11institutetext: Observatoire de Genève, Université de Genève, 51 Chemin de
Pégase, 1290 Versoix, Switzerland 22institutetext: Univ. Lyon, Univ. Lyon1,
Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230,
Saint-Genis-Laval, France 33institutetext: Leibniz-Institut für Astrophysik
Potsdam (AIP), An der Sternwarte 16 14482 Potsdam, Germany 44institutetext:
Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The
Netherlands 55institutetext: Department of Physics, ETH Zürich, Wolfgang-
Pauli-Strasse 27, 8093 Zürich, Switzerland 66institutetext: Department of
Astronomy, University of Wisconsin, 475 N. Charter Street, Madison, WI 53706,
USA 77institutetext: Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, Hawthorn, Victoria 3122, Australia 88institutetext:
Aix Marseille Univ, CNRS, CNES, LAM, 38 rue Frédéric Joliot-Curie, 13013
Marseille, France 99institutetext: ESO Vitacura, Alonso de Córdova
3107,Vitacura, Casilla 19001, Santiago de Chile, Chile

# The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes
around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based
on observations made with ESO telescope at the La Silla Paranal Observatory
under the large program 1101.A-0127

Haruka Kusakabe The MUSE eXtremely Deep Field: Individual detections of
Ly$\alpha$ haloes around rest-frame UV-selected galaxies at $z\simeq
2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at the La
Silla Paranal Observatory under the large program 1101.A-0127e-mail:
<EMAIL_ADDRESS>MUSE eXtremely Deep Field: Individual detections
of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at $z\simeq
2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at the La
Silla Paranal Observatory under the large program 1101.A-0127e-mail:
<EMAIL_ADDRESS>Anne Verhamme The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127 Jérémy Blaizot The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127 Thibault
Garel The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127 Lutz Wisotzki The MUSE eXtremely Deep Field: Individual detections
of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at $z\simeq
2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at the La
Silla Paranal Observatory under the large program 1101.A-0127The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127 Floriane Leclercq The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127 Roland Bacon The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127 Joop
Schaye The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127 Sofia G. Gallego The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127 Josephine Kerutt The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127 Jorryt Matthee The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127 Michael
Maseda The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127 Themiya Nanayakkara The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127 Roser Pelló The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127 Johan Richard The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127The MUSE eXtremely Deep Field: Individual
detections of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at
$z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at
the La Silla Paranal Observatory under the large program 1101.A-0127 Laurence
Tresse The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127 Tanya Urrutia The MUSE eXtremely Deep Field: Individual detections
of Ly$\alpha$ haloes around rest-frame UV-selected galaxies at $z\simeq
2.9$–$4.4$ ††thanks: Based on observations made with ESO telescope at the La
Silla Paranal Observatory under the large program 1101.A-0127The MUSE
eXtremely Deep Field: Individual detections of Ly$\alpha$ haloes around rest-
frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on
observations made with ESO telescope at the La Silla Paranal Observatory under
the large program 1101.A-0127 Eloïse Vitte The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127The MUSE eXtremely Deep Field:
Individual detections of Ly$\alpha$ haloes around rest-frame UV-selected
galaxies at $z\simeq 2.9$–$4.4$ ††thanks: Based on observations made with ESO
telescope at the La Silla Paranal Observatory under the large program
1101.A-0127The MUSE eXtremely Deep Field: Individual detections of Ly$\alpha$
haloes around rest-frame UV-selected galaxies at $z\simeq 2.9$–$4.4$ ††thanks:
Based on observations made with ESO telescope at the La Silla Paranal
Observatory under the large program 1101.A-0127

(Received September 27th, 2021; accepted January 14th, 2022)

Hydrogen Ly$\alpha$ haloes (LAHs) are commonly used as a tracer of the
circumgalactic medium (CGM) at high redshifts. In this work, we aim to explore
the existence of Ly$\alpha$ haloes around individual UV-selected galaxies,
rather than around Ly$\alpha$ emitters (LAEs), at high redshifts. Our sample
was continuum-selected with $F775W\leq 27.5$, and spectroscopic redshifts were
assigned or constrained for all the sources thanks to the deepest (100- to
140-hour) existing Very Large Telescope (VLT)/Multi-Unit Spectroscopic
Explorer (MUSE) data with adaptive optics. The final sample includes 21
galaxies that are purely $F775W$-magnitude selected within the redshift range
$z\approx 2.9$-$4.4$ and within a UV magnitude range $-20\leq
M_{1500}\leq-18$, thus avoiding any bias toward LAEs. We tested whether
galaxy’s Ly$\alpha$ emission is significantly more extended than the MUSE PSF-
convolved continuum component. We find 17 LAHs and four non-LAHs. We report
the first individual detections of extended Ly$\alpha$ emission around non-
LAEs. The Ly$\alpha$ halo fraction is thus as high as $81.0^{+10.3}_{-11.2}$%,
which is close to that for LAEs at $z=3$–$6$ in the literature. This implies
that UV-selected galaxies generally have a large amount of hydrogen in their
CGM. We derived the mean surface brightness (SB) profile for our LAHs with
cosmic dimming corrections and find that Ly$\alpha$ emission extends to 5.4
arcsec ($\simeq 40$ physical kpc at the midpoint redshift $z=3.6$) above the
typical $1\sigma$ SB limit. The incidence rate of surrounding gas detected in
Ly$\alpha$ per one-dimensional line of sight per unit redshift, $dn/dz$, is
estimated to be $0.76^{+0.09}_{-0.09}$ for galaxies with $M_{1500}\leq-18$ mag
at $z\simeq 3.7$. Assuming that Ly$\alpha$ emission and absorption arise in
the same gas, this suggests, based on abundance matching, that LAHs trace the
same gas as damped Ly$\alpha$ systems (DLAs) and sub-DLAs.

###### Key Words.:

Galaxies: high-redshift – galaxies: formation – galaxies: evolution –
galaxies: haloes – cosmology: observations

##  1 Introduction

The circumgalactic medium (CGM) is the gas surrounding galaxies and
corresponds to the reservoir of material fuelling galaxy formation. It serves
as the interface between the interstellar medium (ISM) and the intergalactic
medium (IGM). The boundary of the CGM has not been well-defined yet, but is
commonly considered to be outside the ISM and inside the virial radius (e.g.,
Tumlinson et al. 2017). Gas is exchanged between the CGM and the ISM in
galaxies via inflows and outflows. Outflows enrich the CGM with metals, and
part of the outflowing gas is expected to be recycled through a halo fountain
(e.g., Oppenheimer & Davé 2008). Local observations suggest that the CGM is a
multiphase medium in terms of its density, temperature, ionization state,
kinematics, and metallicity (e.g., Lanzetta et al. 1995; Werk et al. 2014,
2016). State-of-the-art cosmological simulations predict the time evolution of
complicated multiphase structures in the medium, such as the Evolution and
Assembly of Galaxies and their Environment (EAGLE) simulations (e.g., Schaye
et al. 2015; Rahmati et al. 2015; Oppenheimer et al. 2016) and the Illustris
TNG50 simulations (e.g., Nelson et al. 2019; Pillepich et al. 2019; Nelson et
al. 2021), but physical mechanisms of gas exchanges, heating by feedback, and
metal pollution are still poorly constrained. As a result, the typical mass
distribution and kinematics of the various phases at play in the CGM are not
well understood yet (e.g., Davies et al. 2020).

Observations of the CGM are traditionally based on transverse absorption-line
studies (or tomographic mapping), providing the H i column densities along the
line of sight to bright background sources such as quasars and bright galaxies
(e.g., Wolfe et al. 1986; Tumlinson et al. 2017; Péroux & Howk 2020). This
technique is sensitive to low H i column densities, $N(\mbox{H\,{\sc i}})$,
and allows us to study a wide range of $N(\mbox{H\,{\sc i}})$. Neutral gas
clouds with $N(\mbox{H\,{\sc i}})>2\times 10^{20}$ cm-2 are often referred to
as damped Ly$\alpha$ systems (DLAs, e.g., Wolfe et al. 2005), while partially
ionized gas regions with $10^{19}\leq N(\mbox{H\,{\sc i}})\leq 2\times
10^{20}$ cm-2 are identified as sub-DLAs (e.g., Peroux et al. 2003; Dessauges-
Zavadsky et al. 2003). Lyman-limit systems (LLSs), whose lower boundary
corresponds to unit optical depth at the Lyman limit, have $1.6\times
10^{17}\leq N(\mbox{H\,{\sc i}})\leq 10^{19}$ cm-2 (e.g., Tytler 1982). This
method is sensitive to multiple ionization states of the gas, can provide
information on metallicity and kinematics information, and is commonly used to
study gas reservoirs from low to high redshifts, $z$, (e.g., Steidel et al.
2002; Noterdaeme et al. 2012; Werk et al. 2014; Schroetter et al. 2016;
Krogager et al. 2017; Zabl et al. 2019; Ho et al. 2020). However, it is
limited to the lines of sight to rare bright sources, which cannot probe the
spatially resolved distribution of the CGM except for sources within the local
Universe (e.g., Tumlinson et al. 2017).

The CGM can be also observed in emission, which enables us to directly “take a
picture” of gas in and around galaxies. While hot gas is routinely detected
around very massive objects through its X-ray emission (e.g., Spitzer 1956; Li
& Wang 2013), detecting emission from cooler gas is extremely challenging.
Observations of the H i CGM with 21cm emission are only possible in the local
Universe. Even with forthcoming telescopes such as the Square Kilometre Array
(SKA), 21cm direct mapping of the CGM will not be possible at $z\gtrsim 2$.
Popular probes of the CGM at $z\gtrsim 1$ are spatially extended emission
(i.e., haloes) in Ly$\alpha$ $\lambda$1216 Å (e.g., Momose et al. 2014;
Wisotzki et al. 2016; Leclercq et al. 2017), Mg ii $\lambda\lambda$2796, 2803
Å (e.g., Rubin et al. 2011; Erb et al. 2012; Martin et al. 2013; Burchett et
al. 2021; Zabl et al. 2021; Leclercq et al. 2022), [O ii]$\lambda\lambda
3726,3729$ (e.g., Yuma et al. 2013, 2017; Epinat et al. 2018; Johnson et al.
2018), Fe ii*$\lambda 2365$, $\lambda 2396$, $\lambda 2612$, and $\lambda
2626$ (e.g., Finley et al. 2017), and [C ii] $\lambda$ 158 $\mu$m (e.g.,
Fujimoto et al. 2019; Ginolfi et al. 2020). Among them Ly$\alpha$ haloes have
several advantages. Ly$\alpha$ is intrinsically the brightest nebular
recombination line of hydrogen atoms and often the strongest feature in the
rest-frame UV spectra of galaxies. The emissivity of Ly$\alpha$ does not
depend on metallicity, unlike the other emission lines. At $z\gtrsim 2$,
Ly$\alpha$ can be observable with ground-based telescopes. Moreover,
Ly$\alpha$ haloes have been explored intensively in both theoretical and
observational studies over wide redshift and mass ranges.

One of the popular methods of detecting Ly$\alpha$ haloes has been narrow-band
(NB) stacking analyses, in particular at $z\gtrsim 2$, due to the faintness of
Ly$\alpha$ haloes and the cosmic dimming effect (e.g., Hayashino et al. 2004;
Steidel et al. 2011; Matsuda et al. 2012; Momose et al. 2014; Matthee et al.
2016, see also Kakuma et al. 2021 and Kikuchihara et al. 2021 for the NB
intensity mappings). Until recently, individual detections have been limited
to local galaxies, active galactic nuclei (AGNs), quasi-stellar objects
(QSOs), and high-$z$ gravitationally lensed galaxies (e.g., Keel et al. 1999;
Kunth et al. 2003; Swinbank et al. 2007; Östlin et al. 2009; Matsuda et al.
2011; Hayes et al. 2013, see also Rauch et al. 2008 for 92-hour long-slit
spectroscopy). Large samples of individual Ly$\alpha$ haloes around high-$z$
star-forming galaxies have become available thanks to wide-field optical
integral field units (IFUs) like the Very Large Telescope (VLT)/ Multi-Unit
Spectroscopic Explorer (MUSE; e.g., Bacon et al. 2010; Wisotzki et al. 2016;
Bacon et al. 2017; Herenz et al. 2017; Inami et al. 2017; Leclercq et al.
2017; Urrutia et al. 2019) and the Keck II telescope/ Keck Cosmic Web Imager
(KCWI; e.g., Morrissey et al. 2018; Chen et al. 2021). For instance, Leclercq
et al. (2017) found 145 Ly$\alpha$ haloes around MUSE Ly$\alpha$ emitters
(LAEs) at $z\approx 3$–$6$. While the physical origins of Ly$\alpha$ haloes
are still unclear, various scenarios have been suggested: CGM scattering for
Ly$\alpha$ from star-forming regions (e.g., Laursen & Sommer-Larsen 2007;
Zheng et al. 2011), gravitational cooling radiation (cold streams; e.g.,
Haiman et al. 2000; Fardal et al. 2001; Rosdahl & Blaizot 2012), star
formation in satellite galaxies (one-halo term; e.g., Zheng et al. 2011; Mas-
Ribas et al. 2017a), fluorescence (photo-ionization; e.g., Furlanetto et al.
2005; Cantalupo et al. 2005; Kollmeier et al. 2010; Mas-Ribas & Dijkstra
2016), shock heating by gas outflows (e.g., Taniguchi & Shioya 2000), major
mergers (e.g., Yajima et al. 2013), and combination of the aforementioned
(e.g., Furlanetto et al. 2005; Lake et al. 2015; Smith et al. 2019; Byrohl et
al. 2021; Garel et al. 2021; Mitchell et al. 2021, see also Ouchi et al. 2020
and reference therein). Despite intensive observations of Ly$\alpha$ haloes
and studies on their origins, no clear correlations between Ly$\alpha$ halo
properties and their galaxy hosts’ properties have been found at high
redshifts (e.g., Wisotzki et al. 2016; Leclercq et al. 2017). So far, the most
remarkable correlation is that between the Ly$\alpha$ peak velocity shift and
the width of Ly$\alpha$ lines both at ISM and CGM scales, which supports a
Ly$\alpha$ halo scenario of resonant scattering in the outflowing medium
(Claeyssens et al. 2019; Leclercq et al. 2020, see also Verhamme et al. 2018
and Chen et al. 2021).

Although simulations have predicted the presence of the CGM around high-$z$
galaxies, most of the observational Ly$\alpha$ halo studies so far have
focused on LAEs (e.g., Leclercq et al. 2017; Wisotzki et al. 2016). Only
$\simeq$ 10 to 30% of star-forming galaxies are LAEs at $z\simeq 3$–$6$ (e.g.,
Kusakabe et al. 2020). Ly$\alpha$ haloes around UV-selected galaxies (Lyman
break galaxies, LBGs) have previously been studied with NB stacks, which are
biased s overdense regions (e.g., Steidel et al. 2011; Xue et al. 2017), and
stacking analyses cannot provide information on the individual presence of
Ly$\alpha$ haloes. The sample in KBSS-KCWI (Keck Baryonic Structure Survey
using the KCWI) includes continuum-selected galaxies as well as LAEs, and
their sample construction is not easy to characterize (Chen et al. 2021).
Therefore, it is still unknown whether star-forming galaxies such as UV-
selected galaxies generally have a Ly$\alpha$ halo. To minimize biases s LAEs
and LBGs in overdense regions, a spectroscopically complete sample without
preselection on the Ly$\alpha$ emission basis is required. Moreover, only the
large field of view of MUSE with a long integration time enables us to do a
volume-limited search for diffuse CGM emission at high redshifts.

In this study, we construct a sample of UV-selected galaxies with
spectroscopic redshifts, rather than Ly$\alpha$ emission selected-galaxies, in
the MUSE eXtremely Deep Field (MXDF; Bacon et al. 2021, Bacon et al. in
prep.), making use of more than 100-hour integration time of MUSE adaptive
optics (AO) data. The high spatial resolution and the unprecedented depth are
key to obtain spectroscopic redshifts for galaxies and spatial profiles of
diffuse emission. Using the MUSE data, we investigate the existence of
Ly$\alpha$ haloes around the galaxies and for the first time derive the
Ly$\alpha$ halo fraction for UV-selected galaxies. We can resolve compact and
faint haloes and assess the presence of a Ly$\alpha$ halo with the highest
accuracy to date. This allows us to connect the separate views of H i gas
observed through Ly$\alpha$ emission and Ly$\alpha$ absorption, by extending
the work by Rauch et al. (2008) and Wisotzki et al. (2018).

The paper is organized as follows. In Section 2, we describe the data and the
sample construction. Section 3 presents methods and results of halo tests with
individual Ly$\alpha$ surface brightness (SB) profiles, Ly$\alpha$ halo
fractions, and completeness simulations. In Section 4, we discuss implications
from our Ly$\alpha$ fractions and incidence rates of Ly$\alpha$ emission
compared with those of Ly$\alpha$ absorbers, as well as implications from non-
Ly$\alpha$ haloes. Finally, the summary and conclusions are given in Section
5. Throughout this paper, we assume the Planck 2018 cosmological model
(Aghanim et al. 2020) with a matter density of $\Omega_{\rm m}=0.315$, a dark
energy density of $\Omega_{\Lambda}=0.685$, and a Hubble constant of
$H_{0}=67.4$ km s-1 Mpc-1 ($h_{100}=0.67$). Magnitudes are given in the AB
system (Oke & Gunn 1983). All distances are in physical units (kpc), unless
otherwise stated.

##  2 Data and sample

We constructed a sample of UV-selected galaxies with spectroscopic redshifts
to search for and investigate Ly$\alpha$ haloes, using a 3D data cube of the
deepest MUSE observations with AO, the MXDF. The details of the MXDF data set
are given in Section 2.1, the MXDF catalog and our sample selection are
explained in Section 2.2, and continuum subtractions for the MXDF data cube
are described in Section 2.3.

###  2.1 Data

The MXDF data were obtained as a part of the MUSE guaranteed time observations
(GTO) program (PI: R. Bacon). The survey design of MXDF is presented in Bacon
et al. in prep. (see also Bacon et al. 2021). The field has a circular shape,
centered at R.A.=53.∘16467 and DEC.=-27.∘78537 (J2000 FK5) with a radius of
$r=44$ arcsec (1.7 arcmin2), and is located inside the Hubble eXtreme Deep
Field (XDF; Illingworth et al. 2013) with deep Hubble Space Telescope (HST)
data. It is also covered by the MUSE-Hubble Ultra Deep Field (HUDF) with 10-
to 30-hour MUSE integration in a 9 arcmin2 area (Bacon et al. 2017). The MXDF
is the deepest MUSE survey with AO, reaching up to 140 hours at $r\lesssim 29$
arcsec and 100 hours out to $r=31$ arcsec, while the outer edge has a 10-hour
integration ($r\lesssim 41$ arcsec). In this paper we use the very deep area
with 100-to 140-hour integration, located inside a radius of 31 arcsec from
the center of the field (0.84 arcmin2, see Figure 1 in Bacon et al. 2021),
which we used in this paper. The corresponding survey volume in this work is
$4.0\times 10^{3}$ cMpc3 ($z=2.86$–$4.44$, excluding an AO gap, see below for
more details).

The MUSE data cover the optical wavelength range from 4700 Å to 9350 Å, which
is 50 Å longer at the blue edge of the spectrum than that of the MUSE-HUDF
Survey. It has an AO gap from 5800 Å to 5966.25 Å, and Ly$\alpha$ lines at
$z=2.86$–$3.77$ and $3.91$–$6.65$ are observable. The spectral resolving power
of MUSE varies from $R=1610$ to 3750 at 4700 Å to 9350 Å, respectively, and
the median value for $\lambda\simeq 4700$–$7000$ Å, which is used for
Ly$\alpha$ in this paper, is $R\simeq 2200$. The FWHM of the Moffat point
spread function (Moffat PSF, Moffat 1969) is $0\aas@@fstack{\prime\prime}6$ at
4700 Å and $0\aas@@fstack{\prime\prime}4$ at 9350 Å (PSF calibrated for DR2
v0.8 catalog; see Bacon et al. in prep. for more details). The average
$5\sigma$ surface brightness limit in the region with more than 100-hour depth
is $1.3\times 10^{-19}$ erg s-1 cm-2 arcsec-2 at 7000 Å, which is not affected
by OH sky emission, for an unresolved emission line with a line width of 3.75
Å (3 spectral slices) and 1 arcsec2 ($5\times 5$ spaxels). The corresponding
$5\sigma$ limiting flux for a point source with the same line width is
$2.3\times 10^{-19}$ erg s-1 cm-2 (see Bacon et al. in prep. for more
details). Here we derived the variance in the same manner as that used for the
MUSE-HUDF data, while the MUSE pipeline formally underestimates the noise in
standard deviation by a factor of 1.6 (2.7dev development version; see Section
4.6 in Weilbacher et al. 2020, for more details). Figure 1a shows a spectrum
of the night sky emission as a function of wavelength. The background sky is
relatively stable at $5000$–$7000$ Å, compared to that at longer wavelengths.

Figure 1:  (a) Night sky spectrum as a function of observed wavelength. The
black line shows the night sky spectrum with an arbitrary normalization. The
light gray and dark shaded areas indicate the wavelength range of the AO gap
and the wavelength range that is not used in this work, respectively. (b)
5$\sigma$ noise surface brightness (SB) for the typical parameters for
optimized NBs (see Section 3.2) as a function of redshift (black line). The
light gray shaded area indicates the redshift range of the AO gap. (c)
$M_{1500}$ as a function of $z$ for the sample. The large filled blue stars,
large open blue stars, and small open blue stars indicate our sources with
ZCONF=2,3, ZCONF=1, and ZCONF=0, respectively. The black dots show nonisolated
galaxies (see Section 2.2). The black and green lines represent the $F775W$
apparent magnitude cut, and the criteria for the UV-bright sample,
respectively.

###  2.2 Catalog and sample selection

Table 1: Overview of the galaxy sample

RID | MID | line for $z_{\rm s}$ | $z_{\rm s}$ |  $z_{\rm p}$ (95%) | F775W |  $M_{1500}$($1\sigma$) | ZCONF | Method | L17 | Isolated | UV-bright
---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  | (mag) | (mag) |  |  |  |  |
4587 | 8465 | Ly$\alpha$ | 3.001 | $2.976^{+0.194}_{-0.196}$ | 27.05 | $-18.5^{+0.05}_{-0.05}$ | 2 | ODHIN | No | Yes | No
4764 | 8339♢ | Ly$\alpha$♢,+ | 3.192♢ | $3.291^{+0.189}_{-0.201}$ | 26.07 | $-19.45^{+0.02}_{-0.02}$ | 3 | ORIGIN♢ | No | Yes | Yes
4838 | 8469 | Abs. | 3.064 | $3.092^{+0.178}_{-0.192}$ | 26.7 | $-18.68^{+0.04}_{-0.04}$ | 2 | ODHIN | No | No | No
5479 | 7089 | Ly$\alpha$⋆ | 4.156 | $3.893^{+0.277}_{-0.303}$ | 26.75 | $-19.39^{+0.03}_{-0.02}$ | 3 | ORIGIN | No | Yes | Yes
6693 |  |  | 4.167 | $4.21^{+0.25}_{-0.27}$ | 27.17 | $-18.97^{+0.02}_{-0.02}$ | 0 |  | No | Yes | Yes
7067 | 7091 | Ly$\alpha$+ | 4.406 | $4.302^{+0.238}_{-0.242}$ | 26.76 | $-19.52^{+0.01}_{-0.01}$ | 3 | ORIGIN | Yes | Yes | Yes
7847 | 8332 | Ly$\alpha$+ | 2.999 | $2.998^{+0.182}_{-0.198}$ | 26.84 | $-18.67^{+0.04}_{-0.04}$ | 3 | ORIGIN | No | No | No
7876 | 103∗ | Abs.⋆ | 2.994 | $3.218^{+0.182}_{-0.198}$ | 26.85 | $-18.73^{+0.04}_{-0.03}$ | 3 | ORIGIN | No | No | Yes
7901 | 180 | Ly$\alpha$ | 3.460 | $3.393^{+0.197}_{-0.203}$ | 27.28 | $-18.49^{+0.03}_{-0.03}$ | 3 | ORIGIN | Yes | Yes | No
9814 | 149 | Ly$\alpha$⋆ | 3.721 | $3.602^{+0.228}_{-0.222}$ | 27.0 | $-18.96^{+0.03}_{-0.03}$ | 3 | ORIGIN | Yes | Yes | Yes
9863 | 106 | Ly$\alpha$⋆ | 3.277 | $3.3^{+0.18}_{-0.19}$ | 26.51 | $-19.15^{+0.03}_{-0.03}$ | 3 | ORIGIN | Yes | Yes | Yes
9944 | 103∗ | Abs.⋆ | 2.994 | $3.009^{+0.181}_{-0.189}$ | 26.49 | $-18.94^{+0.03}_{-0.03}$ | 3 | ORIGIN | No | No | Yes
10018 | 6700 | Ly$\alpha$⋆ | 2.998 | $3.16^{+0.18}_{-0.19}$ | 25.67 | $-19.9^{+0.01}_{-0.01}$ | 3 | ORIGIN | Yes | Yes | Yes
22230 | 163 | Ly$\alpha$ | 3.464 | $3.337^{+0.193}_{-0.197}$ | 27.16 | $-18.65^{+0.03}_{-0.03}$ | 2 | ORIGIN | No | Yes | No
22386 | 8518 | Ly$\alpha$+ | 2.929 | $3.075^{+0.195}_{-0.205}$ | 27.25 | $-18.17^{+0.05}_{-0.04}$ | 3 | ODHIN | No | Yes | No
22490 | 8377 | Ly$\alpha$+ | 3.000 | $3.17^{+0.18}_{-0.19}$ | 26.21 | $-19.21^{+0.03}_{-0.03}$ | 2 | ORIGIN | No | Yes | Yes
23124 | 7073 | Ly$\alpha$ | 3.595 | $3.628^{+0.202}_{-0.218}$ | 26.62 | $-19.21^{+0.02}_{-0.02}$ | 3 | ODHIN | Yes | Yes | Yes
23135 | 8392 | Ly$\alpha$ | 3.943 | $0.76^{+0.11}_{-0.38}$ | 27.5 | $-18.44^{+0.03}_{-0.03}$ | 1 | ORIGIN | No | Yes | No
23408 | 174 | Ly$\alpha$+ | 2.993 | $3.125^{+0.195}_{-0.205}$ | 27.24 | $-18.28^{+0.05}_{-0.05}$ | 2 | ORIGIN | No | Yes | No
23839 | 118 | Ly$\alpha$⋆ | 3.021 | $2.989^{+0.171}_{-0.179}$ | 26.63 | $-18.82^{+0.02}_{-0.03}$ | 3 | ORIGIN | No | Yes | Yes
54891 |  |  | 2.937 | $2.306^{+0.184}_{-0.186}$ | 27.22 | $-18.08^{+0.06}_{-0.05}$ | 0 |  | No | Yes | No

111RID: ID in Rafelski et al. (2015), MID: MUSE ID in MXDF (Bacon et al. in
prep.), line for $z_{\rm s}$: line used to measure spec-$z$ for ZCONF$\geq 1$
sources in the v0.8 catalog (Ly$\alpha$ and Abs. indicate Ly$\alpha$ emission
and UV absorption lines, respectively; see Section 2.2 for 2 ZCONF$=0$
sources), $z_{\rm s}$: spec-$z$ in MXDF, $z_{\rm p}$: photo-$z$ with 95%
uncertainties in Rafelski et al. (2015), $F775W$: F775W magnitude in Rafelski
et al. (2015), $M_{1500}$: absolute UV magnitude with 1$\sigma$ uncertainties,
ZCONF: Confidence level for spec-$z$ for MUSE sources in MXDF, Method: the
detection method in the MXDF (the two sources without a detection method are
not included in the catalog but discussed in Section 2.2), L17: included in
Leclercq et al. (2017) or not, Isolated: isolated source or not (nonisolated),
and UV-bright: included in the UV-bright sample or not. ♢: RID=4764 has an
update in a new version of the MXDF catalog (v0.9, Bacon et al. in prep.) as
follows: MID=8357, line for $z_{\rm s}$=Abs., $z_{\rm s}$=3.188, and
Method=ODHIN, which do not change the result of our halo test. ∗:RID=7876 and
9944 were assigned for MID=103. ⋆ (+): Sources that have at least one emission
line with S/N$\geq 5$ (2$\leq$S/N$<$5) in the v0.9 catalog. We note that the
Ly$\alpha$ emission line was used to measure the spec-$z$ for most of the
sources in the v0.8 catalog, though 13 sources have at least one emission line
other than Ly$\alpha$ (see ⋆ and +). It is because Ly$\alpha$ emission
typically has the highest-S/N value among all spectral features. We note that
it does not mean that our sample is biased s the LAE selection, and that the
choices of lines used to measure spec-$z$ are not relevant for our halo test
as we took a wide wavelength range when we optimized NBs (Section 3.2). The
spec-$z$ values are planned to be improved in an updated MXDF catalog.

Figure 2: Examples of the overview with two sources (a LAH RID=4764 and a non-
LAH RID=5479). The first two rows show RID=4764, while the last two rows show
RID=5479. (a): HST $F775W$ image (rest-frame UV). The Rafelski’s ID (RID), the
MUSE ID (MID), $z_{\rm s}$, ZCONF, and M1500 are indicated. The smaller and
larger cyan circles present $r_{\rm in}$ and $r_{\rm CoG}$ (Sections 3.1 and
3.2). (b): MUSE broad band image summed over the rest-frame UV range 1300–1800
$\AA$. The image is smoothed with a 2D Gaussian filter with a standard
deviation of 1 pixel. Spectroscopic redshifts of sources in the MXDF catalog
in the minicube are indicated. (c): Optimized narrow band for Ly$\alpha$ with
the neighboring object mask (purple areas). The image is smoothed with a 2D
Gaussian filter with a standard deviation of 1 pixel. The white contours
indicate a SB of $2\times 10^{-19}$ erg s-1 cm-2 arcsec-2. (d): 1D spectrum
around the wavelength of Ly$\alpha$ extracted inside the target’s continuum-
component mask. The spectra and the 1$\sigma$ uncertainty are represented by
the black line and the gray shaded area, respectively. The spectral width of
the flux-maximized NB and the wavelength of Ly$\alpha$ converted from $z_{\rm
s}$ in the MXDF catalog are shown by the cyan dashed and solid lines,
respectively. The spectral slices used to produce the optimized NB are
indicated by the yellow shaded areas for sources with high S/N spectral slices
at r$=$rin–rCoG. (e): 1D spectrum around the wavelength of Ly$\alpha$
extracted in r$=$rin–rCoG. (f): Radial SB profile of Ly$\alpha$ emission in
log scale measured on the optimized NB image. The cyan shaded areas represent
the radial range, $r=r_{\rm in}$–$r_{\rm CoG}$ (see Section 3.3). The panel
shows whether the source is an isolated or nonisolated object, and whether it
is a Ly$\alpha$ halo (LAH) or non-LAH. All images are 15 arcseconds each on a
side. We note that the segmentation maps and the masks as well as zoomed-in
HST $F775W$ cutouts (4′′ $\times$ 4′′) are shown in Figures 19–20. Figure 3:
Overview of the first 7 sources in order of RID except for RID=4764 and 5479.
Each row shows a different object. Panels (a)–(f) are the same as those of
Fig. 2. In panel (a), MID=0 means that no MUSE ID is assigned in the MXDF
catalog (i.e., ZCONF=0). In panels (d) and (e), the spectral slices used to
produce the optimized NB are indicated by the yellow and orange shaded areas
for sources with high S/N spectral slices at r$=$rin–rCoG and those with low
S/N spectral slices at r$=$rin–rCoG, respectively (see Section 3.2). We note
that the emission ring shown in the NB of RID=7876 is caused by the mask for a
source with extended emission. Since the ring is located outside $r_{\rm
CoG}$, it does not affect our results.  Figure 4: Same as Figure 2, but for
the middle 6 sources in order of RID. Each row shows a different object.
Panels (a)–(f) are the same as those of Fig. 2. We note that the emission
rings shown in the NB of RID=9944 is caused by the mask for a source with
extended emission. Although the ring feature of RID=9944 overlaps with
r=rin–$r_{\rm CoG}$, this object is not included in the isolated sample (as
well as RID=7876), and the main conclusion about the Ly$\alpha$ halo fraction
is not affected by the ring.  Figure 5: Same as Figure 2, but for the last 6
sources in order of RID. Each row shows a different object. Panels (a)–(f) are
the same as those of Fig. 2.

The MXDF catalog was constructed in two ways, a blind emission search in the
MUSE cube (ORIGIN method) and spectra extraction with prior information (ODHIN
method). The two types of information were merged into one catalog (Bacon et
al. in prep.). Appendix A.1 gives a brief summary of the ORIGIN and ODHIN
methods, the flow of the visual inspection, assignment of Rafelski et al.
(2015)’s ID (RID), and the criteria of confidence levels (ZCONF) of
spectroscopic redshifts (spec-$z$ or $z_{\rm s}$). The MUSE sources that are
included in the catalog of Inami et al. (2017) keep the same ID (MID) in the
MXDF catalog. Most of the continuum-bright sources in Rafelski et al. (2015)
are spectroscopically confirmed in the MXDF catalog. For instance, in the
region with more than 100-hour integration ($r<31$ arcsec), 87% of
HST/Advanced Camera for Surveys Wide Field Channel (ACS/WFC) $F775W\leq 27.5$
sources have reliable spectroscopic redshifts, ZCONF=2 or 3, and 7% have
ZCONF=1 redshifts. Moreover, 25 sources out of 26 $F775W\leq 27.5$ galaxies,
whose photometric redshifts (photo-$z$ or $z_{\rm p}$) are within the targeted
redshift range below, have ZCONF=2 or 3 (see Figure 14 in Appendix A.2). The
spec-$z$ for the remaining 1 source was assigned as explained below. We note
that we used a preliminary version of the MXDF catalog (DR2 v0.8) in this
study.

We targeted galaxies at $z=2.86$–$4.44$ (excluding the Ly$\alpha$ redshift
range in the AO gap) to investigate their Ly$\alpha$ haloes. There are two
main reasons for this redshift range choice. First, at $z\leq 4.7$ for
Ly$\alpha$ ($4700$–$7000$ Å), the background noise level is stable compared to
those at longer wavelengths (see the black shaded area indicating $z\geq 4.44$
in Figure 1a). The 5$\sigma$ median SB noises for the typical parameters for
the halo search (see Section 3.2) at $z=2.86$–$4.44$ are shown in Figure 1b.
Second, at $z\leq 4.44$, the HST band ACS/WFC $F775W$ can capture the UV
continuum of galaxies without being contaminated by Ly$\alpha$ emission (the
same threshold as those used in Hashimoto et al. 2017; Kusakabe et al. 2020).
In fact, McKinney et al. (2019) reported that some local galaxies show a wide
Ly$\alpha$ absorption feature, which could extend to $\lambda\simeq 1260$ Å.
These features were also confirmed at high redshifts (for stacked MUSE LAEs at
$z\simeq 2.9$–$4.6$, Feltre et al. 2020). The threshold of $z=4.44$ for rest-
frame 1270 Å corresponds to 6900 Å, at which $F775W$ filter has 3%
transmission (see Section 4.3 in Matthee et al. 2021, for more details on the
conservative choice of 1270 Å). In addition, we limited the field to the very
deep area with 100- to 140-hour integration ($r<31$ arcsec) to have a
homogeneous depth.

In order to build a spectroscopically complete sample, our parent sample is
based on the HST catalog in Rafelski et al. (2015) with deep 5$\sigma$
limiting magnitudes from 27.8 to 30.1 mag. The catalog is confirmed to be
complete in UV at the redshift and $M_{\rm 1500}$ ranges that we used in this
paper (complete for $M_{\rm 1500}\leq-17$ mag at $z=2.9$–$4.4$, see Figure 2
in Kusakabe et al. 2020). Out of a total of 9969 sources in the catalog, 797
sources are within the footprint of the more than 100-hour integration region.
Among them, 142 sources are brighter than 27.5 mag in $F775W$, which
corresponds to a rest-frame UV band for sources at $z=2.86$–$4.44$. This
apparent magnitude cut is 0.5 mag fainter than that for the HST prior
detection in the mosaic field in the MUSE-HUDF Survey in Inami et al. (2017).
As mentioned above, 123 sources (87% of 142 $F775W\leq 27.5$ sources) have a
reliable spec-$z$ from MUSE with ZCONF=2 or 3, and 10 sources have a possible
spec-$z$ (ZCONF=1). The remaining nine sources are not in the MXDF catalog as
they do not show a clear feature in their spectra, but their continua are
detected in the MXDF data cube (see below for more details).

Among the 123 ZCONF=2 or 3 sources, 18 galaxies are located at $z=2.86$–$3.77$
and $z=3.91$–$4.44$, while 105 galaxies are outside the redshift range.
Unfortunately, one galaxy, which is categorized as an LAE in the catalog of
Inami et al. (2017) and shows UV lines in the MXDF data cube, has Ly$\alpha$
emission in the AO gap. Due to the limited spatial resolution of MUSE,
RID=7876 and 9944 were assigned to a unique MUSE source (MID=103 at $z_{\rm
s}$=2.99). Such nonisolated sources were separately treated as described
later.

Among the 10 ZCONF=1 sources, nine sources have a possible spec-$z$ at $z_{\rm
s}\leq 2.86$ (0.71, 1.10, 1.25, 1.67, 1.85, 1.91, 1.99, 2.34, and 2.67). Eight
sources have a spec-$z$ consistent with their photo-$z$ in Rafelski et al.
(2015), and one source with $z_{\rm s}=1.25$ has a $z_{\rm
p}=1.69^{+0.13}_{-0.14}$ (see Figure 14 in Appendix A.2). All of them show
clear continua at the blue edge of the MUSE spectra, implying that they should
not be located at $z\geq 2.86$. The remaining ZCONF=1 source has $z_{\rm
s}=3.94$ (RID=23135). It has ORIGIN-detected Ly$\alpha$ emission with a line
flux signal-to-noise ratio (S/N) higher than 5 in the catalog (6.4). However,
the Ly$\alpha$ center given by ORIGIN is spatially offset by
$0\aas@@fstack{\prime\prime}3$ from the position in Rafelski et al. (2015),
and the spec-$z$ does not match with $z_{\rm p}=0.76^{+0.11}_{-0.38}$.
Moreover, the emission is close to the edge of the AO gap. We included the
source in our parent sample, but it is not selected for a subsample with a UV
absolute magnitude cut used to calculate the Ly$\alpha$ halo fractions,
because of its faintness.

We inspected the MXDF data for nine sources that are not in the MXDF catalog.
Seven sources of those nine sources at $z_{\rm p}=0.06^{+0.04}_{-0.05}$,
$0.82^{+0.07}_{-0.55}$, $1.11^{+0.14}_{-0.58}$, $1.63^{+0.12}_{-0.13}$,
$2.03^{+0.15}_{-0.16}$, $2.43^{+0.13}_{-0.54}$, and $2.55^{+0.16}_{-0.17}$
show clear continua at the blue edge of the MUSE spectra, which is not the
case at $z\geq 2.86$. One of the remaining two sources, RID=54891, has $z_{\rm
p}=2.31^{+0.18}_{-0.19}$ and does not have an ORIGIN-detected emission line.
However, it shows weak potential Ly$\alpha$ emission at $z=2.94$ with a line
flux S/N of $3.9$. Because of the low S/N, the noisy spectrum, and the
missmatch between $z_{\rm s}$ and $z_{\rm p}$, it was not categorized as a
ZCONF=1 source and was not included in the MXDF catalog. To minimize a sample
selection bias in this work, we assigned it a tentative spec-$z$ of $z_{\rm
s}=2.94$. This object is not included in the UV-bright sample described later
in this Section. We confirmed that our main results can hold up with the
subset. The other remaining source at $z>2.86$ that is not in the MXDF catalog
(RID=6693) has $z_{\rm p}=4.21^{+0.25}_{-0.27}$ and shows a break around 6250
Å in the MUSE spectrum, which can be interpreted as a Ly$\alpha$ break. The
source has an emission line in the 1D spectrum, which could be interpreted as
a Ly$\alpha$ emission line at $z\simeq 4.17$, but is contamination from a
neighboring LAE. Then, we performed a cross correlation using the MARZ
spec-$z$ software (Hinton et al. 2016; Inami et al. 2017) on different spectra
extracted from 1 to 5-pixel radius apertures and did not find realistic
solutions. In order to obtain our best estimate of a tentative spec-$z$, we
stacked the 1D spectra centered at wavelengths of different combinations of UV
absorption lines among Si ii$\lambda$1260.42, O i$\lambda$1302.17,Si
ii$\lambda$1304.37, C ii$\lambda$1334.53, Si
iv$\lambda\lambda$1393.75,1402.77, Si ii$\lambda$1526.71, C
iv$\lambda\lambda$1548.20,1550.78, Fe ii$\lambda$1608.45, and Al
iii$\lambda$1670.79. It is challenging to determine a spec-$z$ for faint
sources at high redshifts with this method, but we note that we can get
correct spec-$z$ for brighter sources at $z>4$ with ZCONF=3, RID$=5479$ and
7067. Although we did not find a significant absorption line at any redshift
solution, $z_{\rm s}=4.167$ shows 3 consecutive pixels with more than a
$1\sigma$ dip compared to the continuum ($1.2\sigma$, $1.8\sigma$, and
$1.6\sigma$) as a result of stacking of Si ii$\lambda$1260.42, C
ii$\lambda$1334.53, and Si iv$\lambda$1393.75 lines. This is consistent with
the interpretation of the Ly$\alpha$ break. We note that Si iv$\lambda$1402.77
at $z_{\rm s}=4.167$ overlaps with a skyline. Therefore, we assigned a
tentative spec-$z$, $z_{\rm s}=4.167$. We did not discard these two objects
(RID=54891 and 6693) to minimize a selection bias. RID=6693 can meet criteria
for a UV-bright subsample described later in this Section, while RID=54891
does not, which means that it does not affect our main conclusion. We took
into account the effect of uncertainties in the spec-$z$ estimation (see
Section 3.4.1).

In total, we have 21 galaxies at $z=2.86$–$3.77$ and $z=3.91$–$4.44$ with
$F775W\leq 27.5$ mag as the parent sample listed in Table 1. An overview of
the 21 sources is given in Figures 2 to 5 (see Figure 2 for enlarged panels
for two sources as examples). We calculated the rest-frame UV magnitude
($M_{1500}$) and the UV slope ($\beta$) using $z_{\rm s}$, $F775W$, $F850LP$,
and $F105W$ in the same manner as in Kusakabe et al. (2020). The $M_{1500}$
ranges from $-19.9$ to $-18.1$ with an average value of $-18.9$, which is
fainter than $M^{*}$ at $z\simeq 3.7$, -20.88 mag (Bouwens et al. 2015). The
average $M_{1500}$ corresponds to a typical dark matter halo mass of $M_{\rm
h}\simeq 1\times 10^{11}$–$2\times 10^{11}\ {\rm M}_{\odot}$, which is
estimated from a $M_{1500}$–$M_{\rm h}$ relation from the GALICS semi-analytic
model in Garel et al. (2015). The UV slopes range from $-2.3$ to $0.2$, with
an average value of $-1.6$. The distribution of $M_{1500}$ and $z_{\rm s}$ of
the sample is shown in Figure 1c. Out of the 21 galaxies, six galaxies,
RID=7067, 7901, 9814, 9863, 10018, and 23124 (MID=7091, 180, 149, 106, 6700,
and 7073) were included in the Ly$\alpha$-selected sample for the previous
MUSE-LAH study in the HUDF, and all of them are confirmed to be LAHs (Leclercq
et al. 2017). Among the 15 new sources, five galaxies, RID=5479, 7876, 22230,
23408, and 23839 (MID=7089, 103, 163, 174, and 118), are included in the MUSE-
HUDF catalog in Inami et al. (2017) as well as in the updated version in Bacon
et al. (in prep.), but they were not selected in the sample in Leclercq et al.
(2017), due to their low ZCONF values ($\leq 1$), low S/N values of Ly$\alpha$
($<6$), or close neighboring objects. In order to validate that our sample is
not biased s the LAE selection, we checked LAE fractions ($X_{\rm LAE}$) for
our sample following Kusakabe et al. (2020). Rest-frame equivalent widths of
Ly$\alpha$ emission ($EW(\mbox{Ly$\alpha$})$) were calculated with Ly$\alpha$
fluxes at the galaxy’s stellar-component scale (see Appendix A.3 for a
description of EW measurements and $X_{\rm LAE}$ calculations). With
$EW(\mbox{Ly$\alpha$})\geq 20$ Å, which is a common criterion of LAEs, the
$X_{\rm LAE}$ for our entire sample ($-20\leq M_{1500}\leq-18.0$,
$z=2.9$–$4.4$) is $0.33^{+0.11}_{-0.09}$. For a fair comparison, we also
calculated the $X_{\rm LAE}$ with $EW(\mbox{Ly$\alpha$})\geq 65$ Å for our
entire sample as $0.14^{+0.09}_{-0.06}$, which is similar to $X_{\rm
LAE}=0.04^{+0.02}_{-0.01}$, $0.07^{+0.04}_{-0.02}$, and $0.11^{+0.07}_{-0.04}$
for $EW(\mbox{Ly$\alpha$})\geq 65$ Å and $-21.75\leq M_{1500}\leq-17.75$ at
z=3.3, 4.1, and 4.7, respectively, in Kusakabe et al. (2020). It suggests that
our sample is unbiased. The small difference in the $X_{\rm LAE}$ between the
two samples could be explained by the cosmic variance due to our small survey
volume in the MXDF ($4\times 10^{3}$ cMpc3).

As in the case of RID=7876 and 9944 (MID=103), the MUSE spatial and spectral
resolutions are not always high enough to disentangle the spec-$z$ assignment.
It can also make it difficult to assign extended Ly$\alpha$ emission to close
HST sources. Following Inami et al. (2017), we checked if galaxies have close
projected neighbors within $0\aas@@fstack{\prime\prime}6$ using the catalog of
Rafelski et al. (2015). We did not consider MUSE LAEs as neighbors here,
because extended Ly$\alpha$ emission from satellites is one of the candidates
for the powering sources of Ly$\alpha$ haloes. In our sample, 6 sources
(RID=4764 , 4838, 5479, 7876, 9944, and 10018) have one HST-detected galaxy
within $0\aas@@fstack{\prime\prime}6$. We used the MXDF catalog to check the
spec-$z$ of the HST neighbors. The HST neighbors of RID=4764 and 10018 are
located at different redshifts and do not contaminate the Ly$\alpha$ NB used
in the halo tests (RID=10516 at $z_{\rm s}=1.42$ and RID=10046 at $z_{\rm
s}=2.59$, respectively). Unfortunately, the HST neighbor of RID=5479,
RID=5498, does not have a spec-$z$, but the photo-$z$, $z_{\rm
p}=2.99^{+0.27}_{-0.28}$, is not close to the spec-$z$ of RID=5479, $z_{\rm
s}=4.16$. Therefore, we regarded these three sources as isolated sources.
Meanwhile, the HST neighbor of RID=4838 (RID=6666 at $z_{\rm s}=3.06$) has a
velocity offset of $\Delta V=-25.4$ km s-1 from RID=4838, which indeed
contaminates the Ly$\alpha$ NB used in the halo test (see Figures 3 and 16).
They belong to a group of galaxies within the cosmic web detected with
Ly$\alpha$ emission in Bacon et al. (2021), see Appendix A.4 for more details.
Since both RID=7876 and 9944 are assigned to counterparts of MID=103 at
$z_{\rm s}=2.09$, they are interpreted to share Ly$\alpha$ emission in their
Ly$\alpha$ NBs. In addition, MID=103 has another neighbor within
$0\aas@@fstack{\prime\prime}6$, RID=7847 at $z_{\rm s}=3.00$ in our sample
($\Delta V=458$ km s-1 from RID=7876 and 9944), which leads to mutual
contamination of their Ly$\alpha$ NBs (see Figures 3 and 4). Although RID=7847
is located further than $0\aas@@fstack{\prime\prime}6$ from the positions of
RID=7876 and 9944, these three sources also belong to a larger structure of
cosmic web found in Bacon et al. (2021), as shown in Figure 17. Therefore,
RID=4838, 7847, 7876, and 9944 might live in a different kind of environment
from the rest of our sample, which may affect the existence of a Ly$\alpha$
halo and Ly$\alpha$ halo properties. Additional details of four nonisolated
sources are given in Appendix A.4. We calculated Ly$\alpha$ halo fractions for
the isolated sources and the nonisolated sources as well as all sources in
Section 3.4.

In Figure 1c, we introduce an unbiased subsample, the ”UV-bright sample”, with
a redshift range of $z=2.86$–$4.44$ with $-20.0\leq M_{1500}\leq-18.7$ mag. It
contains 12 galaxies, of which 10 are isolated sources and two are nonisolated
galaxies.

In summary, our sample was built in two steps. First, we selected galaxies
brighter than $F775W=27.5$ in the catalog of Rafelski et al. (2015), which
corresponds to rest-UV for galaxies at $z\sim 3$–$4$. Second, we applied a
selection on the spectroscopic redshift of these objects to keep only galaxies
with $z=2.86$–$4.44$. We note that all galaxies except nine have a
spectroscopic redshift from the MUSE catalog. These nine galaxies have a
photometric redshift and their continuum is detected in the MUSE cube. Seven
of them have $z_{\rm p}=0$–$2.5$ with clear continuum detection at the blue
edge of the MUSE cube: there is no sign of a Lyman break, which is very
unlikely for sources at $z>2.86$. We did not include these sources in our
sample. The remaining two sources were included in our sample, with ZCONF=0,
in order to minimize a possible selection bias in favor of Ly$\alpha$
emitters. Therefore, we stress that our sample of 21 galaxies is rest-UV
selected.

###  2.3 Continuum subtraction

For the following analysis, we provided $15\aas@@fstack{\prime\prime}0\times
15\aas@@fstack{\prime\prime}0$ cutouts of the MUSE cube (minicube), the
HST/ACS/WFC $F775W$ image (Beckwith & Stiavelli 2006; Illingworth et al. 2013)
and the HST segmentation map (Rafelski et al. 2015) for each source. We used
continuum-subtracted minicubes for most of the analysis in this paper, such as
the Ly$\alpha$ narrow bands explained in Section 3.

The continuum subtraction is useful not only to investigate line emission, but
also to remove neighboring sources around a targeted source. The continuum
minicubes were provided from a spectral median filtering on the original
minicubes in a 100-pixel spectral window ($\pm 50$ pixels) in a similar manner
to those in previous MUSE papers (with a 200-pixel window, e.g., Leclercq et
al. 2017, see also Herenz et al. 2017 for a 150-pixel window) and in addition
excluded $\pm 400$ km s-1 around the Ly$\alpha$ wavelength. Although the
method with a 200-pixel window was validated for the MUSE-HUDF and MUSE Wide
data sets, in particular for LAEs, it can overestimate the continuum around a
Ly$\alpha$ break (Ly$\alpha$ absorption) for UV-bright galaxies in the MXDF,
since the MXDF data are deep enough to detect the UV continuum and the break.
The oversubtraction due to the general 200-pixel window leads to artificial
absorption at the position of a targeted UV source on a Ly$\alpha$ narrow-band
image for some sources. We examined different settings for the continuum
minicubes: 1) the general setting with a 200-pixel window, 2) a 200-pixel
window with a mask around the Ly$\alpha$ wavelength ($\pm 400$ km s-1), 3) a
100-pixel window with a mask around the Ly$\alpha$ wavelength, and 4) a
60-pixel window with a mask around the Ly$\alpha$ wavelength. The Ly$\alpha$
masks cover 10 to 14 spectral slices at $z=3$ to $4.4$, respectively.

We found a trend that the continua around Ly$\alpha$ were increasingly
overestimated from settings 4) to 1) (see Figure 18 in Appendix B). This trend
becomes stronger for galaxies showing a Ly$\alpha$ absorption feature. We also
found that the 60-pixel window was too narrow to derive an accurate continuum.
We confirmed that the continuum at $\lambda>1270$ Å in the rest frame did not
change among the four settings. Therefore, we adopted the third setting with a
100-pixel window, with a mask around Ly$\alpha$. In Appendix B, we discuss two
examples of the difference in the radial SB profiles for four different
settings as described below (see Figure 18).

The obtained continuum minicube was subtracted from the original minicube to
provide the continuum-subtracted minicube. Even with this optimized choice, we
have a potential uncertainty in the continuum estimation around the Ly$\alpha$
wavelength at the position of a targeted UV-selected source, which however
does not affect the extended Ly$\alpha$ emission beyond the galaxy’s stellar
component. For this reason, we did not use the spatial pixels on the main part
of the galaxy’s stellar component when we tested for the existence of
Ly$\alpha$ haloes in the third step (see Figure 6).

##  3 Ly$\alpha$ haloes around UV-selected galaxies

The main part of our analysis consists of four steps. First, we created a mask
for the continuum-like component (target’s continuum-component mask) and a
neighboring object mask for neighbors for each source (Section 3.1). The
target’s continuum-component mask was used to obtain an inner radius. Second,
we provided a flux-maximized Ly$\alpha$ NB with a curve-of-growth radius by
tuning the width of the NB and the radius to maximize the halo flux and then
provided optimized NBs only with high-S/N spectral slices (Section 3.2).
Third, we tested for the existence of a Ly$\alpha$ halo around each source
(Section 3.3). Fourth, we derived the Ly$\alpha$ halo fractions (Section 3.4).
The flow of the analysis is illustrated in Figure 6.

###  3.1 Masks and inner radii

We used a target’s continuum-component mask to extract the 1D spectrum within
the galaxy’s stellar-component scale and to define the inner radius used to
adjust the Ly$\alpha$ NB (Section 3.2). The continuum-component masks were
created with the HST segmentation maps in a similar manner to those used to
create object masks for HST prior extractions in Inami et al. (2017). The HST
segmentation map indicates areas in which galaxies are detected and defines
the boundaries of the objects (more details are given in Appendix C, see also
Figures 19 and 20). If a pixel does not belong to the target on the cutout
segmentation map, we replaced the corresponding pixel of the $F775W$ cutout
with zero and provided an HST target image. We convolved the HST target image
with the MUSE PSF at the Ly$\alpha$ wavelength. Then, we resampled the PSF-
convolved HST target image with the spatial resolution of MUSE, aligning it
with the MUSE sky coordinate. We normalized the PSF-convolved image so that
the peak became 1. To provide the target’s continuum-component mask for each
source, we applied a threshold value of 0.2 to the normalized convolved image
(see Figures 19 and 20). This threshold was used to extract the spectra from
non-AO MUSE cubes for the HST-prior sources in the catalog in Inami et al.
(2017). For the MXDF data, the target’s continuum-component masks typically
include 66% of the total fluxes in the target’s continuum-component images. We
defined an inner radius, $r_{\rm in}$, beyond which the normalized PSF-
convolved profile is below 0.2. We used $r_{\rm in}$ in the SB profile
measurements for the Ly$\alpha$ halo tests later, to exclude the SB inside the
galaxy’s stellar-component scale. The $r_{\rm in}$ ranges from 0.8 arcsec to
1.0 arcsec with an average value of 0.81 arcsec (in physical scales at
different redshifts, 5.5 to 7.0 kpc with an average of 6.2 kpc).

Figure 6: Flowchart of the main part of our analysis with the four steps. The
input data are indicated by the yellow rounded boxes at the top of the panel,
while output data are indicated by the orange rounded boxes. The analysis and
classification are shown by rectangles and diamonds, respectively. The
obtained samples and parameters are presented by circles. The details of each
step are provided in Sections 2.3, 3.1, 3.2, 3.3, and 3.4. The numbers colored
blue indicate the Sections as a reference. The flux-maximized NBs were used to
obtain the average SB profiles in Section 4.2.1.

We used a neighboring object mask to exclude pixels that might be affected by
bright neighbors on a MUSE NB when we adjusted the Ly$\alpha$ NB and measured
the Ly$\alpha$ radial SB profile. To mask the bright-continuum emission from
the neighbors, we created a broad band (BB) image from the original MUSE
minicube without continuum subtraction at rest-frame 1300 to 1800 Å for the
target (see Figures 2 to 5). Then we clipped pixels whose S/N are higher than
20. With this threshold, we can mask the main part of continuum-bright
galaxies on the optimized NBs and the flux-maximized NBs. A lower S/N
threshold for the BBs, 10, changed the S/N values for extended Ly$\alpha$
emission on the optimized Ly$\alpha$ NBs used in the halo tests (see Section
3.3.1) because we lost the area with Ly$\alpha$ emission. However, it did not
change the results for the tests for haloes for any sources, except for one
(RID=23408). Since we used continuum-subtracted minicubes for most of the
analysis and would like to keep as many spatial pixels as possible, the higher
threshold of 20 was adopted. The two masks for each source are shown in
Figures 19 and 20. We note that the emission rings showing up at the left
bottom of the NBs of RID=7876 and 9944 in Figures 3 and 4 are caused by a
source whose emission extends beyond the neighboring-object masks. The main
conclusion about the Ly$\alpha$ halo fraction is not affected by the ring
features, since the objects are not included in the isolated sample.

###  3.2 3D curve-of-growth for narrow bands

To define a 3D volume in a minicube that includes all the potential flux of a
Ly$\alpha$ halo, we adjusted the NB width and the annulus used for the halo
photometry simultaneously, using the spec-$z$ and the spatial coordinate of
the HST targets. The inner radius of the annulus is $r_{\rm in}$. The outer
radius of the annulus is a curve-of-growth radius (CoG; $r_{\rm CoG}$), which
is commonly used to derive the total Ly$\alpha$ flux from a NB image (e.g.,
Drake et al. 2017; Leclercq et al. 2017). It is the minimum radius among
consecutive 1pix-width annuli with increasing radius around a target, whose
flux reaches or dips below zero (see Drake et al. 2017, for more details).

First, we created 400 NBs from a minicube with a combination of widths to
redder and bluer wavelengths from 0 to 20 adjacent pixels around the
Ly$\alpha$ wavelength. We applied the 2D neighboring object mask to the
created NBs. Then, we derived $r_{\rm CoG}$ by annulus photometry with
PHOTUTILS (Bradley et al. 2021) on each NB and measured the flux between
$r_{\rm in}$ and $r_{\rm CoG}$ centered at the spatial coordinate of the HST
target. Finally, we chose the combination of a NB width and $r_{\rm CoG}$ that
gives the highest $r_{\rm in}$–$r_{\rm CoG}$ flux. The flux-maximized NB
widths range from 21.25 Å to 48.75 Å (4.1 Å to 12.2 Å, or 1014.9 km s-1 to
3012.1 km s-1) with the average of 31.8 Å (7.5 Å, or 1848.0 km s-1) in
observed wavelength (rest-frame wavelength or velocity difference). The
$r_{\rm CoG}$ ranges from 1.4 arcsec to 7.2 arcsec (10.5 to 56.8 kpc) with the
average of 4.2 arcsec (32.0 kpc). The $r_{\rm CoG}$ and NB width are shown in
Figures 2 to 3. The $r_{\rm CoG}$ and the flux-maximized NB were used to
measure a surface brightness profile in the third step and in Section 4.2.1,
respectively.

We optimized the Ly$\alpha$ NBs by selecting spectral slices with S/N$>1.5$
for the flux between $r_{\rm in}$ and $r_{\rm CoG}$. We inspected the spectral
slices visually and discarded the pixels whose signals might be enhanced by
noise peaks. Out of 21, 18 sources have at least five spectral slices (6.25 Å)
with S/N$>1.5$. The total wavelength width ranges from 8.75 Å up to 22.5 Å,
with an average value of 14.5 Å in the observed frame (corresponding to 539.7
km s-1 to 1298.2 km s-1, and an average of 838.5 km s-1). The remaining three
sources (RID=6693, 23135, and 54891) do not have a sufficient number of high
S/N pixels. In particular, RID=23135 and 54891 do not show a realistic line
profile. Their pixels with S/N$>1.5$ seem to be affected by noise. Therefore,
we created the optimized NBs for these sources using the 1D spectra inside the
target’s continuum-component mask. RID=23135 has six S/N$>1.5$ spectral
slices, which were used to create the optimized NB. However, RID=6693 and
54891 have only four and two S/N$>1.5$ spectral slices, and the optimized NB
was created from the five highest-S/N spectral slices. The chosen spectral
slices are shown by yellow or orange shaded areas on the spectra in Figures 2
to 5. With the average width of optimized NB and the average unmasked area
between $r_{\rm in}$ and $r_{\rm CoG}$, the median 5$\sigma$ SB limit is
estimated to be $4.1\times 10^{-19}$ erg s-1 cm-2 arcsec-2 over the redshift
range (see Figure 1b), and the 5$\sigma$ flux limit is $3.1\times 10^{-18}$
erg s-1 cm-2 over the redshift range. The optimized NB were used to measure a
surface brightness profile in the third step.

###  3.3 Test for the presence of Ly$\alpha$ haloes

Table 2: Summary of the tests for the existence of Ly$\alpha$ haloes.

RID | $r_{\rm in}$ | $r_{\rm CoG}$ | S/N($r_{\rm in}$-$r_{\rm CoG}$) | $p_{0}$ | DoF | R. $\chi^{2}$ | R. $\chi^{2}$ ($p_{0}$=0.05) | LAH
---|---|---|---|---|---|---|---|---
| (arcsec/kpc) | (arcsec/kpc) |  |  |  |  |  |
4587 | 0.8/6.31 | 3.0/23.65 | 5.75 | 6.04e-03 | 5 | 3.26 | 2.21 | Yes
4764 | 0.8/6.19 | 5.0/38.67 | 16.44 | 2.84e-49 | 17 | 16.39 | 1.62 | Yes
4838 | 0.8/6.27 | 6.0/47.01 | 11.94 | 4.65e-19 | 19 | 6.98 | 1.59 | Yes
5479 | 1.0/7.0 | 3.2/22.39 | 12.94 | 3.78e-01 | 6 | 1.07 | 2.1 | No
6693 | 0.8/5.59 | 7.2/50.31 | 4.84 | 2.18e-22 | 8 | 15.11 | 1.94 | Yes
7067 | 0.8/5.45 | 6.6/44.99 | 13.63 | 6.25e-30 | 14 | 12.51 | 1.69 | Yes
7847 | 0.8/6.31 | 3.4/26.81 | 9.23 | 4.39e-06 | 10 | 4.33 | 1.83 | Yes
7876 | 0.8/6.31 | 5.0/39.45 | 9.13 | 1.39e-12 | 13 | 6.52 | 1.72 | Yes
7901 | 0.8/6.02 | 2.8/21.06 | 17.48 | 1.09e-05 | 7 | 5.01 | 2.01 | Yes
9814 | 0.8/5.86 | 3.6/26.35 | 20.0 | 1.28e-16 | 9 | 10.61 | 1.88 | Yes
9863 | 0.8/6.13 | 5.2/39.86 | 14.46 | 4.08e-05 | 7 | 4.57 | 2.01 | Yes
9944 | 0.8/6.31 | 7.2/56.81 | 9.22 | 1.12e-13 | 17 | 5.85 | 1.62 | Yes
10018 | 0.8/6.31 | 2.4/18.93 | 27.98 | 7.44e-03 | 5 | 3.16 | 2.21 | Yes
22230 | 0.8/6.02 | 1.4/10.53 | 6.72 | 2.73e-01 | 2 | 1.3 | 3.0 | No
22386 | 0.8/6.35 | 3.2/25.41 | 16.05 | 1.32e-39 | 7 | 28.53 | 2.01 | Yes
22490 | 0.8/6.31 | 6.6/52.04 | 13.01 | 1.24e-38 | 16 | 13.98 | 1.64 | Yes
23124 | 0.8/5.93 | 3.2/23.74 | 14.9 | 1.76e-16 | 8 | 11.51 | 1.94 | Yes
23135 | 0.8/5.72 | 1.6/11.44 | ¡0.0 | Nan | Nan | Nan | Nan | No
23408 | 0.8/6.31 | 3.4/26.83 | 6.72 | 3.54e-02 | 4 | 2.58 | 2.37 | Yes
23839 | 0.8/6.3 | 6.2/48.79 | 14.21 | 2.99e-68 | 13 | 27.44 | 1.72 | Yes
54891 | 0.8/6.35 | 2.2/17.46 | 1.29 | Nan | Nan | Nan | Nan | No

222 RID: ID in Rafelski et al. (2015), $r_{\rm in}$: inner radius for the test
defined in Section 3.1, $r_{\rm CoG}$: curve of growth radius used as the
outer radius for the test (Section 3.2), S/N($r_{\rm in}$-$r_{\rm CoG}$): S/N
of the flux measured at $r=r_{\rm in}$-$r_{\rm CoG}$ (halo candidates have a
S/N($r_{\rm in}$-$r_{\rm CoG})\geq 3$), DoF: degrees of freedom for the test
(Section 3.3.2), $p_{0}$: probability of the SB profile at $r=r_{\rm
in}$-$r_{\rm CoG}$ to match that of the target’s continuum-component image
(Ly$\alpha$ haloes are confirmed if $p_{0}$¡0.05), R. $\chi^{2}$: reduced
$\chi^{2}$ of the SB fitting test, which is converted to a $p_{0}$ value, R.
$\chi^{2}$ ($p_{0}$=0.05): reduced $\chi^{2}$ corresponding to the threshold
$\hat{p_{0}}$=0.05, LAH: Whether the object has a Ly$\alpha$ halo or not. The
SB profiles of RID=23124 and 54891 were not tested due to the low S/N($r_{\rm
in}$-$r_{\rm CoG}$). We note that RID=23135 has a negative S/N($r_{\rm
in}$–$r_{\rm CoG}$).

We tested for the existence of Ly$\alpha$ haloes with two steps. First, we
checked the S/N of fluxes in the annulus from $r_{\rm in}$ to $r_{\rm CoG}$ to
select LAH candidates (Section 3.3.1). Second, we tested for the existence of
Ly$\alpha$ haloes with the radial SB profiles at $r=r_{\rm in}$–$r_{\rm CoG}$
(Section 3.3.2), the results of which are described in Section 3.3.3. We
investigated non-LAH objects in Section 3.3.4 and Appendix D with completeness
simulations of the halo tests.

####  3.3.1 Selection of LAH candidates based on the S/N at $r=r_{\rm
in}$–$r_{\rm CoG}$

We measured the S/N of fluxes in the annulus from $r_{\rm in}$ to $r_{\rm
CoG}$, S/N($r_{\rm in}$–$r_{\rm CoG}$), on the optimized NBs using PHOTUTILS
with the two masks. The sources that have a S/N higher than or equal to three
were regarded as Ly$\alpha$ halo candidates, which were also visually
inspected. The top panel of Figure 7 shows the histogram of S/N($r_{\rm
in}$–$r_{\rm CoG}$). Among 21 galaxies, 19 are LAH candidates. The two objects
with low S/N values are RID=23135 and 54891, whose NBs were optimized based on
the 1D spectra at $r\leq r_{\rm in}$ in Section 3.2. They have low S/Ns on the
1D spectra at $r=r_{\rm in}$–$r_{\rm CoG}$, and the low values of S/N($r_{\rm
in}$–$r_{\rm CoG}$) on 2D NBs were expected.

####  3.3.2 Test with Ly$\alpha$ radial SB profiles

In order to confirm the presence of extended Ly$\alpha$ emission, we checked
if the emission is not from the outer wing of bright central Ly$\alpha$
emission. To do so, we assessed the null hypothesis that the source does not
have Ly$\alpha$ emission more extended than the PSF-convolved continuum-like
component. In other words, we measured the significance of the deviation of
the observed radial SB profiles from those of the target’s continuum-component
images provided in Section 3.1 ($p_{0}$ test). Our method carefully prevents
potential uncertainties of SB profiles at $r<r_{\rm in}$ due to the continuum
subtraction. We measured the observed SB profile on the optimized NB using
PHOTUTILS with two masks. The default width of the radial bins was one MUSE
spatial pixel, but the bins were combined with the outer bins to have $S/N\geq
2$. If spatial pixels at large radii close to $r_{\rm CoG}$ had too low S/Ns,
which reduced the combined S/N and made it lower than two, we did not use the
pixels in the fitting. We note that it did not change the results of the halo
test for the sample but gives lower $p_{0}$ values (higher reduced
$\chi^{2}$), which helps detect diffuse haloes combined with other conditions.
We measured the effective area considering the masks and derived the SB
profiles by dividing the fluxes with the effective area. Then, we fit the
observed SB profile with that of the target’s continuum-component in the range
of $r_{\rm in}$ to $r_{\rm CoG}$ and measured the reduced $\chi^{2}$, which
was converted into the probability of the null hypothesis, $p_{0}$, with
scipy.stats.chi2.sf. Here, the number of degrees of freedom (DoF) is 1 smaller
than the number of the combined radial bins. The free parameter is the
amplitude of the SB (i.e., flux). If a source has a Ly$\alpha$ halo, the SB
profile from $r_{\rm in}$ to $r_{\rm CoG}$ is significantly different from
that of the target’s continuum-component, which makes $p_{0}$ small. Our
threshold for the probability of the null hypothesis, $\hat{p_{0}}$, is 0.05,
which is the same as that used in Leclercq et al. (2017).

We visually investigated the sources that have a larger reduced $\chi^{2}$
than the threshold (see Table 2). We note that the results of the null
hypothesis tests were the same if we used different thresholds of S/N for the
radial binning, 1.0, 1.5, and 2.0, and when we adopted different $\hat{p_{0}}$
from 0.04 to 0.1. We also checked the results for the four different settings
in the continuum subtraction. The results were the same for all the sources
except for one object (RID=23408). These checks imply that our tests for the
existence of Ly$\alpha$ haloes are robust. The results of the tests are
described in Section 3.3.3 (see also Table 2 and Figures 7 and 8).

With this test, we could miss very faint or diffuse Ly$\alpha$ haloes below
the detection limits and Ly$\alpha$ haloes whose shapes are very different
from our circular assumption (see Section 3.3.4 for more details). The
S/N$\geq 3$ criterion corresponds to SB$\geq 3.2\times 10^{-19}$ erg s-1 cm-2
arcsec-2 and flux $\geq 2.2\times 10^{-18}$ erg s-1 cm-2, in the case of the
average width of the optimized NB and the average unmasked area between
$r_{\rm in}$ and $r_{\rm CoG}$ (see Section 3.2 and Figure 1b).

As a final note, our method is different from Leclercq et al. (2017). Their
method was designed for galaxies with strong central Ly$\alpha$ emission which
can de facto always be fit by the same exponential profile as the continuum.
Our galaxies are UV-selected and do not always show strong central Ly$\alpha$
emission. In practice, their inner Ly$\alpha$ emission is not well modeled by
the continuum so that the method of Leclercq et al. (2017) is not applicable
to our sample. The higher signal-to-noise ratio of our data also makes their
modeling assumptions more difficult in practice in our sample. We thus use a
more general method, which we verified recovers the LAHs of Leclercq et al.
(2017) for the six objects we have in common (and which thus all have strong
central Ly$\alpha$ emission).

####  3.3.3 Results of the halo test

Figure 7: Results of the tests for the existence of a Ly$\alpha$ halo. Top
panel: histogram of the flux S/Ns between $r=r_{\rm in}$ and $r_{\rm CoG}$
measured on the optimized Ly$\alpha$ NBs. Blue and gray histograms indicate
galaxies above and below the threshold of S/N=3 (black dashed line), Non-LAHs
and LAH candidates, respectively. RID=23135 has a negative S/N($r_{\rm
in}$–$r_{\rm CoG}$) and is counted as S/N($r_{\rm in}$–$r_{\rm CoG}$)$=0$ in
the plot. Bottom panel: probability of the null hypothesis that the SB profile
at $r=r_{\rm in}$-$r_{\rm CoG}$ matches that of the target’s continuum-
component profile vs. flux S/N between $r=r_{\rm in}$ and $r_{\rm CoG}$ for
the LAH candidates. A black dashed line represents the border of LAHs and Non-
LAHs.  Figure 8: SB profiles from the optimized NBs with results of the
Ly$\alpha$ halo tests. The gray, black, and blue points indicate the observed
radial profiles, those used for the fit (with binning if needed), and the
best-fit SB profiles of the PSF-convolved continuum-like component,
respectively. The x error bars of the black points mark the range for each
(combined) radial bin. The cyan shaded areas represent the radial ranges,
$r=r_{\rm in}$–$r_{\rm CoG}$ (see Section 3.3). The classification of LAH or
non-LAH, the S/N of the flux at $r=r_{\rm in}$–$r_{\rm CoG}$, and the
probability of the null hypothesis that the SB profile at $r=r_{\rm
in}$-$r_{\rm CoG}$ matches that of the target’s continuum-component profile
are shown at the top of each panel.

Among the 19 LAH candidates, 17 Ly$\alpha$ haloes around the galaxies are
confirmed with $p_{0}\leq 0.05$ (see the bottom panel of Figure 7). All LAH
sources have small $p_{0}$ values, ranging from $3.0\times 10^{-68}$ to 0.035
(corresponding to reduced $\chi^{2}$ values from 28.5 to 2.6), which indicate
significant deviations of the radial SB profiles from those of the PSF-
convolved continuum-component profiles at $r\geq r_{\rm in}$. However, the
remaining two sources, RID=5479 and 22230, are not confirmed to have a
Ly$\alpha$ halo due to their high $p_{0}$ values, 0.37 and 0.27, respectively,
which are higher than the thresholds. Interestingly, both sources have bright
Ly$\alpha$ fluxes and high S/N($r_{\rm in}$–$r_{\rm CoG}$) values, but the
radial SB profiles at $r\geq r_{\rm in}$ are statistically consistent with
those of the target’s continuum-component images (see Section 3.3.4 and
Appendix D.2). The radial SB profiles and the results of the tests for
individual sources are summarized in Figure 8 and Table 2.

In total, we have 17 LAHs and four non-LAHs. The results of this LAH test are
consistent with those in Leclercq et al. (2017) for the six common sources
with RID=7067, 7901, 9814, 9863, 10018, and 23124, which are classified as
LAHs in both studies, though the methods used are different. Interestingly, we
found LAHs around non-LAEs with net negative $EW(\mbox{Ly$\alpha$})$: for
instance, RID=4587 and 4764, which have $EW(\mbox{Ly$\alpha$})_{\rm
net}\leq-10.0$ Å and -14.2 Å, respectively, as demonstrated in Appendix A.3
and Figure 15 (see also the central dip on the SB profiles in Figure 8).
RID=7876 and 9944 might be also non-LAEs with LAHs. However, unfortunately,
they are nonisolated sources, and we cannot decline a possibility that their
LAHs are mainly contributed from other sources in the large-scale structure
like RID=7847 (see Figure 17). This is the first time to confirm the presence
of LAHs around non-LAEs. Further discussion of the Ly$\alpha$ line properties
and galaxy populations is beyond the scope of this paper but it could be
interesting to investigate in the future.

####  3.3.4 Non-LAH objects

Figure 9:  Halo parameter set ($I_{\rm h}$ and $r_{\rm s,h}$) showing 50%
completeness for four non-LAH objects. We explored potential halo parameters
for four non-LAHs by simulating completeness values of the halo tests. We
assumed exponential profiles for the halo and continuum-like component models
(h+c) shown by dashed lines and for halo only models (h) shown by solid lines
(see Appendix D). The gray solid (black dashed), orange solid (red dashed),
magenta solid (violet dashed), and cyan solid (blue dashed) lines represent
RID=5479, RID=22230, RID=23135, and RID=54891 with halo only models (halo and
continuum models), respectively. The black crosses indicate the halo
parameters measured in Leclercq et al. (2017) for the common sources between
Leclercq et al. (2017) and ours.

Faint diffuse Ly$\alpha$ haloes could be undetected because they would be
hidden in the noise. We investigated the four non-LAH objects and simulated
their completeness individually. Here we briefly explain the simulations,
introduce non-LAHs, and comment on a non-LAH included in the UV-bright sample
(Section 2.2). The details of the simulations and the remaining three non-LAHs
are described in Appendix D.

The completeness of our halo test is sensitive to the SB profiles of haloes.
Assuming an exponential SB profile, as used in Wisotzki et al. (2016) and
Leclercq et al. (2017), we applied the same halo test to mock NBs of noise and
PSF-convolved halo models (see Appendix D for more details). We also simulated
haloes with a Ly$\alpha$ continuum-like component, whose flux was matched to
the central Ly$\alpha$ flux of the observed non-LAH objects. Figure 9
summarizes the parameter sets with a 50% completeness of the four non-LAHs for
both cases. Generally, the completeness decreases when the central surface
brightness $I_{\rm h}$ decreases or the scale length for haloes $r_{\rm s,h}$
decreases. The profiles are similar among the four sources but depend on the
noise levels. If a galaxy has a bright Ly$\alpha$ continuum-like component,
the completeness can be enhanced or suppressed depending on the parameters
(see Figure 23). The completeness for individual sources is shown in Figures
21 and 22 in Appendix D, and our halo tests are found to be complete when the
halo fluxes are equal to or brighter than $\simeq 4\times 10^{-18}$ erg s-1
cm-2 to $6\times 10^{-18}$ erg s-1 cm-2 in most of the parameter ranges. We
checked the parameters measured in Leclercq et al. (2017) for the six common
sources with Ly$\alpha$ haloes. These sources are mostly located above the 50%
completeness lines for non-LAH sources.

Out of the four non-LAHs, one object has a high S/N($r_{\rm in}$–$r_{\rm
CoG}$) (¿10), but no extended emission is significantly confirmed (RID=5479).
Another object with S/N($r_{\rm in}$–$r_{\rm CoG}$)=6.7 has anisotropic
spatially offset Ly$\alpha$ emission (RID=22230). Its extended emission cannot
be confirmed with the current method and data set. The remaining two objects
do not have detectable emission at $r\geq r_{\rm in}$. The last three objects
are not included in the UV bright sample, and therefore the results of the
halo tests for the last three sources do not affect the main conclusions of
this paper.

RID=5479 has a high confidence level of ZCONF=3 for $z_{\rm s}=4.16$ in the
MXDF catalog and is UV bright, $M_{1500}=-19.34$. It clearly shows Ly$\alpha$
emission lines on the 1D spectra for both $r\leq r_{\rm in}$ and $r=r_{\rm
in}$–$r_{\rm CoG}$ as shown in Figure 3, with $r_{\rm in}=1^{\prime\prime}$
and $r_{\rm CoG}=3\aas@@fstack{\prime\prime}2$. The S/N($r_{\rm in}$–$r_{\rm
CoG}$) is 12.94. However, the radial SB profile at $r\geq r_{\rm in}$ follows
that of the MUSE PSF-convolved HST profile (continuum-like component), and the
$p_{0}$ value is as high as 0.38 (see Figure 7). The radial SB profiles are
also consistent at $r\leq r_{\rm in}$. According to the completeness
simulations, the completeness is approximately 50%, for instance, when the
parameters are $r_{\rm s,h}$=5.5 kpc and $I_{\rm h}=8.8\times 10^{-19}$ erg
s-1 cm-2 arcsec-2 or $r_{\rm s,h}$=10.3 kpc and $I_{\rm h}=2.4\times 10^{-19}$
erg s-1 cm-2 arcsec-2 (see Figure 21). As discussed in Appendix D, the
completeness can be lowered when a source has a bright continuum-like
Ly$\alpha$ component at the center, which can hide a halo feature. However,
this only happens in a narrow parameter range, and the bright continuum-like
Ly$\alpha$ component can also enhance the completeness for some cases (Figure
23). We conclude that it does not constitute a serious bias in our tests. From
the distribution of the median $r_{\rm CoG}$ in the simulations, we also find
that the measured $r_{\rm CoG}$ prefers the halo parameters with completeness
values lower than 50%. The limitation of our data and method for the halo
detection for RID=5479 is illustrated in Figure 21.

If deeper IFU data with a higher spatial resolution than the MXDF data were
available, it could be possible to detect faint and compact Ly$\alpha$ haloes
among them. However, we would like to recall that our MUSE data were taken
with AO and have an unprecedented depth of 100 to 140-hour integration, the
longest exposure times on the VLT so far. Considering the small sample size
and the small number of non-LAHs, we did not correct for the incompleteness
below.

Figure 10:  Ly$\alpha$ halo fractions for the complete sample (gray bars) and
the UV-bright sample ($-20.0\leq M_{1500}\leq-18.7$; green bars). The $X_{\rm
LAH}$ for isolated sources and that for nonisolated sources are shown in the
second and third columns, respectively. The black error bars indicate 68.3%
confidence intervals.

###  3.4 Ly$\alpha$ halo fraction

####  3.4.1 Calculation of the Ly$\alpha$ halo fraction and its uncertainties

The fraction of Ly$\alpha$ haloes around UV-selected galaxies, $X_{\rm LAH}$,
is defined as follows:

$\ X_{\rm LAH}=\frac{N_{\rm LAH}}{N_{\rm LAH}+N_{\rm Non-LAH}}=\frac{N_{\rm
LAH}}{N_{\rm UV}},\ $ (1)

where $N_{\rm LAH}$, $N_{\rm Non-LAH}$, and $N_{\rm UV}$ are the number of
objects in a LAH sample, a non-LAH sample, and a parent sample, respectively.
We calculated $X_{\rm LAH}$ for isolated sources and nonisolated sources
separately, and for both subsets, for the UV-bright sample and the whole
sample.

We calculated the statistical uncertainty in $X_{\rm LAH}$. Statistical
uncertainties for fractions (i.e., Bernoulli trials) are given by a binomial
proportion confidence interval (BPCI). Following our previous paper on LAE
fractions (Kusakabe et al. 2020), we derived the statistical uncertainties in
$X_{\rm LAH}$ using astropy.stats.binom_conf_interval, with the Wilson score
interval as an approximation formula (Wilson 1927). Our $1\sigma$
uncertainties correspond to 68.3% confidence intervals. For samples including
RID=6693 or 54891, which has a low ZCONF=0, we adopted fractions including
them in the Ly$\alpha$ fractions but took conservative uncertainties
consisting of the minimum and maximum values of 68.3% confidence intervals of
fractions with and without RID=6693 or 54891.

There are three other potential contributions to the uncertainty in $X_{\rm
LAH}$. The first are the uncertainties in $N_{\rm LAH}$ due to the
incompleteness of Ly$\alpha$ halo confirmations. As discussed in Section
3.3.4, the completeness of haloes sensitively depends on the halo SB profiles.
Although spatial and spectral profiles of individual Ly$\alpha$ haloes around
LAEs have been investigated (e.g., Leclercq et al. 2017, 2020; Claeyssens et
al. 2019), we do not know the true distribution of the parameters of the halo
profiles below the detection limits. Therefore, we did not correct for a
completeness factor for $N_{\rm LAH}$ in this study. The number of non-LAHs is
small for our samples and the completeness correction would thus not change
our main conclusions. The second contribution comes from the uncertainty in
the PSF estimation for the MXDF (Bacon et al. in prep.). Since the survey area
of the MXDF is not large, and the MXDF data cubes were obtained by stacking
many different observations, the PSF is smoothed and homogenized. Therefore,
the uniform formula for the PSF applied to the entire field should not have a
significant effect on our Ly$\alpha$ halo tests. Third, we have the field-to-
field variance. Since the survey volume of MXDF is limited to $4.0\times
10^{3}$ cMpc3 ($z=2.86$–$4.44$, excluding the AO gap), our measurement of
$X_{\rm LAH}$ may be different from the cosmic average. There is a possibility
that $X_{\rm LAH}$ depends on the environment. Therefore, we calculated
$X_{\rm LAH}$ for both the sample of all the sources and of isolated sources
as precisely as possible.

####  3.4.2 High Ly$\alpha$ halo fractions

Table 3: Ly$\alpha$ halo fractions for all the sources and the UV-bright
sample

Sample | $X_{\rm LAH}$ | 6693? | 54891?
---|---|---|---
All | $80.95^{+10.35}_{-11.23}$ | Yes | Yes
All/isolated | $76.47^{+12.59}_{-13.55}$ | Yes | Yes
All/nonisolated | $100.0^{+0.0}_{-20.02}$ | No | No
UV-bright | $91.67^{+5.11}_{-13.15}$ | Yes | No
UV-bright/isolated | $90.0^{+6.11}_{-15.68}$ | Yes | No
UV-bright/nonisolated | $100.0^{+0.0}_{-33.36}$ | No | No
333The $X_{\rm LAH}$ values for the “All” sample and the UV-bright sample. It
also shows whether a sample includes RID=6693 or 54891, whose low ZCONF have
to be considered in the uncertainty calculation.

Figure 10 shows a high Ly$\alpha$ halo fraction for the sample including all
sources, $80.1^{+10.1}_{-11.2}$% (the dark gray bar in the first column). We
note that all the non-LAHs are categorized as isolated galaxies (Section 2.2).
However, the fraction remains high even when the sample is limited to the 17
isolated sources, $76.5^{+12.6}_{-13.6}$%. The $X_{\rm LAH}$ increases to
$100.0^{+0.0}_{-20.0}$% for nonisolated galaxies, though it is consistent
within the $1\sigma$ error bars. Since all the sources were selected from the
apparent magnitude cut of $F775W$, we also check $X_{\rm LAH}$ for the UV-
bright sample with $-20.0\leq M_{1500}\leq-18.7$. The Ly$\alpha$ halo fraction
is as high as $91.7^{+5.1}_{-13.2}$% (the green bar in the first column). Even
when we split them into isolated galaxies and nonisolated galaxies, the
$X_{\rm LAH}$ values remain high, $90.0^{+6.1}_{-15.7}$% and
$100.0^{+0.0}_{-33.4}$%, respectively. The numerical values of LAH fractions
are listed in Table 3.

The detection of extended Ly$\alpha$ emission with stacked Ly$\alpha$ narrow
bands for the UV-bright galaxies cannot provide information on the individual
presence of a Ly$\alpha$ halo (e.g., Steidel et al. 2011). The general
presence of Ly$\alpha$ haloes is confirmed for individual UV-selected galaxies
with observations for the first time in this work. It is similar to the high
fraction of Ly$\alpha$ haloes around high-z MUSE LAEs (e.g., about 80% in
Leclercq et al. 2017, Saust et al. in prep.), though the methods are
different. We discuss the cause of the high Ly$\alpha$ halo fractions in the
next section.

##  4 Discussion

We discuss implications from the high Ly$\alpha$ halo fractions, incidence
rates of Ly$\alpha$ emission, and implications from four non-LAHs in Sections
4.1, 4.2, and 4.3, respectively.

###  4.1 Why do most of galaxies have a LAH?

Figure 11:  Typical Ly$\alpha$ SB profiles with cosmic dimming corrections
scaled to $z=3.65$. (a): The violet and blue solid lines show individual SB
profiles of LAHs and non-LAHs, respectively. The black solid line and the gray
shaded area indicate the mean SB profile of 17 LAHs and the $1\sigma$
uncertainty, respectively, while the red dashed line indicates the mean SB
profile of 13 isolated LAHs. The black crosses represent the median profile of
the 17 LAHs. The black dashed holizontal line shows the typical $1\sigma$ SB
limit of the mean LAH stack. (b): The blue circles and cyan crosses show the
median SB profile of stacked MUSE LAEs at $z=3$–$4$ (Wisotzki et al. 2018,
W18) and the same data multiplied by 1.85 to compare the profile shapes.
Figure 12: Cumulative incidence rate of LAHs, $dn/dz({\rm LAH},\,M_{1500}\leq
M_{1500,0})$, as a function of $M_{1500,0}$. The blue solid line and shading
show the $dn/dz({\rm LAH},\,M_{1500}\leq M_{1500,0})$ at $z\simeq 3.65$ and
the uncertainty, respectively. The uncertainty is propagated from the
1$\sigma$ error of the $X_{\rm LAH}$ for all the sources. The solid black and
green lines indicate $M_{1500}$ of the brightest source in our sample and the
upper limit of $M_{1500}$ for the UV-bright sample, respectively (the
$M_{1500}$ of the faintest source is -18 mag). The blue dashed thin and thick
lines represent the $dn/dz$ for DLAs and DLAs+sub-DLAs at $z=3.65$ calculated
from the best-fit formulae of the z evolution of absorbers in Zafar et al.
(2013b).  Figure 13:  Cumulative incidence rate of LAHs, $dn/dz({\rm
LAH},\,M_{1500}\leq M_{1500,0})$, as a function of $M_{1500,0}$ at different
redshifts. The different colors (blue, green, and red) indicate different
redshifts ($z\simeq 3.65$, 4.9, and 5.9 in panels a to c, respectively). The
solid black vertical lines show the $M_{1500}$ of the brightest and faintest
sources in our sample. The green vertical line indicates the upper limit of
$M_{1500}$ for the UV-bright sample. (a): At $z\simeq 3.65$. The blue solid
line and shading show the $dn/dz({\rm LAH},\,M_{1500}\leq M_{1500,0})$ and the
uncertainty, respectively. The blue-dashed thin line, medium-thick line, and
thick line represent the $dn/dz$ for DLAs, DLAs+sub-DLAs, and DLAs+sub-
DLAs+LLSs at the same redshift, respectively. (b): At $z\simeq 4.9$. (c): At
$z\simeq 5.9$.

It is now well established that there is extended Ly$\alpha$ emission around
individual LAEs (Wisotzki et al. 2016; Leclercq et al. 2017). The key result
of the present study is that not only LAEs have Ly$\alpha$ haloes: we found a
very high Ly$\alpha$ halo fraction of $\simeq 80$–90% for our UV-selected
galaxies at $z=2.9$–$4.4$, in other words, star-forming galaxies at high
redshifts. It implies that UV-selected galaxies generally have a significant
amount of cool/warm gas in the CGM.

As introduced in Section 1, various mechanisms have been proposed to power
Ly$\alpha$ haloes: 1) scattering of Ly$\alpha$ from star-forming regions
(e.g., Laursen & Sommer-Larsen 2007; Zheng et al. 2011), 2) gravitational
cooling radiation (e.g., Haiman et al. 2000; Fardal et al. 2001), 3) star
formation in satellite galaxies (e.g., Zheng et al. 2011; Mas-Ribas et al.
2017a, b; Mitchell et al. 2021), and 4) fluorescence (e.g., Furlanetto et al.
2005; Cantalupo et al. 2005; Kollmeier et al. 2010; Mas-Ribas & Dijkstra 2016;
Mas-Ribas et al. 2017b). In process 1), Ly$\alpha$ photons are produced in
star-forming regions inside galaxies and then scattered by H i gas in the ISM
and the CGM (e.g., Barnes & Haehnelt 2010; Dijkstra & Kramer 2012; Verhamme et
al. 2012, see also Kakiichi & Dijkstra 2018 and Garel et al. 2021). From the
spectral shapes of Ly$\alpha$ emission with spatial information, previous
studies suggested that the scattering process happened in outflowing media
(e.g., Claeyssens et al. 2019; Leclercq et al. 2020; Chen et al. 2021, see
also Verhamme et al. 2006, 2018). Resonant scattering in outflowing media can
happen in and around galaxies, if they have a significant amount of
surrounding outflowing gas (see also Kusakabe et al. 2019). In process 2),
Ly$\alpha$ photons are emitted by collisionally excited inflowing gas, which
releases gravitational energy (CGM in-situ emission, e.g., Rosdahl & Blaizot
2012). In the process 3), Ly$\alpha$ photons are produced through star
formation in satellite galaxies, which can appear as a Ly$\alpha$ halo if
individual LAEs are clustered on small scales (Mas-Ribas et al. 2017a).
Finally, the Ly$\alpha$ photons in process 4) are produced by recombination of
the CGM gas photo-ionized by the UV background, near-by bright objects, or the
galaxies (e.g., Mas-Ribas & Dijkstra 2016). These Ly$\alpha$ emission
mechanisms are difficult to distinguish from one another, although they do not
necessarily trace the same gas phases and kinematics.

Mitchell et al. (2021) present a zoom-in cosmological radiation hydrodynamics
simulation of a single LAE at $z=3-6$ to study the origin and dynamics of the
CGM as well as their Ly$\alpha$ signature. Their models can almost reproduce
the average Ly$\alpha$ SB of stacked MUSE LAEs (Wisotzki et al. 2018),
implying that the Ly$\alpha$ haloes are driven by the processes 1 to 3 above
depending on the distance to the galaxy: CGM scattering of galactic Ly$\alpha$
emission, in-situ emission of CGM gas (mostly infalling), and Ly$\alpha$
emission from satellite galaxies (see their Figures 6 and 7 for the
contribution of these processes to the Ly$\alpha$ halo). Byrohl et al. (2021)
predict Ly$\alpha$ SB profiles at $z=2$–$5$ with illustris TNG50 simulations,
which agree with those of the individual MUSE LAEs in Leclercq et al. (2017).
They find scattered photons from star-forming regions to be the major source
of Ly$\alpha$ haloes in their simulations.

In fact, a cool/warm gas reservoir around high-$z$ galaxies is expected from
both observations and simulations. Numerous observational campaigns revealed
the existence of multiphase extended gas reservoirs around galaxies at low
redshifts (e.g., summarized in Figure 7 of Tumlinson et al. 2017). Werk et al.
(2014) use the transverse absorption-line technique and measure the hydrogen
column densities of 33 $L\simeq L_{\star}$ galaxies at $z\simeq 0.2$ in the
COS-Halos survey. They constrain the lower limit of the cool, highly ionized
CGM mass as $6.5\times 10^{10}\,M_{\odot}$ and the extension as 300 kpc (see
also e.g., Zhang et al. 2016; Zabl et al. 2019; Schroetter et al. 2021;
Beckett et al. 2021, for low-z observations). Neutral hydrogen gas is also
detected up to the virial radius and beyond in the CGM of star-forming field
dwarf galaxies at z$\lesssim 0.2$ ($L\lesssim 0.1L^{\star}$, $M_{\star}\simeq
10^{8}$–$10^{9}$ M⊙, Johnson et al. 2017), which are more representative of
our sample. At $z=2$–$3$, Rudie et al. (2012) find covering fractions of
$90\pm 9$% and $30\pm 14$% for $N(\mbox{H\,{\sc i}})>10^{15.5}\ {\rm cm^{-2}}$
and $N(\mbox{H\,{\sc i}})>10^{17.2}\ {\rm cm^{-2}}$, respectively, within the
viral radius of massive LBGs (see also Prochaska et al. 2013). The number
densities (or incidence rates) of absorbers imprinted on quasar spectra are
found to increase from $z=0$ to $z=5$ (e.g., Prochaska et al. 2005; Songaila &
Cowie 2010; Zafar et al. 2013a, for DLAs, LLSs, and Sub-DLAs, respectively).
It implies the presence of denser and more neutral hydrogen CGM gas at higher
redshifts. Simulations of galaxy formation and evolution generally predict
that the CGM contains a significant amount of neutral hydrogen gas (e.g.,
Fumagalli et al. 2011; Van de Voort et al. 2012), though they make different
predictions for the mass, extent, and physical state of the gas (e.g.,
Tumlinson et al. 2017). Until recently, it has been very challenging for
simulations to reproduce the observed high covering fractions of H i at high
redshifts. Rahmati et al. (2015) use the EAGLE cosmological, hydrodynamical
simulations (Schaye et al. 2015) and predict the H i gas distribution around
high-$z$ massive galaxies. They show a high covering fraction of
$N(\mbox{H\,{\sc i}})\geq 10^{17.2}\ {\rm cm^{-2}}$ gas of $\simeq 60$–$70$%
at $z=4$ for halo masses of $M_{\rm h}>10^{11}\ M_{\odot}$, which is found to
be driven by stellar and AGN feedback. Interestingly, massive haloes with
$M_{\rm h}>10^{12}\ M_{\odot}$ are predicted to have nearly scale-invariant
profiles of the H i gas covering fraction at a given redshift, implying the
generality of a rich content of H i gas in the CGM in high-$z$ massive haloes.
The covering fractions increase rapidly with redshifts at a given $M_{\rm h}$
in the simulations, as a result of increasing rates of accretion and the
higher mean density of the Universe (see their Figure 5). This redshift
evolution is also predicted by the FIRE-2 cosmological zoom simulations in
Stern et al. (2021), which also show that a large fraction of the inner CGM
volume is occupied by cool neutral gas in haloes with $M_{\rm h}\leq
10^{12}\,M_{\odot}$ and that it extends to the outer region of haloes with
$M_{\rm h}\lesssim 10^{11}$ $M_{\odot}$ (i.e., comparable to the typical
$M_{\rm h}$ of our sample, $\simeq 1\times 10^{11}$–$2\times 10^{11}\ {\rm
M}_{\odot}$, see Section 2.2). In their simulations, neutral hydrogen gas is
maintained by a shorter cooling time than the free-fall time and a gas density
high enough to be self-shielded from photoionizing radiation. As different
simulations predict different dependences of the H i gas covering fractions on
$M_{\rm h}$, which could be caused by the use of different feedback models and
resolutions (Rahmati et al. 2015; Stern et al. 2021, see also Faucher-Giguère
et al. 2015; Peeples et al. 2019), it is challenging to infer the physics
behind our high Ly$\alpha$ halo fractions from them. Nevertheless, the state-
of-the-art simulations suggest a rich cool/warm gas content in the high-$z$
CGM.

To better understand the role of the CGM gas in galaxy evolution and the
physical mechanisms at play in CGM, it is important to unveil the link between
absorbers and host galaxies. So far, significant efforts have been made to
investigate impact parameters, H i covering fractions, metallicities of
absorbers, and their dependence on properties of the hosts such as
luminosities, masses and star formation rates (e.g., Rudie et al. 2012; Turner
et al. 2014; Rubin et al. 2015; Fumagalli et al. 2015; Krogager et al. 2017;
De Cia et al. 2018; Mackenzie et al. 2019, see also Turner et al. 2017).
Muzahid et al. (2021) succeed in characterizing the gaseous CGM of 96 LAEs at
$z=2.9$–$3.8$ with background quasars from impact parameters of 16 to 315 kpc
in the MUSE Quasar-field Blind Emitters Survey (MUSEQuBES). As introduced in
Section 1, mapping gas with emission is another ideal way to investigate it,
but the connection between the gas detected in absorption and that in emission
has not been uncovered yet, in particular at high redshifts. At $z\simeq
3.25$, Fumagalli et al. (2017) detect extended Ly$\alpha$ emission for a
counterpart DLA with a $\simeq 40$ kpc extend at a projected distance of
$\simeq 30$ kpc from the quasar sightline (see also e.g., Christensen et al.
2004; Kashikawa et al. 2014, for Ly$\alpha$ haloes of DLAs at $z\sim 3$). Very
recently, Zabl et al. (2021) reported an Mg ii emission halo around a star-
forming galaxy at $z=0.7$ near a quasar sightline for the first time thanks to
deep MUSE data reaching a SB limit of $\simeq 1\times 10^{-18}$ erg s-1 cm-2
arcsec-2 ($2\sigma$). As a complementary approach to the individual studies
(e.g., Fumagalli et al. 2017; Zabl et al. 2021) and a practical strategy for
high redshifts, Wisotzki et al. (2018) estimate the incidence rate of extended
Ly$\alpha$ emission of MUSE LAEs and compare it with the incidence rates of
Ly$\alpha$ absorbers (Rauch et al. 2008). Using our unbiased sample, we
investigate whether LAHs of star-forming galaxies can account for absorber
statistics at high redshifts in the next Section, following Wisotzki et al.
(2018).

###  4.2 Incidence rate of the CGM gas visible in Ly$\alpha$ emission

As mentioned in Section 4.1, the typical relations between the gas detected in
absorption and emission have not been revealed. The general presence of LAHs
allows us to estimate the incidence rate of the CGM gas detected in Ly$\alpha$
per line of sight per unit redshift, $dn/dz$, under the assumption that this
extended Ly$\alpha$ emission traces the hydrogen content in the CGM. First, we
derived the mean SB profile for our LAH subsample with cosmic dimming
corrections and obtained the average area visible in Ly$\alpha$ (Section
4.2.1). Second, we calculated the $dn/dz$ for LAHs assuming number densities
from UV luminosity functions (Section 4.2.2). Third, we compared them with
$dn/dz$ for LLSs, sub-DLAs, and DLAs (Section 4.2.3).

####  4.2.1 Mean Ly$\alpha$ radial SB profile with cosmic dimming correction
and Ly$\alpha$ size

In order to compute the mean Ly$\alpha$ radial SB profile of our sample at
different redshifts, we corrected for the cosmological dimming effect as
follows. We used PHOTUTILS with the neighboring object masks, and measured
Ly$\alpha$ fluxes from the flux-maximized NBs with a fixed aperture and annuli
of fixed physical scale, from 1 kpc to 56 kpc, in 15 linear steps. Then, we
converted the SB profile at each redshift and each radius, $SB_{\rm(z)}$(r
[kpc]), in units of erg s-1 cm-2 arcsec-2 with arcsec corresponding to kpc at
the given $z$, to the SB profile at $z=3.56$ (the midpoint of
$z=2.96$–$4.44$), $SB_{\rm(z=3.56)}$(r [kpc]):

$SB_{\rm(z=3.56)}(r{\rm[kpc]})=SB_{\rm(z)}(r{\rm[kpc]})\frac{(1+z)^{4}}{(1+3.56)^{4}},$
(2)

with units of erg s-1 cm-2 arcsec-2 with arcsec at $z=3.56$. We took the means
of the SB in each radial bin among our LAHs. To estimate $1\sigma$
uncertainties on the mean SBs, we summed the variances of the SB in a given
radial bin over the LAH sample, took the square root, and divided it by the
sample size. We also computed the mean SB profile for only isolated LAHs.

Figure 11a shows the mean Ly$\alpha$ SB of 17 LAHs. The Ly$\alpha$ emission is
found to extend to 5.4 arcsec (40 kpc), above the SB limit of the typical
$1\sigma$ uncertainty of $5\times 10^{-21}$ erg s-1 cm-2 arcsec-2. The mean SB
profile of all the LAHs (black line) is consistent with the median for 17 LAHs
(black crosses) and the mean for 14 isolated LAHs (red dashed line). We
compared it with that for median-stacked MUSE LAEs at $z=3$–$4$ from Wisotzki
et al. (2018) in panel (b). Although individual SB profiles show a wide
diversity (Figure 8), it is remarkable that our mean SB profile looks very
similar to the stack of Wisotzki et al. (2018) in terms of typical extent and
slope. The factor two difference in amplitude may be fully explained by the
different samples: galaxies in Wisotzki et al. (2018) are mostly extremely
faint LAEs. Interestingly, our halo _size_ is nevertheless similar to that of
the faint LAEs with the SB limits, irrespective of our stacking methods
described above.

In an ideal case with higher S/N values, we would be able to estimate the halo
size (for instance, 90% luminosity radius) by fitting the SB with two-
component Sersic profiles. This would allow us to also probe the halo-size
dependence on $M_{1500}$, which might exist. However, even with the MXDF data
set, the S/N is not high enough to constrain the area detected with Ly$\alpha$
in such a sophisticated way. Therefore, following Wisotzki et al. (2018), we
calculated the Ly$\alpha$ size corresponding to the typical $1\sigma$ SB
limit, $5\times 10^{-21}$ erg s-1 cm-2 arcsec-2.

####  4.2.2 The incidence rate of LAHs

Assuming that LAHs have the same area ($A_{\rm LAH}$) on average, we
calculated the incidence rate of LAHs, $dn/dz({\rm LAH})$, for our sample. We
use the UV luminosity function (LF) from Bouwens et al. (2015) at redshift
$z\simeq 3.8$, similar to the midpoint redshift of our sample. This LF has a
characteristic magnitude of $M^{\star}$=-20.88 mag, a normalization
$\phi^{*}=1.97$ Mpc-3, and a faint-end slope of $\alpha=-1.64$444We note that
Bouwens et al. (2015) derive the UVLFs for a longer wavelength (rest-frame
1600 Å) than that used in this study (1500 Å), and we assumed that the
wavelength difference can be ignored.. A cumulative $dn/dz({\rm
LAH},\,M_{1500}\leq M_{1500,0})$ for a certain $M_{1500,0}$ limit is given as
follows:

$\frac{dn}{dz}({\rm LAH},M_{1500}\leq M_{1500,0})=\frac{A_{\rm
LAH}n(M_{1500,0})V_{\rm MXDF}X_{\rm LAH}}{A_{\rm MXDF}\Delta{z}},$ (3)

where $n(M_{1500,0})$, $V_{\rm MXDF}$, $A_{\rm MXDF}$, and $\Delta{z}$ are the
number density for $M_{1500}\leq M_{1500,0}$, the survey volume, the survey
area, and the redshift bin width, respectively. We integrated the LF from -23
mag to -18 mag, which is the faintest magnitude in our sample, see Figure 1c.
The obtained $dn/dz({\rm LAH},\,M_{1500}\leq-18)$ is $0.76^{+0.09}_{-0.09}$,
whose uncertainty is propagated from the 1$\sigma$ error of $X_{\rm LAH}$ for
all the sources. The lower $M_{1500}$ limit of -23 mag is brighter than our
brightest LAH with $M_{1500}\simeq-20$ mag, but the contribution from galaxies
with $M_{1500}=-23$ to $-21$ mag to our $dn/dz({\rm LAH},\,M_{1500}\leq-18)$
is small. The high incidence rate of LAHs suggests that about 80% of the sky
is covered by the Ly$\alpha$ emission from galaxies with $M_{1500}\leq-18$ mag
at $z=3$–$4$. The value is similar to that for MUSE LAEs at $z=3$–$4$ with
their SB limit of $\simeq 1.5\times 10^{-20}$ erg s-1 cm-2 arcsec-2, $1.0\pm
0.4$, but is lower than that for the similar SB limit of $\simeq 5\times
10^{-21}$ erg s-1 cm-2 arcsec-2, $2.3\pm 1.3$ (Wisotzki et al. 2018). The
difference could be caused by the sample selections as we discussed above for
the difference in the SB profiles. We also calculated the $dn/dz({\rm
LAH},\,M_{1500}\leq M_{1500,0})$ with different $M_{1500,0}$, which is shown
in Figure 12 and used in the comparison in Section 4.2.3.

####  4.2.3 The incidence rate of LAHs compared with those of strong
Ly$\alpha$ absorbers

We compare the incidence rate of LAHs with those of DLAs and sub-DLAs,
$dn/dz({\rm DLA})$ and $dn/dz({\rm sub-DLA})$, at our median redshift
($z=3.65$) from Zafar et al. (2013b). They show the best-fit redshift
evolution of the observed $dn/dz$ for DLAs and sub-DLAs at $z=0$–$5$ by
scaling the best-fit relation for LLSs in Songaila & Cowie (2010). As shown in
Figure 12, our $dn/dz({\rm LAH},\,M_{1500}\leq-18)=0.76^{+0.09}_{-0.09}$ is in
between $dn/dz({\rm DLA})=0.33$ (blue dashed thick line) and $dn/dz({\rm
DLA})+dn/dz({\rm sub-DLA})=1.4$ (blue dashed thin line). Our incidence rate
for the UV-bright sample, $dn/dz({\rm LAH},\,M_{1500}\leq-18.7)$ (green
vertical line), is closer to $dn/dz({\rm DLA})$ but is also located in between
them. It suggests that Ly$\alpha$ haloes are counterparts of DLAs and sub-
DLAs.

It is interesting to extend the exercise to higher redshifts and fainter
$M_{1500}$ in order to discuss the redshift evolution. We assumed that
galaxies have the same $A_{\rm LAH}$ in comoving kpc2 at redshifts of $z\simeq
4.9$ and $z\simeq 5.9$ as at $z\simeq 3.65$ (e.g., Wisotzki et al. 2016;
Leclercq et al. 2017). We used UV LFs at $z\simeq 4.9$ ($z\simeq 5.9$) from
Bouwens et al. (2015), $M^{\star}$=-21.10 mag, $\phi^{*}=0.79$ Mpc-3, and
$\alpha=-1.76$ ($M^{\star}$=-21.10 mag, $\phi^{*}=0.39$ Mpc-3, and
$\alpha=-1.90$). The $dn/dz({\rm LAH},\,M_{1500}\leq M_{1500,0})$ were
calculated down to $M_{1500,0}=-14$ mag at $z\simeq 3.65$, $z\simeq 4.9$ and
$z\simeq 5.9$ in the same manner as in Section 4.2.2 (see Figure 13). The
incidence rate of LLSs, $dn/dz({\rm LLS})$, as well as $dn/dz({\rm DLA})$ and
$dn/dz({\rm sub-DLA})$, were obtained from the formulae in Songaila & Cowie
(2010) and Zafar et al. (2013b), respectively. The results of the abundance
matching for DLAs evolve with redshift. At $z\simeq 3.7$, $dn/dz({\rm DLA})$
can be matched with $dn/dz({\rm LAH})$ with $M_{1500}\leq-18.9^{+0.1}_{-0.1}$.
Meanwhile, it requires $M_{1500}\leq-17.4^{+0.2}_{-0.1}$ and
$M_{1500}\leq-16.4^{+0.1}_{-0.1}$ at $z\simeq 4.9$ and $z\simeq 5.9$,
respectively. The same trends with redshift are found for $dn/dz({\rm sub-
DLA})$ and $dn/dz({\rm LLS})$. We need to go to fainter $M_{1500}$ limits at
higher redshifts to provide the same level of $dn/dz$ as that for absorbers.

The $z$ evolution seen in this exercise can be explained by the combination of
two redshift evolutions. First, we have the $dn/dz$ evolution of absorbers,
which increases with increasing redshifts, implying the presence of denser and
more neutral hydrogen gas at higher redshifts. This evolution is expected to
be maintained by increasing rates of cold accretion and the higher mean
density of the Universe at higher redshifts (Rahmati et al. 2015). Second, the
UV LFs evolve. The number density of such relatively bright galaxies decreases
with increasing redshifts. Therefore, with the assumption of no dependence of
$A_{\rm LAH}$ on $z$ and $M_{1500}$, fainter $M_{1500}$ sources are required
to be accounted to reproduce $dn/dz$ of absorbers at higher redshifts.

Despite the remarkable progress with the UV-selected, as opposed to
Ly$\alpha$-selected, sample, we caution against overinterpreting the results.
The examination here is a very simple abundance matching with assumptions. The
dependence of $A_{\rm LAH}$ on $z$, $M_{1500}$, or other galaxy’s properties
were not considered. Since UV brighter galaxies and lower-$z$ galaxies tend to
have a larger UV size than their counterparts (e.g., Shibuya et al. 2015), UV
fainter and higher-$z$ galaxies may have a smaller $A_{\rm LAH}$. Would it be
true, $dn/dz({\rm LAH},\,M_{1500}\leq M_{1500,0})$ could be overestimated with
$M_{1500,0}\geq-18$ or at $z\simeq 5$ and $\simeq 6$. However, the correlation
between $M_{1500}$ and halo size is under debate (e.g., Steidel et al. 2011;
Momose et al. 2016; Xue et al. 2017; Leclercq et al. 2017; Wu et al. 2020;
Claeyssens et al. 2022). No clear redshift evolution of the Ly$\alpha$ halo
size has been confirmed (e.g., Momose et al. 2014; Leclercq et al. 2017). Last
but not least, our modeling is based on a simple abundance matching approach
in which one Ly$\alpha$ halo corresponds to one absorber. As shown in Rahmati
et al. (2015) and Stern et al. (2021), for example, many absorbers with
various $N(\mbox{H\,{\sc i}})$ plausibly make up the CGM of individual high-z
galaxies. Simulations of the CGM and absorbers greatly depend on the strength
and the implementation of feedback models (Faucher-Giguère et al. 2015;
Rahmati et al. 2015; Suresh et al. 2015). Since Ly$\alpha$ emission is the
best tracer of the CGM H i gas at high redshifts, which can provide spatial
information, our results have great potential to constrain feedback models. It
will be challenging as demonstrated in Mitchell et al. (2021), but could also
provide information on the mass, extent, dynamics, and physical state of the
CGM gas.

###  4.3 Implications from non-LAHs

It is also interesting that four of our galaxies do not have a significant
Ly$\alpha$ halo, though they could be hidden in the noise as discussed in
Section 3.3.4. Even aside from RID=22230, which shows potential extended
Ly$\alpha$ emission with an anisotropic profile, the remaining three objects
may have different reasons for the suppression of extended Ly$\alpha$
emission. RID=5479 has very bright Ly$\alpha$ emission on the scale of the
galaxy’s UV component as shown in Figure 3, but it does not show extended
Ly$\alpha$. It may imply a small amount of H i gas in the CGM, which allows
Ly$\alpha$ photons to escape directly from the galaxy to the IGM. Such a
galaxy may differ in halo mass from other galaxies or may be in a different
evolutionary phase. A low H i content of the CGM may be due to a phase with
weak stellar feedback which does not push the gas out from the ISM to the CGM
(see Figure 11 in Rahmati et al. 2015, and Appendix B in Faucher-Giguère et
al. 2015). It could also be caused by a phase with very strong stellar and AGN
feedback which either ionizes the gas or significantly disrupts or ejects gas
from the CGM (see Section 5.2 in Trebitsch et al. 2017). A low fraction of
such objects would imply a short duty cycle of the lacking or disrupted phase.
RID=23135 and RID=54891 have faint Ly$\alpha$ emission inside the galaxy’s UV-
component scale, suggesting that Ly$\alpha$ photons produced by the star
formation could be killed by the dust in the ISM or the CGM and that the in-
situ halo mechanism and satellite scenario do not work for these galaxies. In
fact, a wide variety of H i covering fractions are predicted in simulations:
around 25%-45% and around 55%-75% as a 15-85 percentile for $\log(M_{\rm h}\
[M_{\odot}])\simeq 11.1$ at $z\simeq 3$ and $z\simeq 4$, respectively (Rahmati
et al. 2015). It is interesting to explore causes of a poor gas content for
rare galaxies in simulations. In particular, galaxies which can allow ionizing
photons to escape directly from the ISM to the IGM thanks to the low CGM H i
column density would play an important role in cosmic reionization.

##  5 Conclusions

Thanks to the more than $100$-hour integration with MUSE AO in the MXDF (Bacon
et al. 2021), we were able to examine the existence of Ly$\alpha$ haloes
around UV-selected star-forming galaxies at $z\simeq 2.9$–$4.4$. With the MXDF
data, we constructed a sample with a $F775W\leq 27.5$ mag cut, with
spectroscopic redshift constraints. We confirmed that all of 26 sources with
$z_{\rm p}\simeq 2.9$–$4.40$ have a close spec-$z$ estimation to their
photo-$z$, which implies high completeness values of our spec-$z$ assignments.
We used 21 galaxies at $z_{\rm s}=2.9$–$4.4$, which include 17 isolated
sources in HST images. The $M_{1500}$ range of our sample is -20 to -18 mag,
enabling us to construct a UV-bright sample over the redshift range (11
sources, $-20.0\leq M_{1500}\leq-18.7$). Our major results are summarized as
follows.

  1. 1.

Among 21 galaxies, 17 were confirmed to have significant extended Ly$\alpha$
emission. We report the first individual detections of extended Ly$\alpha$
emission around non-LAEs with negative net equivalent widths of Ly$\alpha$
(for instance, RID=4587 and 4764). We measured the Ly$\alpha$ halo fraction
for the sample of all the sources of $81.0^{+7.1}_{-11.2}$%, for the 17
isolated sources of $76.4^{+8.6}_{-13.5}$%, and for the 12 $-20.0\leq
M_{1500}\leq-18.7$ sources of $91.7^{+5.1}_{-13.1}$%. The $X_{\rm LAH}$
increases to $100.0^{+0.0}_{-20.0}$%, for nonisolated galaxies, though it is
consistent within the $1\sigma$ error bars. The high fractions are similar to
that for MUSE LAEs, about 80%, in Leclercq et al. (2017), though the methods
are different.

  2. 2.

The high fractions of Ly$\alpha$ haloes imply that UV-selected galaxies
generally have a significant amount of cool/warm gas in the CGM. Our study
shows for the first time significant extended Ly$\alpha$ emission around most
individual high-$z$ star-forming galaxies in a spec-$z$ complete sample.

  3. 3.

The mean SB profile for 17 LAHs was derived with cosmic dimming corrections
for the midpoint redshift of $z\simeq 3.65$. The mean Ly$\alpha$ radius above
the typical $1\sigma$ uncertainty of the SB is 5.4 arcsec (40 kpc).

  4. 4.

Assuming that extended Ly$\alpha$ emission traces the same cool/warm gas as
absorbing systems, we used the abundance matching technique for incidence
rates in order to investigate the correspondence between gas detected in
absorption and emission. Our $dn/dz({\rm LAH})$ calculated from a UVLF, the
typical LAH size, and the measured $X_{\rm LAH}$ is $0.76^{+0.09}_{-0.09}$ for
$M_{1500}\leq-18$ mag at $z\simeq 3.65$. This is in between $dn/dz({\rm DLA})$
and $dn/dz({\rm DLA})$+$dn/dz({\rm sub-DLA})$ at the same redshift. It
suggests that Ly$\alpha$ haloes trace the same gas as DLAs and sub-DLAs.

  5. 5.

At higher redshifts, we need to go to a fainter $M_{1500}$ limit to reach the
same $dn/dz$ as that for absorbers (DLA, sub-DLA, and LLSs). At $z\simeq 3.7$,
$dn/dz({\rm DLA})$ can be matched with $dn/dz({\rm LAH})$ with
$M_{1500}\leq-18.9^{+0.1}_{-0.1}$, but it requires
$M_{1500}\leq-17.4^{+0.2}_{-0.1}$ and $M_{1500}\leq-16.4^{+0.1}_{-0.1}$ at
$z\simeq 4.9$ and $z\simeq 5.9$, respectively. The $z$ evolution is due to the
increase of $dn/dz$ for absorbers with $z$ and the decrease of number
densities of UV LFs with $z$.

  6. 6.

We found four non-LAHs, though one of them shows potential extended Ly$\alpha$
emission with an anisotropic profile (with $M_{1500}=-18.6$). Another one has
very bright Ly$\alpha$ emission within the scale of the galaxy’s UV component
but does not show extended Ly$\alpha$ (with $M_{1500}=-19.3$), implying a
small amount of the HI gas in the CGM, which may allow Ly$\alpha$ photons to
escape directly from the galaxy to the IGM. The remaining sources have faint
Ly$\alpha$ emission inside the galaxy’s UV-component scale (with
$M_{1500}=-18.0$ and $-18.4$), suggesting that Ly$\alpha$ photons produced by
the star formation could be destroyed by dust in the ISM or the CGM and that
the in-situ halo mechanism and satellite scenario are not at play for these
galaxies.

We plan to extend this work to photometric-redshift samples in the near future
using the MUSE HUDF survey data (9 arcmin2) and upcoming MUSCATEL data (MUSE
Cosmic Assembly survey Targetting Extragalactic Legacy fields; in total 36
arcmin2), which will give us a more general view of $X_{\rm LAH}$. The larger
cosmic volume of those surveys compared to that of the MXDF (0.84 arcmin2 in
this study) will be useful to extend the dynamic range to brighter galaxies.
In order to constrain the physics of Ly$\alpha$ haloes and the trends of
galaxies with and without haloes, we will investigate the LAH properties and
the properties of the host galaxies with a larger sample. Finally, with MXDF
data, our sample will allow spatially resolved spectral analysis of Ly$\alpha$
emission as those in the literature (Claeyssens et al. 2019; Leclercq et al.
2020, see also Patrício et al. 2016 and Matthee et al. 2020, as well as
Claeyssens et al. 2022 for the Lensed Lyman-Alpha MUSE Arc Sample, LLAMAS).

###### Acknowledgements.

We thank the anonymous referee for constructive comments and suggestions. We
would like to express our gratitude to Edmund Christian Herenz, Leindert
Boogard, Miroslava Dessauges, Moupiya Maji, Valentin Mauerhofer, Charlotte
Paola Simmonds Wagemann, Masami Ouchi, Kazuhiro Shimasaku, Akio Inoue, and
Rieko Momose for giving insightful comments and suggestions. HK is grateful to
Liam McCarney for useful suggestions on English writing through the UniGE’s
Tandems linguistiques. HK acknowledges support from Swiss Government
Excellence Scholarships and Japan Society for the Promotion of Science (JSPS)
Overseas Research Fellowship. HK, FL, and AV are supported by the SNF grant
PP00P2 176808. AV and TG are supported by the ERC Starting Grant
757258”TRIPLE”. This work was supported by the Programme National Cosmology et
Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES.
This work is based on observations taken by VLT, which is operated by European
Southern Observatory. This research made use of
Astropy555http://www.astropy.org, which is a community-developed core Python
package for Astronomy (The Astropy Collaboration et al. 2013; Price-Whelan et
al. 2018), and other software and packages:MARZ, MPDAF (Piqueras et al. 2019),
PHOTUTILS, Numpy (Harris et al. 2020), Scipy (Virtanen et al. 2020), and
matplotlib (Hunter 2007).

## References

  * Aghanim et al. (2020) Aghanim, N., Akrami, Y., Ashdown, M., et al. 2020, Astronomy & Astrophysics, 641, A6
  * Bacher (2017) Bacher, R. 2017, PhD thesis
  * Bacon et al. (2010) Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Proceedings of the SPIE, Volume 7735, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 773508
  * Bacon et al. (2017) Bacon, R., Conseil, S., Mary, D., et al. 2017, Astronomy & Astrophysics, 608
  * Bacon et al. (2021) Bacon, R., Mary, D., Garel, T., et al. 2021, Astronomy & Astrophysics, 647, A107
  * Baldry et al. (2014) Baldry, I. K., Alpaslan, M., Bauer, A. E., et al. 2014, Monthly Notices of the Royal Astronomical Society, 441, 2440
  * Barnes & Haehnelt (2010) Barnes, L. A. & Haehnelt, M. G. 2010, Monthly Notices of the Royal Astronomical Society, 403, 870
  * Beckett et al. (2021) Beckett, A., Morris, S. L., Fumagalli, M., et al. 2021, Monthly Notices of the Royal Astronomical Society, 26, 1
  * Beckwith & Stiavelli (2006) Beckwith, S. & Stiavelli, M. 2006, The Astronomical …, 44
  * Benitez (2000) Benitez, N. 2000, The Astrophysical Journal, 536, 571
  * Benitez et al. (2004) Benitez, N., Ford, H., Bouwens, R., et al. 2004, The Astrophysical Journal Supplement Series, 150, 1
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&A, 117, 393
  * Bouwens et al. (2015) Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2015, Astrophysical Journal, 803, 1
  * Bradley et al. (2021) Bradley, L., Sipőcz, W. B., Robitaille, T., et al. 2021, photutils
  * Burchett et al. (2021) Burchett, J. N., Rubin, K. H. R., Prochaska, J. X., et al. 2021, The Astrophysical Journal, 909, 151
  * Byrohl et al. (2021) Byrohl, C., Nelson, D., Behrens, C., et al. 2021, Monthly Notices of the Royal Astronomical Society, 506, 5129
  * Cantalupo et al. (2005) Cantalupo, S., Porciani, C., Lilly, S. J., & Miniati, F. 2005, The Astrophysical Journal, 628, 61
  * Chen et al. (2021) Chen, Y., Steidel, C. C., Erb, D. K., et al. 2021, Monthly Notices of the Royal Astronomical Society, 508, 19
  * Christensen et al. (2004) Christensen, L., Sánchez, S. F., Jahnke, K., et al. 2004, Astronomy & Astrophysics, 417, 487
  * Claeyssens et al. (2022) Claeyssens, A., Richard, J., Blaizot, J., et al. 2022, arXiv:2201.04674, 1
  * Claeyssens et al. (2019) Claeyssens, A., Richard, J., Blaizot, J., et al. 2019, Monthly Notices of the Royal Astronomical Society, 489, 5022
  * Coe et al. (2006) Coe, D., Benítez, N., Sánchez, S. F., et al. 2006, The Astronomical Journal, 132, 926
  * Davies et al. (2020) Davies, J. J., Crain, R. A., Oppenheimer, B. D., & Schaye, J. 2020, Monthly Notices of the Royal Astronomical Society, 491, 4462
  * De Cia et al. (2018) De Cia, A., Ledoux, C., Petitjean, P., & Savaglio, S. 2018, Astronomy & Astrophysics, 611, A76
  * Dessauges-Zavadsky et al. (2003) Dessauges-Zavadsky, M., Peroux, C., Kim, T.-S., D’Odorico, S., & McMahon, R. G. 2003, Monthly Notices of the Royal Astronomical Society, 345, 447
  * Dijkstra & Kramer (2012) Dijkstra, M. & Kramer, R. 2012, Monthly Notices of the Royal Astronomical Society, 424, 1672
  * Drake et al. (2017) Drake, A. B., Garel, T., Wisotzki, L., et al. 2017, Astronomy & Astrophysics, 608, A6
  * Epinat et al. (2018) Epinat, B., Contini, T., Finley, H., et al. 2018, Astronomy & Astrophysics, 609, A40
  * Erb et al. (2012) Erb, D. K., Quider, A. M., Henry, A. L., & Martin, C. L. 2012, Astrophysical Journal, 759
  * Fardal et al. (2001) Fardal, M. A., Katz, N., Gardner, J. P., et al. 2001, Astrophysical Journal, 562, 605
  * Faucher-Giguère et al. (2015) Faucher-Giguère, C.-A., Hopkins, P. F., Kereš, D., et al. 2015, Monthly Notices of the Royal Astronomical Society, 449, 987
  * Feltre et al. (2020) Feltre, A., Maseda, M. V., Bacon, R., et al. 2020, Astronomy & Astrophysics, 641, A118
  * Finley et al. (2017) Finley, H., Bouché, N., Contini, T., et al. 2017, Astronomy & Astrophysics, 605, A118
  * Fujimoto et al. (2019) Fujimoto, S., Ouchi, M., Ferrara, A., et al. 2019, The Astrophysical Journal, 887, 107
  * Fumagalli et al. (2017) Fumagalli, M., Mackenzie, R., Trayford, J., et al. 2017, Monthly Notices of the Royal Astronomical Society, 471, 3686
  * Fumagalli et al. (2015) Fumagalli, M., O’Meara, J. M., Prochaska, J. X., Rafelski, M., & Kanekar, N. 2015, Monthly Notices of the Royal Astronomical Society, 446, 3178
  * Fumagalli et al. (2011) Fumagalli, M., Prochaska, J. X., Kasen, D., et al. 2011, Monthly Notices of the Royal Astronomical Society, 418, 1796
  * Furlanetto et al. (2005) Furlanetto, S. R., Schaye, J., Springel, V., & Hernquist, L. 2005, The Astrophysical Journal, 622, 7
  * Garel et al. (2015) Garel, T., Blaizot, J., Guiderdoni, B., et al. 2015, Monthly Notices of the Royal Astronomical Society, 450, 1279
  * Garel et al. (2021) Garel, T., Blaizot, J., Rosdahl, J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 504, 1902
  * Ginolfi et al. (2020) Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020, Astronomy and Astrophysics, 633, 1
  * Haiman et al. (2000) Haiman, Z., Spaans, M., & Quataert, E. 2000, Astrophysical Journal, 537, L5
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357
  * Hashimoto et al. (2017) Hashimoto, T., Garel, T., Guiderdoni, B., et al. 2017, Astronomy & Astrophysics, 608, A10
  * Hayashino et al. (2004) Hayashino, T., Matsuda, Y., Tamura, H., et al. 2004, The Astrophysical Journal Letters, 128, 2073
  * Hayes et al. (2013) Hayes, M., Östlin, G., Schaerer, D., et al. 2013, The Astrophysical Journal, 765, L27
  * Herenz et al. (2017) Herenz, E. C., Urrutia, T., Wisotzki, L., et al. 2017, Astronomy and Astrophysics, 606
  * Hilton et al. (2012) Hilton, M., Conselice, C. J., Roseboom, I. G., et al. 2012, Monthly Notices of the Royal Astronomical Society, 425, 540
  * Hinton et al. (2016) Hinton, S. R., Davis, T. M., Lidman, C., Glazebrook, K., & Lewis, G. F. 2016, Astronomy and Computing, 15, 61
  * Ho et al. (2020) Ho, M.-F., Bird, S., & Garnett, R. 2020, Monthly Notices of the Royal Astronomical Society, 496, 5436
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90
  * Illingworth et al. (2013) Illingworth, G. D., Magee, D., Oesch, P. A., et al. 2013, The Astrophysical Journal Supplement Series, 209, 6
  * Inami et al. (2017) Inami, H., Bacon, R., Brinchmann, J., et al. 2017, Astronomy & Astrophysics, 608, A2
  * Jaskot et al. (2019) Jaskot, A. E., Dowd, T., Oey, M. S., Scarlata, C., & McKinney, J. 2019, The Astrophysical Journal, 885, 96
  * Johnson et al. (2017) Johnson, S. D., Chen, H.-W., Mulchaey, J. S., Schaye, J., & Straka, L. A. 2017, The Astrophysical Journal, 850, L10
  * Johnson et al. (2018) Johnson, S. D., Chen, H.-W., Straka, L. A., et al. 2018, The Astrophysical Journal, 869, L1
  * Kakiichi & Dijkstra (2018) Kakiichi, K. & Dijkstra, M. 2018, Monthly Notices of the Royal Astronomical Society, 5159, 5140
  * Kakuma et al. (2021) Kakuma, R., Ouchi, M., Harikane, Y., et al. 2021, The Astrophysical Journal, 916, 22
  * Kashikawa et al. (2014) Kashikawa, N., Misawa, T., Minowa, Y., et al. 2014, The Astrophysical Journal, 780, 116
  * Keel et al. (1999) Keel, W. C., Cohen, S. H., Windhorst, R. A., & Waddington, I. 1999, The Astrophysical Journal Letters, 118, 2547
  * Kikuchihara et al. (2021) Kikuchihara, S., Harikane, Y., Ouchi, M., et al. 2021, arXiv:2108.09288
  * Kollmeier et al. (2010) Kollmeier, J. A., Zheng, Z., Davé, R., et al. 2010, Astrophysical Journal, 708, 1048