (RBF) kernel. First, we established
two spec-$z$ samples at the target redshifts of $z=$ 2.34–3.00 ($N=746$) and
at foreground or background redshifts $z<2.34$, $3.00<z$ ($N=105606$) covered
by both the DUD and Wide layers. We here applied the $i$-band magnitude cut
($i<24$ mag) since the number of spec-$z$ references significantly drops at
$i>24$ mag. Using $grizy$ photometry of $746+105606$ training samples, we
obtained the best decision boundaries in five-dimensional space to classify
into these two populations through SVMs with weight by the sample sizes. The
derived total accuracy scores were 0.893 in the DUD layer and 0.889 in the
Wide layer. We then evaluated recall and specificity rates (so-called
completeness) in different $i$-band magnitudes as seen in figure 5, which are
respectively defined by TP/(TP+FN) and TN/(TN+FP). TP (or TN) and FN (or FP)
are true positive (or negative) and false negative (or positive) values, where
the positive and negative classes indicate the sources at $z=$ 2.34–3.00 and
$z<2.34$, $3.00<z$ predicted by the SVMs classifier, respectively.

Figure 5:  Mean values and $1\sigma$ Poisson errors of recall and specificity
rates in the SVMs classification for spec-$z$ sources at $z=$ 2.34–3.00
($N=3559$, the solid line) and at $z<2.34$, $3.00<z$ ($N=135569$, the dotted
line), respectively, as a function of $i$-band magnitude ($\Delta=0.1$ mag).
We adopted identical spec-$z$ sources in the DUD and Wide layers, which are
represented by the yellow and purple lines, respectively. There is no $z=$
2.34–3.00 sample at $i<18$ (the grey area). We did not apply the object
masking for faint sources ($i<24$, the vertical line), where we confirmed low
recall rates due to weak detection and a lack of the training samples.

Consequently, we found that the SVMs classifier can select $z=$ 2.34–3.00 and
$z<2.34$, $3.00<z$ sources with on average $\sim 80$% and $\sim 90$%
completeness down to $i=24$ mag (figure 5). Based on the classification
result, we masked foreground or background neighbours with $i=$ 18–24 mag
around the target quasars to minimise the colour-term contaminants. We
observed that this masking process can significantly improve the colour-term
effect at $z<1.5$ (figure 2d), though it remains imperfect due to the limited
photometric information. The mask areas were determined by three times PSF-
convolved major- and minor-axis based on the second moments of the object
intensity, termed adaptive moments in the $i$-band (i_sdssshape_shape; see
Bernstein & Jarvis 2002). We also masked bright objects with $i<18$ mag and
point sources (i_psfflux_mag$-$i_cmodel_mag$<0.2$; see Strauss et al. 2002;
Baldry et al. 2010). Additionally, quasar itself was masked within 2.5 arcsec
diameter ($2.5\times$ seeing FWHM or $r\lesssim 10$ pkpc) for relatively fair
comparisons of Ly$\alpha$ properties between optically bright and faint
quasars (section 5). Examples of masked $G-RI_{z}$ images are shown in figure
6 and 8 in section 4.

##  4 Quasars with Lyman-Alpha nebulae

Up to this point, we have explained how we selected quasars and established
Ly$\alpha$ images around the targets. This section reviews the broad-band
selection for 8683 quasars at $z=$ 2.34–3.00, and the search for extended
Ly$\alpha$ emission around the targets to select quasars with large gaseous
nebulae (hereafter called _quasar-nebulae_).

Figure 6:  From the left to the right, (a) $gri$ colour image, (b) $g$-band
coadd image, (c) extrapolated $g$-band ($RI_{z}$) image, and (d,e) residual
$G-RI_{z}$ image without and with masks, respectively, for a known quasar-
nebula, SDSS J1025+0452 at $z=3.2$ (Arrigoni Battaia et al., 2019), which is
covered by the HSC-SSP PDR3 Wide layer. The images have a length and width of
34 arcsec ($\sim 260$ pkpc). The colourbar indicates the tentatively-measured
Ly$\alpha$ surface densities ($10^{-17}$ erg s-1cm-2arcsec-2) by eq. 3. The
white contour in the residual map depicts $2\sigma$ excess from the background
deviation (bg_std but with the filter correction). The white open circles
indicate the maximum radius for calculating Area and Area_eff ($=55.32$ and
46.17 arcsec2, respectively). Although the source redshift is a bit out of the
target redshift range $z=$ 2.34–3.00, the residual $G-RI_{z}$ image reproduced
the extended Ly$\alpha$ nebula seen in the deep VLT/MUSE datacube by Arrigoni
Battaia et al. (2019, #10 of figure 1 and figure 5). The grey regions and the
black centre circle in the right panel (f) are the object masks for foreground
or background contaminants (see text) and quasar itself (2.5 arcsec diameter
or $r\lesssim 10$ pkpc), respectively.

We first tested our procedure to a known quasar-nebula source, SDSS J1025+0452
at $z=3.2$, covered by the HSC-SSP PDR3 Wide layer (figure 6). The QSO MUSEUM
survey reported this quasar-nebula (Arrigoni Battaia et al., 2019), extending
across 289 arcsec2 in the deep VLT/MUSE datacube (surface brightness limit of
$4.2\times 10^{-18}$ erg s-1cm-2arcsec-2 in 1 arcsec2 for the 30 Å NB image
according to the literature). We stress that this source redshift is slightly
off from our target redshift slice, $z=$ 2.34–3.00. Therefore, it may have
higher extinction in the $g$-band than our assumption due to IGM absorption
(figure 2). Nevertheless, the resultant residual $G-RI_{z}$ image replicated
extended Ly$\alpha$ emission traced by Arrigoni Battaia et al. (2019, figure 1
and 5), whereas our sensitivity-limited broad-band selection could detect
Ly$\alpha$ signals only up to an area of 55.32 arcsec2 (or 46.17 arcsec2 with
masks).

Figure 7:  Schematic illustration of the selection procedure. (a) We calculate
a pixel area (Area) with $>2\sigma$ excess of residual flux within a radius of
6 arcsec from the centre (the orange circle). The background deviation is
estimated at $r>25$ arcsec ($\gtrsim 100$ pkpc; the grey region) for each
$G-RI_{z}$ cutout image. This work selects quasars with Area_eff $>40$ arcsec2
($>442$ pixel2) as quasar-nebulae. (b) We also derive the mean surface
brightness (SB_ann; eq. 3) in an annulus of radius 3.5–4.0 arcsec
(corresponding to $\sim 30$ pkpc; the purple area), which may be useful for
users to make a strategy of follow-up observation.

We now introduce our selection of the quasar-nebulae. Throughout this paper,
quasars with effective Ly$\alpha$ areas (Area_eff) greater than 40 arcsec2 are
deemed to be quasar-nebulae, where Area_eff is defined as the pixel area with
$2\sigma$ excess from the background deviation (bg_std), excluding the masked
area (figure 6 and 7). Directly obtained Ly$\alpha$ areas without masking
irrelevant sources are defined as Area. Both Area and Area_eff were calculated
within a 37 pixel ($\sim 12$ arcsec or $\sim 100$ pkpc) aperture diameter,
where the aperture limit is set to reduce the effects from the foreground and
background neighbours. The diameter size is also sufficiently smaller than the
mesh size (43 arcsec) for the local sky subtraction in the image processing by
HSC-SSP (Aihara et al., 2022). The background deviation bg_std was estimated
based on pixels at $r>37$ pixels (figure 7). The obtained residual Ly$\alpha$
maps reached typical $2\sigma$ depths per $2\times 2$ binned pixel down to
$\sim 0.9\times 10^{-17}$ erg s-1cm-2arcsec-2 in the DUD layer and $\sim
1.6\times 10^{-17}$ erg s-1cm-2arcsec-2 in the Wide layer, respectively. We
also tentatively estimated the Ly$\alpha$ surface brightness at $r=$ 10–12
arcsec (SB_ann; figure 7), defined as,

$\mathtt{SB\\_ann}=\Delta_{g}w_{G}(z)~{}\mathrm{SB}_{G-RI_{z}}.$ (3)

It may be convenient for users to infer the expected Ly$\alpha$ surface
brightness in the outskirts ($r\sim 30$ pkpc). The sign $\Delta_{g}$ is FWHM
of the $g$-band filter ($=1375$ Å), and $w_{G}(z)$ is an weight parameter for
correcting the $g$-band transmittance (figure 1), which yields, e.g., 1.79 at
$z_{\mathrm{Ly\alpha}}=2.34$ and 0.98 at $z_{\mathrm{Ly\alpha}}=3.00$.
SB${}_{G-RI_{z}}$ is mean surface brightness of the residual Ly$\alpha$ image
($G-RI_{z}$) at $r=$ 10–12 arcsec. One should note that SB_ann values vary
depending on many factors such as imaging depths, contamination by projected
neighbours in the foreground and background, and colour term effects.
Therefore, they should be used _only as a guide_ , e.g., for making a strategy
of a follow-up observation.

We applied these measurements to all quasar targets and then searched for
quasar-nebulae with extended Ly$\alpha$ emission (Area_eff $>40$ arcsec2). The
source catalogue available as online material (table 2) summarises obtained
Area, Area_eff, SB_ann, and bg_std for 366 and 8317 quasars at $z=$ 2.34–3.00
in the HSC-SSP PDR3 DUD and Wide layers (table 1). With the selection
threshold of Area_eff $>40$ arcsec2, we respectively select 7 and 32 sources
as quasar-nebulae. Processed images like figure 6 for all quasar-nebulae in
the DUD and Wide layers are represented in figure 8 and 12, respectively,
showing clear extended Ly$\alpha$ features in both unmasked and masked
$G-RI_{z}$ images. These processed images help catalogue users to visually
check credibility of residual Ly$\alpha$ distributions from the broad-band
selection. Refer to the data availability section for more details on
acquiring the cutout data. If one needs to access the risk catalogue for $z=$
3.0–3.5 quasars unused in this study, please contact the author.

Table 2:  Quasar information and properties of Ly$\alpha$ emission. The full source catalogue is available as online material in CSV format.  object_id | layer | deptha | ra | dec | Z_PIPEb | Z_LYAb | Areac | Area_effc | SB_annd | bg_stdd
---|---|---|---|---|---|---|---|---|---|---
37484563299063297 | dud | 28.16 | 34.93038 | -5.43555 | 2.78811 | 2.85555 | 19.19 | 14.22 | 1.20 | 2.39
36429328489138776 | dud | 26.67 | 36.21685 | -6.01799 | 2.91488 | 2.91186 | 22.47 | 13.32 | 6.88 | 8.73
37484567594046770 | dud | 28.31 | 34.95245 | -5.12826 | 2.54855 | 2.54530 | 4.40 | 3.84 | 0.91 | 2.01
37484717917884104 | dud | 28.36 | 34.83848 | -4.72088 | 2.77543 | 2.80256 | 59.04 | 54.08 | 4.95 | 1.78
37484705032993293 | dud | 28.32 | 34.85126 | -5.19717 | 2.53069 | 2.52831 | 15.13 | 10.16 | 2.61 | 2.74
… (366 rows in total)
36411452835251556 | wide | 26.53 | 30.55460 | -6.38877 | 2.53873 | 2.53747 | 8.47 | 4.40 | 4.31 | 7.52
… (8317 rows in total)
a $5\sigma$ PSF limiting magnitude in the $g$-band from Aihara et al. (2022)
b Excerpts from Lyke et al. (2020)
c arcsec2
d $10^{-18}$ erg s-1cm-2arcsec-2
Figure 8:  Same as figure 6, but seven quasar-nebula candidates in the HSC-SSP
PDR3 DUD layer, all of which have Area_eff $>40$ arcsec2. The colourbars
indicate tentatively-measured Ly$\alpha$ surface brightness in $10^{-17}$ erg
s-1cm-2arcsec-2 (eq. 3). Those in the Wide layer are available in figure 12.

##  5 Discussion: Wheat versus Chaff in Lyman-Alpha emission around quasars

The broad-band colour selection enabled us to extract Ly$\alpha$ emission
around quasars at $z=$ 2.34–3.00. We successfully obtained 7 and 32 quasar-
nebulae with effective Ly$\alpha$ areas greater than 40 arcsec2. This section
investigated what factors distinguish the spatial extent of Ly$\alpha$
emission between _wheat and chaff_ , i.e., quasars with and without large
Ly$\alpha$ nebulae, by examining Area_eff distributions of control samples
with respect to different parameters. Specifically, motivated by the previous
discussions about the limited quasar samples (see, e.g., Arrigoni Battaia et
al. 2019; Cai et al. 2019), we investigated connections of the extent of
Ly$\alpha$ emission to absolute magnitude and radio-loudness.

Figure 9:  Background deviation bg_std ($\ast$ erg s-1cm-2arcsec-2) versus
effective Ly$\alpha$ area Area_eff for our samples in the DUD (yellows) and
Wide (purples) layers. For fair comparisons, we excluded quasars with
relatively shallower data (bg_std $>8.127$) throughout the discussion section.
The threshold was determined by 90% completeness limit of the quasar-nebula
sample in the Wide layer.

We first removed quasars with relatively poor imaging qualities inferred from
figure 9, which showed the background deviation in pixel (bg_std) as a
function of the effective Ly$\alpha$ area Area_eff. We here changed the unit
of Area_eff from arcsec2 to pkpc2 to correct the small redshift difference at
$z=$ 2.34–3.00. We set the selection threshold bg_std $<8.127\times 10^{-18}$
erg s-1cm-2arcsec-2, corresponding to the 90% completeness of quasar-nebulae
in the Wide layer. Given the selection criterion, we established the clean
samples of 328 and 4212 quasars in the DUD and Wide layers, respectively.
Additionally, to check the radio detection, we cross-matched our quasar sample
with the FIRST survey catalogue (version 14Dec17; Becker et al. 1995; White et
al. 1997) within a radius of 1 arcsec. The FIRST survey covers the entire HSC-
SSP field, and the source catalogue contains radio sources with the detection
limit of 1 mJy at $\sim 1.4$ GHz. This paper defined 4 and 112 spatially-
matched quasars as radio-loud quasars in the DUD and Wide layers,
respectively, and the others as radio-quiet quasars. We note that radio-quiet
quasars defined here could be still radio-loud quasars.

Figure 10:  Effective Ly$\alpha$ areas (Area_eff) versus absolute $i$-band
magnitudes normalised at $z=2$ ($M_{i}[z=2]$ from Lyke et al. 2020) for clean
samples in the DUD (yellows) and Wide (purples) layers. The purple solid and
dashed lines depict median values and 68th percentiles given $M_{i}[z=2]$ bins
($\Delta=0.25$ mag) for the Wider layer sample.

Figure 10 compares Area_eff with absolute $i$-band magnitudes normalised at
$z=2$ (M_I from Lyke et al. 2020 with the K corrections in Richards et al.
2006, hereafter $M_{i}[z=2]$) for the clean samples in the DUD and Wide
layers. According to the Spearman’s rank correlation test, we detected
moderate correlation between effective Ly$\alpha$ area (Area_eff) and
$M_{i}[z=2]$ by correlation coefficients $r_{s}=-0.28$ in the DUD layer
($N=328$) and $r_{s}=-0.44$ in the Wider layer sample ($N=4212$) with
sufficiently small $p$-values ($p\ll 0.001$). The moderate correlations
suggest that more luminous quasars tend to involve more extended Ly$\alpha$
emission with high Ly$\alpha$ surface brightness $\gtrsim 1\times 10^{-17}$
erg s-1cm-2arcsec-2.

Such observed tendencies are broadly consistent with results from previous
surveys to $z>2$ quasars. Arrigoni Battaia et al. (2019); Mackenzie et al.
(2021) have reported that more luminous quasars (i.e., lower $M_{i}[z=2]$)
have higher peak Ly$\alpha$ luminosity. The currently known ELANe are mostly
associated with the brightest quasars at $M_{i}\lesssim-27$ mag (Cantalupo et
al., 2014; Hennawi et al., 2015; Cai et al., 2017; Cai et al., 2018; Arrigoni
Battaia et al., 2018). A deep narrow-band Ly$\alpha$ imaging survey also
detected Ly$\alpha$-illuminated cosmic web structures around a hyper-luminous
quasar at $z=2.84$ (Kikuta et al., 2019). Combined with these previous
findings, the results indicate at least that there is a higher chance to
detect very extended and luminous Ly$\alpha$ emission around the brightest
quasars, i.e., more massive black holes (McLure & Dunlop, 2004; Kollmeier et
al., 2006), within reasonable observation times, as seen in the higher
detection rate of quasar-nebulae in more luminous samples. In other words, our
limited-sensitivity would be missing extended but faint Ly$\alpha$ structures,
especially around less luminous quasars. Furthermore, previous studies have
reported a relatively little variation in Ly$\alpha$ properties from redshift
$z\sim 6$ to $z\sim 3$ (Farina et al., 2019), but a lower averaged surface
brightness of Ly$\alpha$ nebulosities at $z=2$ compared to those at $z=3$
(Arrigoni Battaia et al., 2019; Cai et al., 2019). This implies the lower
covering factors of cold gas components in the CGM at $z<3$ than those at
$z>3$, based on the assumption that the Ly$\alpha$ surface brightness is
proportional to the number density of hydrogen and the column density in the
optically thin environment (Cantalupo et al., 2014; Arrigoni Battaia et al.,
2015, 2016; Cai et al., 2019). However, this paper does not delve into the
redshift dependence given the limited redshift range ($z=$ 2.34–3.00) and the
redshift dependent colour-term effect. We leave such detailed work to future
work.

Figure 11:  The obtained $p$-value from the two-sample KS tests is inserted in
each panel. The numbers in parentheses in each legend are the number of
quasars used in each group. In the middle and right panels, the comparisons of
absolute $i$-band magnitude distributions ($M_{i}[z=2]$) for the control
samples are shown.

Next, Area_eff distributions for $M_{i}[z=2]$-matched control samples of
radio-loud and radio-quiet quasars are represented in figure 10. Inset panels
of figure 10 show that we well matched $M_{i}[z=2]$ values in the Wide layer,
while we lacked radio-loud quasars in the DUD layer ($N=4$). The two-sample
Kolmogorov–Smirnov (KS) test indicates no significant difference in
distributions of the effective Ly$\alpha$ areas between radio-loud and radio-
quiet quasars, as seen in $p$-value $=0.274$ (figure 11), suggesting that
their Ly$\alpha$ surface profile are similar in a large sense. The systematic
IFU observation of $z\sim 3$ quasars by Arrigoni Battaia et al. (2019) also
reported similar mean Ly$\alpha$ profiles between radio-loud and radio-quiet
quasars, where only a marginal excess in radio-loud samples at a radius of
30–50 pkpc were detected. It is thus consistent with the statistical trend
obtained in our comparison samples. Contrarily, given the same control
samples, we detected a higher fraction ($5.4\pm 2.2$%) of radio-loud quasars
with relatively large Area_eff ($>2000$ pkpc2) than that of radio-quiet
quasars ($2.4\pm 0.4$%). The higher detection rate of the more extended
Ly$\alpha$ emission around radio-loud quasars could be related to viewing
angles of radio jets and/or evolutionary phases of radio-loud quasars, as many
case studies presented spatial and kinematic interactions between radio jets
and Ly$\alpha$ nebulae (e.g., McCarthy et al. 1990; van Ojik et al. 1996;
Pentericci et al. 1997; Morais et al. 2017; Silva et al. 2018). We tentatively
checked the size measurements of radio sources associated with radio-loud
quasars from Becker et al. (1995); White et al. (1997), which are based on the
elliptical Gaussian model. However, we did not see any systematic relation to
their Ly$\alpha$ areas so far. Assessing individual radio-loud quasars with
multi-wavelength data sets would be important to delve into additional
processes contributing to their extended Ly$\alpha$ emissions. We defer such
detailed analyses of individual objects to future work.

Lastly, we discuss whether or not our quasar-nebulae include the largest class
of ELANe such as the Slug nebula at $z=2.3$ (Cantalupo et al., 2014) and the
MAMMOTH-1 at $z=2.3$ (Cai et al., 2017). These largest ELANe have very
extended Ly$\alpha$ nebulae beyond 150 pkpc with high Ly$\alpha$ surface
brightness $\gtrsim 1\times 10^{-17}$ erg s-1cm-2arcsec-2. Therefore, if we
have such large ELANe in the obtained quasar-nebulae, it is expected to see
Ly$\alpha$ emission extending beyond $\sim 20$ arcsec in their residual
Ly$\alpha$ images (figure 8 and 12). However, apparently none of them
represent such extensive Ly$\alpha$ nebulae significantly beyond 100 pkpc
above the surface brightness limit of $\sim 10^{-17}$ erg s-1cm-2arcsec-2,
despite the large sample of luminous quasars ($M_{i}<-27$) amounting to 29 and
731 objects. The most extended nebula in the current sample is
object_id=37489365072502768 in the DUD layer (the second line in figure 8),
which has the maximum extent of 110 pkpc above $\sim 7\times 10^{-18}$ erg
s-1cm-2arcsec-2 according to the tentative flux estimation (eq. 3). This may
suggest that the largest class of ELANe as ever discovered could be extremely
rare ($\ll 1$ percent) than previously thought (Arrigoni Battaia et al.,
2019). The upcoming huge imaging data by the LSST on the Vera C. Rubin
Observatory over 18000 deg2 (Ivezić et al., 2019), 13 times wider than the
survey area of the HSC-SSP (1400 deg2), may be necessary to establish
statistical ELAN samples with the broad-band selection. Particularly, the LSST
will also conduct imaging with $u$-band, which has $\sim 2$ times narrower
filter width than the $g$-band, and hence more sensitive and useful to detect
the Ly$\alpha$ excess at $z\sim 2$.

##  6 Conclusions

We applied the broad-band colour selection to all available SDSS-IV/eBOSS
quasars at $z=$ 2.34–3.00 from (Lyke et al., 2020) in the HSC-SSP PDR3 field
(Aihara et al., 2022), amounting to the total of 8683 sources, to search for
extended Ly$\alpha$ emission associated with them. Our broad-band selection
could extract only bright Ly$\alpha$ emission approximately down to $1\times
10^{-17}$ erg s-1cm-2arcsec-2. However, we had a huge advantage of adopting
the very wide-field imaging data covering 35 and 890 deg2 in the HSC-SSP DUD
and Wide layers, allowing us to estimate the extent of Ly$\alpha$ emission for
two orders of magnitude more sources than any existing narrow-band imaging and
IFU spectroscopic surveys.

Consequently, we measured Ly$\alpha$ areas for all 8683 targets, and then
selected 7 and 32 quasars with extended Ly$\alpha$ emission larger than 40
arcsec2 as quasar-nebulae in the DUD and Wide layers, respectively. Although
some of them may be potential ELAN candidates, none of them have remarkably
large Ly$\alpha$ nebulae as seen in the Slug and MAMMOTH-1 nebulae (Cantalupo
et al., 2014; Cai et al., 2017), suggesting that such a largest class of ELANe
could be extremely rare in the universe ($\ll 1$ percent). The source
catalogue of our quasar targets and their Ly$\alpha$ properties derived
through this paper are available as online material, and their processed
images (i.e., $gri$ colour, $G$, $RI_{z}$, and $G-RI_{z}$ images) also appear
in figure 8 and 12. Based on the obtained effective Ly$\alpha$ areas of
quasars, we detected higher fractions of relatively large Ly$\alpha$ nebulae
in more luminous and radio-loud quasars by reference to the public catalogues
(Becker et al., 1995; White et al., 1997; Lyke et al., 2020). On the other
hand, overall there is no statistical difference of effective Ly$\alpha$ areas
between radio-loud and radio-quiet quasars. These obtained trends of the
extent of Ly$\alpha$ emission towards luminosity and radio-loudness are
broadly consistent with previous findings with deep IFU observations for
$<100$ quasars at $z>2$ (Arrigoni Battaia et al., 2019; Cai et al., 2019;
Farina et al., 2019; Mackenzie et al., 2021). Forthcoming paper II will
address their Ly$\alpha$ morphologies and environmental dependence, including
additional $u$-band selected quasar-nebulae at $z\sim 2$, based on a deep
multi-band photometric catalogue in the DUD layer.

Catalogue users can easily access the reduced coadd images of our sample on
the HSC-SSP data release site (see the data availability section). The source
catalogue (table 2) also includes the spatial properties of Ly$\alpha$
emissions for the non quasar-nebulae, allowing users to crosscheck their
samples with all the quasars adopted in this study. We note that SB_ann is the
preliminary estimate of the surface Ly$\alpha$ brightness with large
uncertainties. Users are advised to adopt this value at their own risk. _It
will be very helpful if catalogue users share success rates of their follow-up
observations, which will improve the selection method for future work._ We
plan to extend the sample to available spec-$z$ sources, including non-quasar
objects at lower and higher redshifts by using more broad-band data. Such a
series of efforts will help us scrutinise the redshift evolution and
environmental dependence of large Ly$\alpha$ nebulae, and greatly push this
field forward with the LSST on the Vera C. Rubin Observatory in the near
future (Ivezić et al., 2019).

## Acknowledgements

This research is based on data collected at Subaru Telescope, which is
operated by the National Astronomical Observatory of Japan. We are honoured
and grateful for the opportunity of observing the Universe from Maunakea,
which has the cultural, historical and natural significance in Hawaii.

The Hyper Suprime-Cam (HSC) collaboration includes the astronomical
communities of Japan and Taiwan, and Princeton University. The HSC
instrumentation and software were developed by the National Astronomical
Observatory of Japan (NAOJ), the Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High
Energy Accelerator Research Organization (KEK), the Academia Sinica Institute
for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University.
Funding was contributed by the FIRST program from Japanese Cabinet Office, the
Ministry of Education, Culture, Sports, Science and Technology (MEXT), the
Japan Society for the Promotion of Science (JSPS), Japan Science and
Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK,
ASIAA, and Princeton University. This paper makes use of software developed
for the Large Synoptic Survey Telescope. We thank the LSST Project for making
their code available as free software at http://dm.lsst.org.

The Pan-STARRS1 Surveys (PS1) have been made possible through contributions of
the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project
Office, the Max-Planck Society and its participating institutes, the Max
Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for
Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham
University, the University of Edinburgh, Queen’s University Belfast, the
Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory
Global Telescope Network Incorporated, the National Central University of
Taiwan, the Space Telescope Science Institute, the National Aeronautics and
Space Administration under Grant No. NNX08AR22G issued through the Planetary
Science Division of the NASA Science Mission Directorate, the National Science
Foundation under Grant No. AST-1238877, the University of Maryland, and Eotvos
Lorand University (ELTE) and the Los Alamos National Laboratory.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High Performance Computing at the University of Utah. The SDSS
website is www.sdss.org.

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

GAMA is a joint European-Australasian project based around a spectroscopic
campaign using the Anglo-Australian Telescope. The GAMA input catalogue is
based on data taken from the Sloan Digital Sky Survey and the UKIRT Infrared
Deep Sky Survey. Complementary imaging of the GAMA regions is being obtained
by a number of independent survey programmes including GALEX MIS, VST KiDS,
VISTA VIKING, WISE, Herschel-ATLAS, GMRT and ASKAP providing UV to radio
coverage. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and
the participating institutions. The GAMA website is www.gama-survey.org. This
work is in part based on observations taken by the 3D-HST Treasury Program (GO
12177 and 12328) with the NASA/ESA HST, which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract
NAS5-26555. Funding for PRIMUS is provided by NSF (AST-0607701, AST-0908246,
AST-0908442, AST-0908354) and NASA (Spitzer-1356708, 08-ADP08-0019,
NNX09AC95G). This research uses data from the VIMOS VLT Deep Survey, obtained
from the VVDS database operated by Cesam, Laboratoire d’Astrophysique de
Marseille, France.

We thank anonymous referee for helpful feedback. We would like to thank
Editage (www.editage.com) for English language editing. This work made
extensive use of the following tools, NumPy (Harris et al., 2020), Matplotlib
(Hunter, 2007), the Tool for OPerations on Catalogues And Tables, TOPCAT
(Taylor, 2005), a community-developed core Python package for Astronomy,
Astopy (Astropy Collaboration et al., 2013), and Python Data Analysis Library
pandas (Reback et al., 2021).

## Data Availability

The data underlying this article are available on the public data release site
of Hyper Suprime-Cam Subaru Strategic Program
(https://hsc.mtk.nao.ac.jp/ssp/data-release/). The source catalogue and
processed images are also accessible as online material. When one wants to
obtain coadd imaging data for specific sources, the author recommends using
the user-friendly cutout tool (https://hsc-
release.mtk.nao.ac.jp/das_cutout/pdr3/) or the interactive sky viewer hscMap
(https://hsc-release.mtk.nao.ac.jp/hscMap-pdr3/app). For any additional
information, including the risk catalogue for $z=$ 3.0–3.5 quasars, please
contact the author.

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##  Appendix A Additional figures

Figure 12:  Same as figure 8, but in the HSC-SSP PDR3 Wide layer.  Figure 13:
continued Figure 14: continued Figure 15: continued