Mon. Not. R. Astron. Soc. 000, 1–17 (2013)

Printed 22 March 2014

(MN LATEX style file v2.2)

The environments of Ly α blobs I: Wide-field Ly α imaging
of TN J1338-1942, a powerful radio galaxy at z ≃ 4.1
associated with a giant Ly α nebula ⋆Tomoki Saito1 †, Yuichi Matsuda2,3 , Cedric G. Lacey4 , Ian Smail4 , Alvaro Orsi5,6 ,Carlton M. Baugh4 , Akio K. Inoue7 , Ichi Tanaka8 , Toru Yamada9 , Kouji Ohta10 ,CarlosDe Breuck11 , Tadayuki Kodama2,3 , Yoshiaki Taniguchi12
1

Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Studies, The University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
2 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
3 The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan
4 Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
5 Instituto de Astrofisica, Facultad de Fisica, Pontificia Universidad Católica, Av. Vicuña Mackenna 4860, Santiago, Chile
6 Centro de Astro-Ingenieria, Pontificia Universidad Católica, Av. Vicuña Mackenna 4860, Santiago, Chile
7 College of General Education, Osaka Sangyo University, 3-1-1, Nakagaito, Daito, Osaka 574-8530, Japan
8 Subaru Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA
9 Astronomical Institute, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan
10 Department of Astronomy, Kyoto University, Kyoto 606-8502, Japan
11 European Southern Observatory, Karl Schwarzschild Straße 2, 85748 Garching, Germany
12 Research Center for the Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

Draft version 20 Mar. 2014

ABSTRACT

We present wide-field Ly α imaging observations of the field around TN J1338–1942,
a powerful radio galaxy associated with an extended Ly α nebula (> 100 kpc) at
z = 4.11, with Subaru Prime-focus Camera to probe the environment of the radiogalaxy. We used a sample of Ly α emitters (LAEs) down to the Ly α luminosity oflog(LLyα [ erg s−1 ]) ∼ 42.8 to measure the galaxy density of this field, calibrating bydirect comparison with a control sample in a blank field taken with the same instrument. We found that the radio galaxy resides in a region with a peak overdensity ofδLAE = 3.1±0.5, after being smoothed on 8 h−1 Mpc scales on the sky and 160 h−1 Mpc
along the line of sight (both in comoving coordinates). Adjacent to this overdense region, we found a highly underdense region where virtually no LAEs are detected.
We used a semi-analytical model of LAEs derived from the Millennium Simulation tocompare our results with theoretical predictions. This comparison suggests that, while
the density distribution of the simulation is consistent with that of the blank field,
overdense regions such as the one found in the radio galaxy field are very rare, with
the number density of 2 × 10−7 h3 Mpc−3 (comoving), corresponding to the densest< 0.1 percentile at these redshifts. We also found a diﬀerence in the Ly α luminosity
function in the radio galaxy field compared with the blank field: the number of bright
LAEs (log(LLyα [ erg s−1 ]) ≳ 43.3) is enhanced, while the number of fainter LAEs isrelatively suppressed. These results suggest that some powerful radio galaxies associated with Ly α nebulae reside in extreme overdensities on ∼ 10–20 h−1 Mpc scales,
where star-formation and AGN activities may be enhanced via more frequent galaxy
mergers or higher rates of gas accretion from the surroundings.
Key words: galaxies: evolution – galaxies: formation – galaxies: high-redshift –galaxies: individual: TN J1338–1942⋆

Based on data collected at Subaru Telescope, which is operated
by the National Astronomical Observatory of Japan.
c 2013 RAS⃝† E-mail:
tomoki.saito@ipmu.jp
yuichi.matsuda@nao.ac.jp (YM)

(TS),

and

2

T. Saito et al.

1

INTRODUCTION

Galaxies are thought to form through accretion of baryonicmaterial (Pre-Galactic Medium, PGM) from their surrounding environment, which provides the cold gas necessary forthe star-formation process to proceed. The classical pictureof this accretion is that the PGM is immediately heated to
the virial temperature of the dark haloes (typically ∼ 106 K)
to form hot haloes (e.g. Rees & Ostriker 1977). Recent theoretical studies, in contrast, predict that cold gas accretes
in the form of cold flows (with temperatures of ≲ 105 K)
which penetrate the hot haloes surrounding the galaxies andwhich over cosmic time maintain the star-formation activity in galaxies (e.g. Kereš et al. 2005; Dekel et al. 2009). At
these low temperatures the gas in the PGM will predominantly cool via Ly α emission. The star-formation episodes
powered by this accretion in turn provide a stellar feedback
mechanisms which can then re-heat and eject material in theform of galactic-scale outflows (galactic winds: e.g. Veilleux
et al. 2005; Steidel et al. 2010), which subsequently interact
with the ambient material in the Circum-Galactic Medium(CGM). Hence both the accretion and outflows mean thatgalaxies interact with their surrounding environments, potentially resulting in extended Ly α emission either throughcold accretion of the PGM (e.g. Fardal et al. 2001; Dijkstra
et al. 2006; Dijkstra & Loeb 2009; Faucher-Giguére et al.
2010; Goerdt et al. 2010), or from galactic winds ejected into
CGM (e.g. Tenorio-Tagle et al. 1999; Taniguchi & Shioya
2000; Mori & Umemura 2006; Dijkstra & Kramer 2012).
Such Ly α nebulae may therefore reflect either the structureof the surrounding material, or gas circulation processes during the formation/evolution of these galaxies (Furlanetto etal. 2005).
The precise mechanisms responsible for forming Ly α
nebulae are still unclear. Some Ly α nebulae (e.g., those in
the SA 22 protocluster at z = 3.1) have been extensively
observed, and are thought to be driven by starburst eventsin massive galaxies forming galactic winds (e.g. Ohyama etal. 2003; Wilman et al. 2005; Matsuda et al. 2006; Geach etal. 2005; Geach et al. 2009; Uchimoto et al. 2008, 2012).
Moreover, recent surveys targeting Ly α “blobs” have alsosuggested a possible connection between their properties(specifically morphologies) and the environments they residein (Erb et al. 2011; Matsuda et al. 2011, 2012). Such an environmental dependence is also qualitatively consistent withthe observations of relatively isolated Ly α nebulae, which
may point to the possibility that these are accretion-driven(Nilsson et al. 2006; Smith & Jarvis 2007; Saito et al. 2008).
However, to determine the true significance of environment
in the formation of extended Ly α emission haloes, more detailed and systematic observations with suﬃcient depth andarea are essential.
It has been long known that powerful radio galaxies athigh redshifts are often associated with large, extended Ly α
nebulae (e.g. Chambers et al. 1990; Röttgering et al. 1995;
van Ojik et al. 1996, 1997; Venemans et al. 2007; VillarMartin et al. 2007). Although these Ly α nebulae appear
linked to the radio emission, their properties are similar
to the Ly α blobs described above. For example, the large
velocity widths exceeding ∼ 1000 km s−1 (van Ojik et al.
1997) or absorption across the full extent of the Ly α nebulae (Röttgering et al. 1995; van Ojik et al. 1996) are also

seen in the Ly α nebulae in protoclusters (e.g. Wilman etal. 2005; Matsuda et al. 2006). There appears to be a size
dependence of the Ly α nebulae on the size of radio sources(van Ojik et al. 1997), as well as a hint of environmental dependence on the size of the Ly α nebulae (Venemans et al.
2007). Even for those Ly α blobs not directly associated withradio sources, these are sometimes found to be harbouring
AGNs (e.g. Basu-Zych & Scharf 2004; Geach et al. 2009).
These results suggest that Ly α nebulae are common phenomena reflecting the interaction between massive galaxies
and their surrounding environments, regardless of the presence of AGNs. It is thus quite essential to probe the environments of Ly α nebulae with and without radio sources.
We have conducted a systematic, wide-field imaging observations of the environments around known giant Ly α
nebulae, as traced by Ly α emitters (LAEs). Here we present
the results from the imaging of the first target, the powerfulradio galaxy TN J1338–1942 (hereafter TNJ1338) locatedat z = 4.11 (De Breuck et al. 1999). This radio galaxy is
known to have a Ly α nebula extending up to ∼ 100 kpc withan asymmetric morphology (Venemans et al. 2002). It has
been suggested that this source is associated with a highly
overdense region traced by LAEs and Lyman break galaxies, and thus represents an ancestor of present-day clusters,i.e., a protocluster (Miley et al. 2004; Venemans et al. 2002,
2007; Intema et al. 2006; Overzier et al. 2008). Theoretical simulations also suggests that the overdensity associatedwith TNJ1338 is likely to be an ancestor of a present-day
cluster (Chiang et al. 2013). Multiwavelength observations
have shown that this source has radio lobes with an extent
of ∼ 70 kpc. (De Breuck et al. 2004; Venemans et al. 2007).
The extended Ly α nebula around this source has signaturesof star-formation induced by the radio jet, well outside thehost galaxy at radii of ∼ 20 kpc or more (Zirm et al. 2005).
Finally, Chandra X-ray observations indicate that there is
weak extended emission (∼ 30 kpc) which may arise frominverse-compton scattering of cosmic microwave backgroundor locally-produced far-infrared photons (Smail & Blundell2013).
Together these observations suggest a number of processes responsible for intense interaction between the central radio galaxy and the surrounding environment. However, due to the lack of the wide-field imaging data, thesurrounding environment of this radio galaxy is still not
well characterised. The existing LAE survey data cover asmall field (two 7′ × 7′ ) making it hard to map any overdensity, and there is no matched blank field observations whichmeans that even the magnitude of the overdensity is uncertain. (Venemans et al. (2007) used the Large-Area Lyman
Alpha (LALA) survey results (Rhoads et al. 2000; Dawson
et al. 2004) for the reference, which are taken with the diﬀerent telescope and instrument, targeting a slightly diﬀerent
redshift). Accordingly the relationship between the structure hosting the radio galaxy (and the protocluster) and thewider surrounding environment cannot be probed with theexisting data.
The goal of our study is to better quantify the environment of the powerful radio galaxy TNJ1338. To this end wehave obtained wide-field intermediate-band images to identify the LAEs lying at the redshift of the radio galaxy, andso quantify the environment using the LAE number density. The magnitude of the overdensity was determined fromc 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blob
Table 1. Summary of Observations
Filterλcent /∆λ a[Å/Å]Exposure Time
[sec]

m5σ b
[AB mag]

PSF c
[′′ ]

IA624
B
R
BRd

6226/302
4417/807
6533/1120
6226/1927

28800 (1800 × 16)
4800 (1200 × 4)
5940 (540 × 11)
–

26.94
26.87
26.92
26.90

0.74
0.80
0.55
0.74

a The central wavelength and FWHM of the filters.

b The 5σ limiting magnitudes within a 1.5′′ diameter aperture.
c The median PSF size (FWHM).
d The weighted mean of the B and R-band images.

comparison with a control sample taken from a blank field,
SXDS (Furusawa et al. 2008), at the same redshift and withthe same instrumental setup (Saito et al. 2006). This enables
us to probe “on what scale does a significant overdensity exist?”, i.e., the amplitude of the overdensity and the spatial
extent of the protocluster. We also compare our observations
with predictions derived from combing the Millennium Simulation (Springel et al. 2005) with a semi-analytical modelfor LAEs (Orsi et al. 2008). This allows us to estimate howrare is the overdensity found around the radio galaxy, andmore generally how well the simulation can reproduce suchenvironments. This is the first truly panoramic (∼ 30′ × 30′ )systematic and quantitative study of the environment of aradio galaxy field at z ∼ 4.
The rest of this paper is organized as follows: We introduce the data and observational details in §2. The procedure
to select LAEs from these data are presented in §3. In §4,
we compare the observed density field and luminosity function of LAEs in the radio galaxy field and the blank field,
and then compare the observations to the mock LAEs fromthe theoretical simulations. Throughout this paper, we use
the standard ΛCDM cosmology with ΩM = 0.3,ΩΛ = 0.7,
H0 = 100h = 70km s−1 Mpc−1 , unless otherwise noted. All
the magnitudes are in AB system (Oke 1974; Fukugita etal. 1995).

2
2.1

THE DATA
Subaru imaging data

We obtained 8.0 hours integration through theIA624 intermediate-band filter centred at (α, δ) =(13h 38m 13.9s , −19◦ 42′ 29′′ ) (J2000.0) on 2008 May 31 andJune 01 (UT) with Suprime-Cam (Miyazaki et al. 2002)
on the 8.2-m Subaru Telescope (Iye et al. 2004), under the
proposal ID S08A-072 (PI: Y. Matsuda). For the continuum
correction we obtained archival broad-band imaging in the
B and R-bands taken by Intema et al. (2006) from thearchive system SMOKA (Baba et al. 2002). Details of theobservations are summarized in Table 1. Suprime-Cam has
a pixel scale of 0′′ .202 and a field of view of 34′ × 27′ . Theintermediate-band filter, IA624, has a central wavelength of
6226Å and bandwidth of 302Å (FWHM), which corresponds
to the redshift range for Ly α at z = 3.996–4.245 (R23
IA filter system: Hayashino et al. 2000; Taniguchi 2004).
Fig. 1 shows the transmission curves of the IA624, B andc 2013 RAS, MNRAS 000, 1–17⃝

3

R-band filters, and the observed-frame wavelength of the
Ly α line at the redshift of TNJ1338 (z = 4.11).
The raw data were reduced with sdfred20080620(Yagi et al. 2002; Ouchi et al. 2004) and iraf. We flat-fieldedusing the median sky image after masking sources. We thensubtracted the sky background adopting a mesh size of 64
pixels (13′′ ) before combining the images. Photometric calibration was obtained from the spectroscopic standard stars,
PG1323−086, and PG1708+602 (Massey et al. 1988; Stone
1996). The magnitudes were corrected for Galactic extinction of E(B − V ) = 0.10 mag (Schlegel, Finkbeiner, & Davis
1998). The variation of the extinction in this field is suﬃciently small (±0.01 mag from peak to peak) that it does
not aﬀect our results.
The combined images were aligned and smoothed with
Gaussian kernels to match their PSF to a FWHM of 0′′ .74.
The PSF sizes for some exposures in the B band were notas good as the other bands (the median PSF size was 0.8′′ ),so that we removed these bad-seeing data, using only thefour best frames for our analysis. The total size of the field
analysed here is 32′ ×24′ after the removal of low-S/N regions
near the edges of the images. We also masked out the haloesof the bright stars within the field, resulting in the eﬀective
area of 689 arcmin2 in total. This corresponds to a comoving
volume of 1.7 × 105 h−3 Mpc3 at z = 4.1, covering a radial
comoving distance of 160.5 h−1 Mpc for sources with Ly αemission lying within the wavelength coverage of the IA624
filter.
The blank-field data used for the control sample were taken as part of the Subaru/XMM-Newton
Deep Survey (SXDS) project (Furusawa et al. 2008)
and a subsequent intermediate-band survey (Saito et al.
2006). The SXDS field consists of five pointings, centred at (α, δ) = (02h 18m 00.0s , −5◦ 00′ 00.0′′ ) (J2000).
The intermediate-band (including IA624) data were taken
only in the south field (SXDS-S) centred at (α, δ) =(02h 18m 00.0s , −5◦ 25′ 00.0′′ ) (J2000). The data were takenwith the same instrument on the same telescope, and reduced in the same manner with the same software as our
TNJ1338 observations. The PSF was matched to 0′′ .78(FWHM), and the 5σ limiting magnitudes are 26.60, 27.42
and 27.91 for the IA624, B and R, respectively. After masking out the regions near the edges and bright stars, the total
area coverage was 691 arcmin2 , which is almost the same as
the TNJ1338 field.
2.2

Mock catalogue of Ly α emitters

In order to compare the observations with the predictions
from a cosmological N -body simulation (Millennium Simulation: Springel et al. 2005), we exploited a LAE catalogue
generated with a semi-analytical model of galaxy formation (GALFORM Cole et al. 2000; Le Delliou et al. 2005,
2006). This catalogue contains ∼ 106 LAEs with a wide
range of luminosity and the Ly α equivalent widths (EWs).
The details of this catalogue are described in Orsi et al.
(2008). The LAEs in this catalogue were generated by placing model galaxies into dark haloes of masses above thethreshold value appropriate for the simulation’s mass resolution. The star-formation history for each halo was calculated by using a Monte-Carlo merger tree. The IMF wasassumed to be top heavy for those stars formed during any

T. Saito et al.
Redshift for Lyα
3.0
3.5
4.0
4.2
4.4

2.5
4.0

0.6

2.0

Transmission
0.2
0.4

6000

B

4000

4.5

5.0

6500

IA624

4

4500

5000 5500 6000
Wavelength [Å]

R

6500

7000

7500

where λB and λR are the central wavelengths of B and R
bands, respectively, and the λLyα,obs is the observed-frame
wavelength of the Ly α line at z = 4.11. The source detection and photometry were made using the source- detection
and classification tool, SExtractor (Bertin & Arnouts 1996).
The sources detected here have at least five connected pixels above a threshold corresponding to 1.5σ of the sky noise.
Using the position of these sources detected in the IA624 image, photometry was measured in the other bands with thesame aperture, after matching the PSF size. We measured
photometry for a total of 205,011 sources, after masking.
Based on the photometry catalogue from these three
images (B, R, and IA624), we selected the LAE candidates
at z ≃ 4.1 by applying the following conditions.
20 < IA624 < 26.6

Figure 1. The response curves of our filters. The transmissionof the filters are plotted against the wavelength. The lower axis
shows the observed wavelength, and the upper axis gives the corresponding redshift for Ly α line. The thick black curve shows
the intermediate-band filter (IA624) used to select sources with
Ly α emission. The two broadband filters (B and R) are shownwith thin lines. The thick magenta curve shows a model SED ofa star-forming galaxy created with GALAXEV (Bruzual & Charlot 2003) with a Gaussian-profile Ly α emission line, redshifted toz = 4.1. The box in the upper-left shows a close-up view of theIA624 filter transmission, together with the redshift of TNJ1338
indicated with a vertical thick bar.

starbursts, dN/d ln(m) ∝ m−x with x = 0, with a standard
solar neighbourhood IMF (Kennicut 1983) for those stars
which quiescently form in discs, i.e. x = 0.4 for m < 1M⊙
and x = 1.5 for m > 1M⊙ . Both IMFs covers the stellarmass range 0.15 M⊙ < m < 125 M⊙ . The Ly α line luminosity is then calculated from the number of ionising photons
emitted by the corresponding stellar population.
Orsi et al. (2008) compared the properties of model
LAEs from their simulation with existing LAE surveys andshowed that both the luminosity function (LF) and the clustering properties are broadly consistent with the observations. The number density of model LAEs in the luminosity
range of ∼ 1042.5 –1043 erg s−1 are slightly higher than observed in the SXDS at z = 3.1, but slightly below the SXDS
at z = 5.7. The diﬀerence is up to ∼ 0.5 dex, so that the accuracy of the model prediction for the LFs should be around∼ ±0.5 dex. From this catalogue we selected LAEs using
similar colour constraints to those applied to the observed
data, see §3 for details of the selection procedure.

3
3.1

SAMPLE SELECTION
The TNJ1338 field sample

We used the IA624 image for detection, and the wavelengthweighted mean of B and R band images (hereafter BR) to
determine the continuum level at a rest-frame wavelength of1216Å. The BR image was generated by combining the two
images with:BR =(λLyα,obs − λB )R + (λR − λLyα,obs )B
λR − λB(1)

BR − IA624 > 0.3(2)

B > 27.87, or, B − R > 2.17

(3)

BR − IA624 > (BR − IA624 )4σ(4)We first applied the magnitude cut (eq. 1) to remove brightforeground contaminants (IA624 > 20) and a faint limit
to remove false detections (IA624 > 5σ). Note that the
5σ threshold here is set according to the SXDS data, not
the TNJ1338 data, in order to make a fair comparison withthe control sample obtained in the SXDS field. The brightthreshold, 20 mag, was determined from visual inspectionof the sources. This value roughly corresponds to Ly α luminosities corresponding to the brightest high-redshift radiogalaxies (e.g., De Breuck et al. 2001; Reuland et al. 2003).
Eq. 2 selects those sources with Ly α excess in the intermediate band filter, corresponding to an equivalent widthof ≳ 200Å (≳ 40Å in the rest frame). Then we applieda colour selection designed to detect the Lyman-break atz ∼ 4 (eq. 3). Finally, eq. 4 requires that the IA624 excess
has a significance level of at least 4σ. Note that we used the
BR matched-continuum to estimate the IA624 excess, although the B band should detect almost no flux from z ∼ 4sources because the wavelength coverage of the B band ismostly below the Lyman limit. However, the distribution of
the R − IA624 colour is not centred at zero, so that defining
IA624-excess sources using just the R-band continuum levelis somewhat unclear. We thus used the BR to measure thecontinuum levels.
Fig. 2 shows the colour-magnitude diagram used for our
LAE selection. We need to be aware of the possible contamination due to the noise in the IA624 excess measurements: the LAEs should lie well above the scatter aroundBR − IA614 = 0. For some cases, i.e., when the IA624 isrelatively shallow, false detections may dominate sources selected at the 3σ level. We carefully visual inspected all thesources selected here, and we found one source that is obviously aﬀected by bad regions of the CCD. This source is ina region aﬀected by a neighbouring bright source. Excluding
this, we constructed a sample of 32 LAEs in the TNJ1338
field.
Fig. 3 shows the sky distribution of the LAEs selected
above, overlaid on the IA624 image. The reader should notethe apparent “void” around the north-western part of the
field, where relatively few LAEs are detected, and does notseem to be an artifact of the bright stars.
c 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blob
3

TNJ1338-1942

BR - IA624

2colour distribution. We derived the colour oﬀset necessary
to force the centre of the colour distribution to zero within
the magnitude range 20 < IA624 < 26.60. Except for applying this colour term, we employed exactly the same colour
constraints to select the LAEs in this field. The total numberof sources identified is 34. The colour-magnitude diagram forthis sample is shown in Fig. 2 together with the TNJ1338
sample.

SXDS
BR-IA624=4σ
BR-IA624=0.3
IA624=5σRadio Galaxy

5

1

0

3.3
20

22

24

26

20
IA624

22

24

26

Figure 2. Colour-magnitude diagram. BR − IA624 colour as afunction of IA624 magnitude for the TNJ1338 field. (Left) The
black dots show all the sources, and the red triangles show 4σexcess LAE candidates. The vertical grey dashed line shows themagnitude cut (IA624 > 26.6), the horizontal magenta dashedline indicates the BR − IA624 > 0.3 threshold. The red dashedcurves show 4σ level of the IA624 excess. (Right) Same as the left
panel, but for the SXDS blank field.

E
N
Figure 3. The sky distribution of our LAEs in the TNJ1338
field. The symbols for our photometrically-selected LAE sample
are the same as Fig. 2, and the position of TNJ1338 is shownwith the cyan box. The background is the IA624 image takenwith Suprime-Cam. East is up, and north is to the right

3.2

The control sample in SXDS field

We constructed a control sample of LAEs, using similar
imaging data in a blank field (the SXDS-S field, hereafter
SXDS). These data were taken with the same instrument
and filters as used in the TNJ1338 observations as noted
above, and the field is not biased to any known overdense
regions at z ∼ 4. In order to make a fair comparison between
the two fields, we defined the colour constraints based on
the shallower data of the two, i.e., 5σ limiting magnitudes
are assumed to be IA624 = 26.60 mag, R = 26.94 mag,and B = 26.87 mag. We also corrected for the oﬀset of
BR − IA624 colour distribution for the SXDS field, presumably due to an error in the magnitude zero point. We thenapplied a colour term ∆(BR − IA624 ) = 0.15. This colour
term was estimated by fitting a Gaussian function to thec 2013 RAS, MNRAS 000, 1–17⃝

The mock LAE sample

In order to make a meaningful comparison between the observations and the simulation, we selected LAEs from themock LAE catalogue at z = 4.17 described in §2, which is
the output redshift closest to that of TNJ1338. We used thepredicted Ly α fluxes and EWs contained in the catalogue, tocalculate the colours and magnitudes of the LAEs. Note thatthe catalogue contains z = 4.17 LAEs, while we are going toconstrain the observed (apparent) colours of z ≈ 4.11±0.12.
However, the diﬀerence between these two epochs is verysmall, ∼ 55 Myr, and z = 4.17 is well within the coverage of
the IA624 filter. We thus calculated the apparent (observed)
colours at z = 4.11. This should be a reasonable assumption
to compare the simulated LAEs with the observations, since
the timescale of galaxy evolution (e.g., star formation) ismuch longer than this diﬀerence.
We first calculated the absorption of the UV continuum
by the intervening IGM, following the formalism of Madau(1995). Here the UV continuum was assumed to be flat interms of flux density per unit frequency bin, fν = Const.
The flux density was obtained by dividing the Ly α flux by
EW (observed), fλ = F (Lyα)/Wobs . Then the IGM absorption was calculated by assuming the redshift of z = 4.11 toobtain the continuum component of the spectrum expected
at the redshift of the radio galaxy. The UV continuum contribution to the photometry was calculated by convolving
the flat-continuum spectrum with the filter response curves.
The IGM absorption on the Ly α line is included in the escape fraction, fesc used in generating the mock catalogue of
LAEs (see Orsi et al. 2008). Then suﬃciently narrow line
profiles (i.e., narrower than the IA624 passband) was convolved with the filter response curves, and the line contribution to the photometry was obtained.
Adding the contributions from both the Ly α line andthe UV continuum, we calculated the R- and IA624 band
magnitudes to apply the colour constraints. Since our calculation gives exactly the same continuum colour for all
sources, we did not apply the constraints on the B−R colour.
This does not aﬀect our results because the mock LAE catalogue does not contain any foreground contamination. Furthermore, the B-band magnitude cannot be predicted fromour calculation with suﬃcient reliability, because we are assuming a very simple IGM absorption model. Since the BR
magnitude used for the observed data is almost the same as
R for high-redshift sources, we thus used the R-band magnitudes, instead of the BR. The colour constraints for themock LAE sample are thus:
20 < IA624 < 26.6

(5)

R − IA624 > 0.3(6)

R − IA624 > (BR − IA624 )4σ .

(7)

6

T. Saito et al.

For the significance level of the IA624 excess, (BR −IA624 )4σ , the same value as in eq. 4 was used to match theobserved sample. For the comparison with the observed samples, we applied the magnitude cut of IA624 < 26.6 for eq. 5,
and the observed IA624-excess threshold of (BR−IA624 )4σ .
In total we select 30,012 model LAE sources in a comoving
volume corresponding to (500 h−1 Mpc)3 .

Table 2. Statistics of the observed density field
Field
TNJ1338SXDS

Mean a[h2 Mpc−2 ]0.02090.0204

10

Percentiles b
25
50
75

90

0.05
0.40

0.44
0.66

1.90
1.68

0.95
0.97

1.32
1.29

Gc
0.415
0.268

a Mean surface density over the field in comoving scale.

4

RESULTS AND DISCUSSION

4.1

Density field

4.1.1

The high density region around the radio galaxy

We quantified the diﬀerence between the TNJ1338 and
SXDS fields by constructing their LAE surface density maps.
We smoothed the spatial distribution of the LAEs with aGaussian kernel with a radius (half width at half maximum, HWHM) of 4 h−1 Mpc (projected comoving distanceat z = 4.1), and counted the number of LAEs within thesame radius at each grid point, with a grid spacing of
0.5 h−1 Mpc. Then the surface density was obtained by dividing the number by the area of the Gaussian aperture
with the HWHM of 4 h−1 Mpc. In deriving the average surface density, the areas within 5 h−1 Mpc of the edge of the
FoV were flagged to avoid underestimating the surface density near the field edges. The kernel size was chosen based on
the typical separation between the sources. We measured the
distance to the nearest source for each LAE in our sample,
and chose the smoothing kernel size to include ∼ 68 percentof the whole sample. We confirmed that diﬀerent sizes of thesmoothing kernel also give a similar density distribution.
The density maps we obtained are shown in the Fig. 4.
We can clearly see that the region around the radio galaxy
is strongly overdense, and equivalently strong density peaks
are not seen in the SXDS field. The density peak in the
TNJ1338 field is ≳ 4 times the density averaged over thefield (1 + δLAE = 4.13 when the density is normalised withthe average within the field), while the maximum peak in
the SXDS field is only 1 + δLAE = 2.36. We then estimatedthe uncertainty of the density with this smoothing scale bycomputing the standard deviation of the density map of the
SXDS field, determing the 1σ dispersion in δLAE as 0.47.
The radio galaxy TNJ1338 is located in the densest region
in the field, with 1 + δLAE = 3.46 at its position. The peakdensity is 1 + δLAE = 4.13, located 2.57 h−1 Mpc oﬀset fromthe position of the radio galaxy. This overdensity can betraced on ∼ 10–20 h−1 Mpc scales around the radio galaxy.
Outside this region, in contrast, the density appears to drop
quite rapidly: on the northwestern side of the field there isa strongly underdense region just ∼ 20 h−1 Mpc from thedensity peak. Such a strong variation in the density of LAEs
is not seen in the SXDS field. Although the overdensity of
the TNJ1338 field had previously been suggested by Venemans et al. (2002), their FoV was much smaller than ours,
and they were forced to estimate the overdensity (a factorof ∼ 3–5) through comparison to a separate field survey ata similar redshift (Rhoads et al. 2000). With our wide-fieldimaging of this field, we have not only confirmed the overdensity by comparing with an identically-observed control
field, but have also determined the spatial scale and structure of the overdense region.

b In units of the normalized density (1 + δ
LAE ).
c Gini coeﬃcient of the density distribution.

The diﬀerence between the TNJ1338 field and SXDS
control field becomes clearer when comparing their density
histograms, as shown in Fig. 5. In the SXDS field the distribution is concentrated near the average value, while the
TNJ1338 field shows a much broader distribution extending
toward both high- and low densities. In order to quantify
the diﬀerence between the distributions in these two fields,
we first compared the 10- and 90 percentiles for the density
maps of the two fields. The upper panel of Fig. 5 shows the
cumulative density distributions for the two fields, together
with the percentiles. The statistics of the two fields are also
summarised in Table 2. The TNJ1338 field has a wider density distribution compared with the SXDS field, especiallyat the lower-density end. The 10 percentile for the TNJ1338
field is 1 + δLAE = 0.05, which is 80 times lower than thatof the SXDS field. The ratios of the two percentiles, i.e.,the dynamic range of the density, for the TNJ1338 and the
SXDS fields are 38 and 4.2, respectively. The TNJ1338 field
has thus nearly an order of magnitude higher range in galaxy
density than that seen in the SXDS field. The diﬀerence becomes even more obvious when we look into the highest- andthe lowest-density bins: e.g., 1 + δLAE < 0.01 corresponds tothe lowest 2 percent of density cells in the TNJ1338 field,
while in the SXDS field only ∼ 0.04 percent of the total grid
points have such a low density.
A useful statistic to quantify the range of the density
distribution is the Gini coeﬃcient of the density field. The
Gini coeﬃcient, G, measures how uniformly LAEs are distributed within the field, and takes a value of 0 < G < 1.
The G value corresponds to the area surrounded by the two
Lorentz curves corresponds to the given distribution and
G = 0 (shown in Fig. 5). If all the LAEs are concentrated
within one grid point, then G is unity. If the LAEs are distributed uniformly over the field, then G is zero. The Lorentz
plot shown in Fig. 5 clearly shows that the TNJ1338 field
has much higher G than the SXDS blank field, and the blankfield agrees well with the simulation. The Gini coeﬃcientsof the density maps were calculated to be 0.415 (0.268) for
the TNJ1338 (SXDS) field. This diﬀerence shows that theLAEs are more concentrated into high-density regions (especially into the high-density peak around the radio galaxy)in the TNJ1338 field, compared with the SXDS field. Together these statistics suggest that the galaxy density in
the TNJ1338 field traced with LAEs is highly concentrated
within the high-density region near the radio galaxy, butthat there are also unusually low-density regions in the field
where the number of LAEs is highly suppressed. This is quite
diﬀerent from the density field in the SXDS field.
c 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blob
TN J1338-1942

7

SXDS

N

E
N

5 h−1 Mpc

Simulation(maximum density)

5 h−1 Mpc

W

5 h−1 Mpc

Simulation(maximum Gini)

5 h−1 Mpc

Figure 4. A comparison of the density field of LAEs. The top panels are the observed density map of the TNJ1338 field (left), and the
SXDS field (right). The position of the radio galaxy TNJ1338 is shown with the blue cross mark near the density peak. The bottom
panels are simulated density maps generated from the mock LAE catalogue using the same selection as those applied to the observed
data, showing the same FoV centred on density peaks which are higher than that measured at the position of the radio galaxy: the fieldaround the maximum density peak (left) and the field with the highest Gini coeﬃcient (right). Each panel shows the 50 × 38 h−2 Mpc2
(comoving) field. The contour interval is 0.5× the average density, with a lowest contour of 0.5 (δLAE = −0.5, 0.0, 0.5, 1.0, . . .). The thickblue contour traces the average density over the field (δLAE = 0.0). The cyan diamonds mark the positions of LAEs, and the sizes ofthese symbols represent the Ly α luminosities. The sources with log(LLyα [h2 erg s−1 ]) ≳ 43.8 are marked with filled symbols.

4.1.2

Density contrast within the TNJ1338 field

Although the TNJ1338 field has a very large dynamic range
in LAE density, the average density of this field over the FoVof Suprime-Cam is still almost the same as that of the SXDS
field. The average surface density of LAEs for these two fields
are 0.0209 h2 Mpc−2 and 0.0204 h2 Mpc−2 for the TNJ1338
and the SXDS field, respectively. This suggests that the density traced by LAEs is almost uniform within 2.5 percent at∼ 50 h−1 Mpc scales, when the density field is averaged over
∼ 160 Mpc along the line of sight (both in comoving scale).
Even with this smoothing, there is a significant overdensity
around the radio galaxy, and a similarly significant underdense region just adjacent to it. This “void” region next tothe high-density region correspond to the peak of the density distribution near zero in the histogram (Fig. 5). The
shape of this distribution is quite diﬀerent from that for the
SXDS field.
Due to the limited number of sources, ∼ 30 in eachfield, it is not clear whether the underdense region is truly
a void. However, the detectable (i.e., bright and large-EW)
c 2013 RAS, MNRAS 000, 1–17⃝

LAEs were not found in this region, especially in the northwestern quarter of the field. This appears to be a real eﬀectsince there are no bright stars in this region that would
significantly aﬀect the detection and photometry, as seen in
the Fig. 3. Such a large underdense region is not seen in the
SXDS field, again showing that this radio galaxy field has
an unusually high density contrast. The real density contrast
in this radio galaxy field is possibly higher than estimated,since we are smoothing the spatial distribution along the lineof sight as a result of the relatively wide redshift coverageof the IA624 filter. Although the apparent contrast would
be enhanced due to the redshift-space distortion if the highdensity region is actively accreting the material, such aneﬀect is thought to be small because of the wide redshift
coverage.
Such a large density contrast within a single field suggests that the high-density region around the radio galaxy
is attracting material from well within the scale of theSuprime-Cam FoV (38 × 50 h−2 comoving Mpc2 on the sky,when the edges are flagged out), because the average density

T. Saito et al.
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Figure 5. The statistics for the LAE surface density distribution. (Left) A comparison of the LAE surface density distributions for thetwo fields. The red hatched and the blue filled histograms show the density distribution for the TNJ1338 field and the SXDS control field,
respectively. Overplotted with the thick green line is the histogram for the simulated density map obtained from the mock LAE sample.
The vertical black dot-dashed line shows the density calculated at the position of the radio galaxy. The cumulative distributions areshown on the top panel. The red, blue and green lines denote the TNJ1338 , the SXDS and the simulated map, respectively. The 10-th
and 90-th percentiles are shown with the vertical dashed lines with the corresponding colours. We can see that the density distribution in
the TNJ1338 field is much wider than that in the SXDS. The simulated density distribution is closer to the SXDS than to the TNJ1338
field. (Right) Lorentz curves for the density distribution. The normalised cumulative distribution is plotted against the normalised
number of the grid points. The red, blue and green curves show the TNJ1338, the SXDS and the simulated map, respectively. Again thesimulated distribution is closer to that of the SXDS field rather than the TNJ1338 field. The grey curves denote the 25 fields centred
at the high-density peaks found in §4.3.1. The “G478” field shown with the cyan dashed curve is one of the 25 high-density fields withexceptionally high Gini coeﬃcient, G = 0.478. Except this G478 field, the TNJ1338 field has much higher G than any high-density fields
found in the simulation.

is almost the same as the blank field. If LAEs are tracing
the matter distribution, then the surrounding dark haloes
within this scale should have been merging into this overdensity. Since we do not have spectroscopic data for all thesources, we cannot draw any clear conclusions on the true
spatial structure of the overdensity based solely on our current observations: it is not clear whether the density peak
represents a single extremely overdense halo, or a less overdense filamentary structure elongated toward the line ofsight (the latter case includes the case that two or moreclumps are aligned along the line of sight). Nevertheless, thedensity contrast must have grown to a level high enoughto form such a high density peak and a large void region.
Even for the latter case, the high-density filament must haveaccreted material from its surroundings and grown to a suﬃcient length to evacuate the void region. Hence in both cases,
the spatial extent of the high-density region should be fairly
compact (or the filament should be narrow), as the TNJ1338
field shows a large void fraction and the high-density region
extends only up to ∼ 20 h−1 comoving Mpc scales.
This requires that matter is concentrated into a highdensity region of ∼ 10–20 h−1 Mpc (comoving) size, wellbefore the observed epoch of z ∼ 4.1. Such a concentration should aﬀect the star-formation and AGN activity ofgalaxies within the overdensity, in the form of, e.g., frequentgalaxy mergers. This may therefore lead to an excess of massive galaxies harbouring active star-formation and/or AGN
activity. The corresponding high matter concentration will
also lead to a higher rate of gas accretion from the surrounding environment, again resulting in the enhancementof star-formation and AGN activity.

4.2

Luminosity function

4.2.1

Comparison with the blank field

As described above, we have found that the TNJ1338 field
has a high density region around the radio galaxy, and astrong density contrast between this and the large void region just adjacent to the peak. To investigate the variation in the LAE LF Fig. 6 compares the Ly α LFs of theLAEs in the TNJ1338 and the SXDS fields. We can seethat the faint-end slope of the LF in the TNJ1338 field
is shallower than the SXDS, below a Ly α luminosity ofc 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α bloblog(LLyα [h2 erg s−1 ]) ∼ 43.6. On the other hand, the LF
in the SXDS field increases nearly monotonically down to
our completeness limit, log LLyα ∼ 43.1 (corresponding tolog LLyα ∼ 42.8 assuming h = 0.7), as the L∗ is still slightly
below the faintest data point (Ouchi et al. 2008, hereafterO08). In the TNJ1338 field, a similar trend can be seen in
the LF for LAEs within the overdense region. We plotted
the LF of the subsample of LAEs lying within regions withdensities higher than the average of the whole Suprime-Cam
field (δLAE ⩾ 0). The faint end of this LF agrees with thatof the SXDS field, but has higher values than in the SXDS
by up to an order of magnitude. Note that the radio galaxy
itself (log LLyα ≈ 45.0) is excluded in the LFs plotted here.
The LAE population in the TNJ1338 field is thus thought tobe highly biased to bright sources, and the fraction of faintLAEs is reduced in this field. The shape of the bright end
may suggest that our LAE sample consists of two diﬀerent
components, e.g., star-forming galaxies dominating the faintend, and AGN hosts dominating the bright end.
We have also compared the SXDS control sample with anarrowband-selected LAE sample at a similar redshift in thesame field, to check the reliability of our control sample. The
LF of the SXDS control sample agrees quite well with the LF
of the narrowband-selected LAE sample at z ≃ 3.7 (O08),
down to the completeness limit (log(LLyα ) ∼ 43.1). Since
the bandpass of the IA624 filter is several times larger thanthe NB570 narrowband filter, the survey volume is comparable to that of O08, even with only one FoV of Suprime-Cam.
This reduces the field-to-field variance, as the density fluctuations are smoothed out along the line of sight. Thus we
confirmed that our SXDS sample is a valid control sample
in terms of LF, representing the typical number density ofLAEs at z ∼ 4. The LF in the TNJ1338 field, on the other
hand, lies beyond the variance expected from the results of
O08. At the brightest end of the LF, log LLyα ≳ 44, we did
not find any sources in the SXDS field, while we still foundsources in the TNJ1338 field even when we exclude the radiogalaxy itself. Such bright sources are almost never seen inblank-field surveys for LAEs at similar redshifts (Dawson etal. 2007; Ouchi et al. 2008).
These results reinforce the idea that the TNJ1338 field
is unusual, not only in terms of the overdensity of LAEs,
but also the Ly α LF. Since our IA624 data is deeper in the
TNJ1338 field than in the SXDS field, this should not be
due to the diﬀerence in the completeness. We mentioned in§4.1.2 that the density contrast in this field implies that thehigh-density region is accreting material from well within∼ 50 h−1 Mpc scale. At this scale, such accumulation of thematerial is likely to be aﬀecting the star-formation activity in galaxies and hence galaxy formation and evolution,
leading to a change in the LF. This suggestion is also supported by comparing the UV LFs of these two fields (Fig. 6
right). The UV LF of the TNJ1338 field shows significant
enhancement at the very bright end (MUV ≲ 22.7), while at
MUV ≳ 21.5 the number of galaxies is relatively suppressed.
If we derive the UV LF from LAEs only within the overdense regions, the faint end of the LF appears to agree withthat in the SXDS field within the errors.
We should note that the samples in both the TNJ1338
and SXDS fields have relatively low completeness at the faintend. Our LAEs are selected based on the intermediate-band
filter images, so that the samples are biased to sources withc 2013 RAS, MNRAS 000, 1–17⃝

9large EWs. This results in a relative faintness of the UV
continuum in these systems. Indeed, about half of the both
samples have very faint UV continua, often below 3σ, andas a result the UV LFs shown in Fig. 6 are based on 14 and19 sources for the TNJ1338 and SXDS fields, respectively.
As a result the size of the magnitude bins is large (2 mags)
and the shape of the LFs are thus heavily smoothed. However, the two data points of the SXDS control sample at
MUV ≲ −21 show fairly consistent values with the z ∼ 3.7
SXDS sample of O08, so that we can make a meaningfulcomparison between the two fields in this luminosity range.
Within this range, the bright-end shape of the UV LF ismuch flatter than that in the SXDS field, which is a similar
trend to that seen in the Ly α LF, although the errors arelarge. The shape of the UV LF in this field is very flat, andapparently not Schechter-like at this luminosity range. The
formation of actively star-forming galaxies, as well as AGNs,
are thus likely to be enhanced in the TNJ1338 field, whichhost the extremely high-density region.
4.2.2

Implications for galaxy formation

The high-density region around the radio galaxy is so unusual that it faces the large void region. The material originally in the void region must have moved into the surroundings by the epoch of z ≃ 4.1, and among the “surroundings”,
the high-density region around the radio galaxy is the mostprominent peak. This suggests that some large fraction of
the material originally in the void region may have travelled to the vicinity of the radio galaxy. Then, how well canthis scenario account for such a high density contrast as wefound? We made a rough estimate to test this scenario. The
separation between the density peak and the void regionis 15 − 20 h−1 Mpc in comoving scale, which corresponds to∼ 4 − 6 Mpc in physical scale at z = 4.1. If the material
travelled this distance within a Hubble time at this redshift,
the velocity is required to be ∼ 4 − 6 × 102 km s−1 . This isaltough a very naive estimate, as is just the velocity required
to travel linearly from the centre of the void to the density
peak. In terms of the void evolution, the required velocity
is slightly smaller: the apparent radius of the completely
empty void is r ∼ 2 − 3 Mpc, leading to the peculiar velocity
at the edge of the void is around 13 H(t)r ∼ 2−3×102 km s−1 .
These values are well below the typical velocity dispersionof the present-day (virialised) galaxy clusters. Although therequired peculiar velocity may be larger than this because
the distance assumed here is just the projected distance,
the high-density region can be to some extent responsible
for accreting the material initially in the void region.
It is however quite unlikely that all of the material initially in the large void had been simply accreted onto thehigh-density region by the epoch of z ≃ 4.1. The material
should in principle flow out in all directions from the centre,
so that the single overdense region cannot be fully responsible for the formation of the void. The simplest interpretation
for the observed (apparent) density contrast is that the initial density fluctuation is quite large, and the contrast had
existed since an epoch well before z ≃ 4.1. Another interpretation is the enhancement of star-formation activity within
overdense regions (e.g. Steidel et al. 2005; Koyama et al.
2013), leading to the enhancement of actively star-forming
galaxies possibly dominating the bright end of the LF. This

10

T. Saito et al.
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SFR [h2Msunyr−1]

100

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log(n [h3 Mpc−3mag−1])log( nLAE [h3 Mpc−3 dex−1] )

−3.0
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mock (whole)
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−5.0
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TN J1338−1942
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43.6
43.8
44.0
log( L Lya [h2 erg s −1] )

44.2

−19

−20

−21
MUV [mag]

−22

−23

Figure 6. (Left) The Ly α luminosity function (LF) of the observed samples of LAEs. The red triangles show the LF of the total LAE
sample in the TNJ1338 field. The subsample lying within the overdense regions (higher than the average of the field) is shown with theorange diamonds. The blue squares denotes the SXDS control sample. The black circles shows the LF of z ≃ 3.7 LAEs in the SXDS field,
taken with a narrowband filter (Ouchi et al. 2008). The green diamonds show the LF of the mock LAE catalogue by Orsi et al. (2008),
and the grey lines show the LF derived from the subsample of the mock LAEs residing within the Suprime-Cam-sized fields centred
at the positions of 25 highest-density peaks. The radio galaxy TNJ1338 is omitted to show the luminosity range of the normal LAEs.
Note that the data points are slightly shifted to improve the visibility. We can see that the number of bright LAEs is enhanced in theradio-galaxy field, and the fraction of the faint LAEs is reduced. The LF within the overdense regions has almost the same shape as thatwithin the whole field, but the absolute number density agrees with that in the SXDS at a luminosity of log(LLyα [h−2 erg s−1 ]) ∼ 43.3.
(Right) UV luminosity functions. The symbols are same as the left panel. The LF for the LAEs in our field appear to be enhanced at
the bright end, while being relatively suppressed at the faint end. Note that the lowest luminosity bin shown here has low completeness.
The mock sample is not shown here since the UV LF is still not well calibrated with Ly α-selected galaxies.

may result in a drastic enhancement of the galaxy bias forbright sources. The excess of extreme starbursts within protoclusters found in some observational studies (e.g. Blain etal. 2004; Capak et al. 2011; Ivison et al. 2013) is consistent
with this idea. Because of the lack of spectroscopic data, wecannot discriminate between star-formation and AGN activities. It is thus also possible that AGNs are dominating thebright end of the LF, which is highly enhanced in the radiogalaxy field. Such an enhancement of AGN activity in overdense environments has been found observationally in somecases (e.g. Pentericci et al. 2002; Croft et al. 2005; Lehmer
et al. 2009; Digby-North et al. 2010). Since our samples are
relatively biased to bright LAEs, such eﬀects will enhance
the apparent density contrast.
The diﬀerence between the LFs in the two fields depends strongly on the luminosity. When we examine the LF
for the overdense regions in the TNJ1338 field, the diﬀerence for the luminosity range log LLyα ≳ 43.6 (corresponding to the brightest two data points for the SXDS field:≳ 43.3 if h = 0.7 is assumed) is about an order of magnitude. This luminosity range contains 17 sources for the
TNJ1338 field (all in the overdense regions), while only 7 lie
within this range in the SXDS field. On the other hand, both
LFs agree with each other within their error bars (factor of∼ 1.6) at log LLyα ∼ 43.3. The diﬀerence in the faintest
data point roughly corresponds to the diﬀerence in the total
number density for the two fields (the whole SXDS field andthe overdense region of the TNJ1338 field). We estimatedthat the mean density within the overdense regions shown
here is ∼ 1.6 times the average of the SXDS, correspondingto δLAE ∼ 0.6. Since the LF for the overdense regions in

TNJ1338 exceeds the LF in the SXDS field by an order ofmagnitude on the bright end, the overdensity of the bright(log LLyα ∼ 43.9) LAEs is δLAE ∼ 5 or so. This means that,
if we assume the galaxy bias for LAEs at log LLyα ∼ 43 to
be b ∼ 2.4 − 4 (e.g. Ouchi et al. 2005, 2010; Kovač et al.
2007; Chiang et al. 2013), and the faint LAEs are correctly
tracing the matter density of this field, the bias for brighter
LAEs must be b ∼ 20 − 40.
Such a strong luminosity dependence of the bias seems
to be rather diﬀerent from the prediction of the model of Orsiet al. (2008), which predicted only a modest dependence ofbias on LAE luminosity. This may suggest that the brightend of the LF is dominated by populations other than thenormal star-forming galaxies included in that model, suchas hosts of AGN or AGN-induced star-formation activities.
However, it is still not clear if this result is truly against
the prediction. The bias measurement of Orsi et al. (2008)
is based on clustering on large scale, so that the results are
diﬀerent from ours. Furthermore, their Fig. 6 shows large
uncertainty on the bias at the very bright end of the model
LAEs, log LLyα ∼ 43 − 43.3, and it is still possible that thebias of such bright LAEs depends strongly on the luminosity,
even for the model LAEs. Orsi et al. (2008) did not present
predictions of the clustering bias for LAEs brighter thanlog LLyα ∼ 43.3, because their simulation did not containenough such LAEs for an accurate measurement on large
scales.
We here showed only the simplest estimate of the galaxybias, since we are heavily aﬀected by small number statistics
due to having only ∼ 30 LAEs in each field. We cannot
probe the scale-dependence of the galaxy bias either: the bias
c 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blob

Comparison with the mock catalogue

4.3.1

Density field of the whole simulated map

We compared the density field shown in §4.1 with the mock
LAE sample, and evaluated the density distributions of
the TNJ1338 field, as well as the control field. The simulated density maps are obtained by applying the same
analyses to the mock LAE catalogue described in §3.3. We
used the same smoothing radius, 4 h−1 comoving Mpc, inthis process. The simulation covers a comoving volume of(500 h−1 Mpc)3 . Our IA624 filter covers a radial comoving
distance of ≈ 160 h−1 Mpc, so that we can obtain three independent slices perpendicular to the line of sight to create
mock sky distributions of LAEs. After selecting the LAEs
with similar colour constraints to the observed samples, we
extracted the LAEs within a slice of thickness (distancealong z-axis of the simulation box) of 160.5 h−1 Mpc, andprojected them onto the xy-plane. In this process we took account of the eﬀect of redshift-space distortions. The redshiftspace coordinates were computed by taking the z axis as theline-of-sight direction, adopting the distant observer approximation. We then smoothed the spatial distribution of LAEs
projected on the xy-plane, and counted the LAEs within asmoothing radius centred at each grid point. The simulated
LAE density map covers ∼ 100 times larger area for eachslice than a single pointing of the Suprime-Cam, and thus
∼ 300 times larger volume for the 3 slices together.
We first used this whole simulated map to compare
the density distribution with the observational data. Fig. 5
shows the density histogram of the whole simulated map,
overlaid on the observed density histograms. We see thatthe density distribution of the simulated map is at least
qualitatively consistent with that of the SXDS field. The
distribution is close to Gaussian with a slightly longer tailtoward the high density, peaked around the mean density.
The peak amplitude and the width of the peak both lookclose to that of the control sample. At higher density, on theother hand, the simulated map has a longer, more extended
tail than that of the control sample. This looks still consistent with the control sample, because the field coverage ofthe observational data is much smaller than the simulation.
However, the high density tail seen in the TNJ1338 field islarger than that in the whole simulated map.
Statistical tests also support this diﬀerence between the
SXDS and TNJ1338 fields, in terms of the comparison withthe simulated map. The 10- and 90 percentiles of the density
in the simulated map are 0.35 and 1.74 respectively, and theratio between the two percentiles is 5.0, which is closer tothat in the SXDS (4.2) than in the TNJ1338 field (38.0):
see Fig. 5 left. We also calculated the Gini coeﬃcient of
the simulated density map, G = 0.306, and compared withc 2013 RAS, MNRAS 000, 1–17
⃝

0

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estimated above is on a comoving scale ∼ 20 − 30 h−1 Mpc,
which corresponds to the area inside the contour of averagedensity in Fig. 4. Note again that this is smoothed over
∼ 160 h−1 comoving Mpc along the line of sight. We can thenqualitatively say that there apparently exists a large density
contrast within ∼ 50 h−1 comoving Mpc scale around theradio galaxy TNJ1338, apparently enhanced to some extent
by highly biased nature of the bright LAEs including AGN
hosts.

11

0.05

0.00
0

1

2
3
Relative density (1+δLAE)

4

Figure 7. Comparison of the density distributions between the
TNJ1338 field and the simulated map with various conditions forthe simulation. The filled red histogram shows the observed density distribution of the TNJ1338 field (the same as in Fig. 5 left).
The green outlined histogram is the density distribution for thewhole simulation volume. The errors were estimated by computing the density distributions for 300 diﬀerent Suprime-Cam-sized
fields centred at random points, calculating the standard deviation for each density bin. The blue outline is the averaged distribution for the 25 fields centred at density peaks higher than thedensity measured at the radio galaxy position. The orange outlined histogram is for the one out of the 25 fields with the highest
peak density, and the cyan outlined histogram is for that withthe highest Gini coeﬃcient (G478 field). The cumulative distributions are shown in the top panel, together with the 10- and 90percentiles. The histograms are slightly shifted along the x axis toimprove the visibility. The large fractions of pixels in the highestand the lowest-density bins cannot be simultaneously reproducedwith the simulated density map within the errors. Although thehigh-density regions can be reproduced at the peak positions, thehigh volume fraction of the void regions is not seen around typicalpeaks. The G478 simulated field reproduces both the large void
fraction and the high density tail seen in the TNJ1338 field, but
the peak in the density distribution around the average density
seen in the TNJ1338 field is not reproduced by this G478 field.

the observed distributions in the two fields (Fig. 5 right).
The dynamic range of the LAE density for the simulated
map is thus in between those of the two observed fields, andcloser to the SXDS field than the TNJ1338 field. We then assume that the SXDS field has a typical density distributionof LAEs at z ∼ 4, and we can evaluate how rare the highdensity region seen in the TNJ1338 field is. The density measured at the position of the radio galaxy is 1 + δLAE = 3.46.
Such high density regions are quite rare in the simulated
map, corresponding to the densest 0.06 percentile of thewhole volume, while the same overdensity corresponds to
the 1.8 percentile of our survey volume in the TNJ1338 field.

12T. Saito et al.

It is also important to check the size of field-to-field
variations within the simulation volume. To do this, we firstobtained density maps centred at random positions. We selected 100 positions in each of the three slices within thecentral 440 × 440 h−2 Mpc2 , and made density maps within
a FoV of Suprime-Cam centred at these 300 points. Then
we calculated the standard deviation for each bin of thedensity distribution using the 300 maps. Fig. 7 shows thatthe observed density distribution, especially the density contrast within a single field, is very diﬀerent from that for thesimulated map as a whole. The volume fraction within themedium- to high-density (1 + δLAE ∼ 1 − 2.5) bins in the
TNJ1338 field agrees with that obtained from the wholesimulation volume, at 1σ level. On the other hand, the relative frequencies for the lowest- and the highest-density bins
do not agree with those for the simulated map. This alsosuggests that such extreme overdensities / underdensities as
we found observationally are quite rare in the simulation:
the random sampling in the simulated map is unlikely to
reproduce the unusual density distribution observed in ourfield. In fact, we found only 25 density peaks higher thanthat measured at the radio galaxy position, over the wholesimulated map. This is comparable to the number densityof Coma-type protoclusters identified in the same simulation (58 protoclusters: Chiang et al. 2013). The number (25peaks) corresponds to number density of 6.9 × 10−8 Mpc−3
in comoving units (9.1 × 10−6 Mpc−3 in physical units). This
number density is also comparable to that of known brightradio sources at z > 2 (see the section below). However,most of these peaks do not seem to reproduce the high density contrast seen in the TNJ1338 field. This suggests thathigh-density regions that host powerful radio galaxies associated with a giant Ly α nebulae, like our observed field,
should be much rarer than this.
4.3.2

Density fields around the high-density peaks

Next we checked the density distributions around the 25
density peaks found in the simulated map. In order to obtain the density distribution in the same manner as the observed data, we extracted the LAEs within a single SuprimeCam FoV centred at the peak positions. Then we madethe density maps in these fields, and calculated the density distributions using the grid points within the central
40×27.5 h−2 Mpc2 , similarly to the analyses for the observed
LAE sample. Fig. 7 also shows the average density distribution of the fields around the 25 density peaks, together withthe errors. This average distribution is shifted toward higher
density compared with the whole simulated map, smoothedalong the density axis. However, the shape of the distribution does not significantly change: it agrees very closely withthat of the whole map if we normalise the density with theaverage within these 25 fields, instead of the average of thewhole simulated map. The distribution again seems to be different from the distribution in the TNJ1338 field, although
the high-density tail is reproduced well. This implies thathigh-density regions just adjacent to the void regions, like
we observed, are still much rarer than simple high-density
peaks.
To further analyse the density distribution, we calculated the Gini coeﬃcient for each map centred at the 25 highdensity peaks. Fig. 5 shows the comparison of the Lorentz

curves for the observed- and simulated density maps. The
ordinate corresponds to the cumulative sum of the abscissaof the left panel, normalised with the total sum of the LAE
surface density measured at each grid point. This showsthat, while the density distribution of the SXDS field is wellwithin the scatter of the simulated map, the distribution of
the TNJ1338 field is far from the simulated ones, even fromthose around the density peaks. The possible exception is
one of the 25 fields, showing G = 0.478 (hereafter G478
field: Fig. 4 bottom-right panel). The peak density of G478
field is 3.98 times the average over the whole simulated map,and has a large fraction of void regions. The 10- and 90 percentiles of G478 field are 0.157 and 2.419, respectively, andthe ratio of the two quartiles is 15.4. Although the distribution thus seems to be close to that of the TNJ1338 field,
the G478 field does not completely reproduce the properties of the TNJ1338 field. The average density of the G478
field is 1.25 times the average over the whole simulated map,
giving a peak density of 1 + δLAE = 3.19 when normalisedwith the average density within the field. The shape of thedensity distribution is also diﬀerent: the density histogramof G478 does not have a peak around the average density(cyan histogram in Fig. 7).
These results together suggest that the density distribution of the G478 is roughly consistent with that of the
TNJ1338 field, in terms of the density contrast within thefield. The remaining diﬀerences might be explained in termsof changes in the galaxy-formation processes in such unusually high-density regions harbouring powerful radio galaxies.
The simulation does not include Ly α radiation from AGN
activity, which can introduce significant diﬀerences in the
LF, even if the underlying dark matter structure is similar.
We then roughly evaluated how well the G478 field reproduces the TNJ1338 field, in terms of the number density:
we found no other G478-like fields within the whole simulation volume of (500 h−1 Mpc)3 (comoving). This corresponds
to a comoving number density of 3 × 10−9 Mpc−3 with verylarge uncertainty because we have only one such region in
the whole simulation volume. This is two orders of magnitude lower than the number density of Virgo-type protoclusters identified in the same Millennium Simulation, and still
an order of magnitude lower than Coma-type protoclusters(Chiang et al. 2013). The number density of radio galaxies in
the universe at 2 < z < 5 is observed to be a few 10−8 Mpc−3(e.g. Venemans et al. 2007; Miley & De Breuck 2008), comparable to that of the Coma-type protoclusters. This meansthat the environment of the radio galaxy TNJ1338 is evenrarer than the known radio galaxies at z > 2. In fact, not
all the high-z radio sources have Ly α nebulae extended to≳ 100 kpc (van Ojik et al. 1997). Such extended Ly α nebulae should reflect exceptionally active interaction between
the radio galaxy and its surroundings.
Note that we found only one field like G478 in thewhole simulation volume, so the theoretically predicted
number density of such high-density region remains significantly uncertain. The observational constraints are also very
weak, since there are very few high-z powerful radio galaxies known to date, and the technique finding high-z radiosources, i.e., selecting based on ultra-steep radio spectra,
will miss a significant fraction of high-z galaxies (e.g. Ker et
al. 2012). Even larger simulations together with more realistic models for LAEs including AGN are needed to calculate
c 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blob
accurate statistics for rare density peaks like that in the
TNJ1338 field, and to simulate the density field and the LF
found around them. In addition, deep and large surveys forhigh-z radio sources are needed to more accurately estimate
the observed number density of TNJ1338-like regions.
4.3.3

Density peak profiles

In order to test how well the simulated map reproduces
the observed spatial distribution of the LAE density in the
TNJ1338 field, we computed the radial overdensity profileof this peak, and compared with the simulated density map.
Fig. 8 shows the comparison of the density profiles between
the observed peak in the TNJ1338 field and high-density
peaks in the simulated map. The leftmost panels show theobserved density profile. As shown in 4.1.1, the peak density
in the TNJ1338 field is 1+δLAE = 4.13, and the radio galaxy
position is slightly oﬀset (∼ 2.5 h−1 comoving Mpc) fromthe peak, at which the density is ≈ 84 percent of the peak.
Although the redshift uncertainty is fairly large, we canroughly estimate the spatial scale wherein the high-density
peak is accumulating the material from the surroundings,
based on this profile. The radius of half-maximum is ∼ 6 h−1
projected comoving Mpc, and the average density within
this radius is 1 + δLAE ∼ 3. This could be produced byspherical collapse from a region with radius of ∼ 9 h−1 Mpc(comoving). Although this is a very rough estimate, it isclear that the accumulation of material is occurring wellwithin our survey volume. The profile does not significantly
change even when normalized with the average density over
the SXDS field.
For comparison with this observed density peak profile,
we selected the 25 high-density fields described above (including the G478 field). We found that none of these fields
have peak density as high as the observed one when we
normalised the density with the average within the same
Suprime-Cam-sized FoV. We then applied the threshold forthe peak density of 1 + δLAE > 3.46, which corresponds tothe density at the position of the radio galaxy. Three out of
the 25 peaks have their peak value higher than this threshold density. Fig. 8 shows the comparison of these three peaks
with the observed profile of the TNJ1338 field. The observed
peak density, 1+δLAE = 4.13 when normalised with the average within the same field, cannot be seen in any of the threefields, Peak 1, 13 and 21, when we normalise the density inthe same manner, although the half-maximum radii of thesepeaks are all comparable to that of the observed peak in the
TNJ1338 field. This implies that low-density void region(s)within the same field, which are not seen in the simulation,
are required to reproduce the normalised peak density.
Apart from the peak amplitude, the shape of the radial
density profile seems to be roughly reproduced by the simulated map. When we normalise the density with the wholesimulated map, the density profiles seem to show a better
match with the observational data. The bottom row of Fig. 8
shows a comparison for this case. To make the fair comparison, the density around the observed peak is then normalisedwith the average of the SXDS field, although the diﬀerenceis only 2.5 percent. Peak 1 gives the best match with theobserved one in terms of the peak amplitude, but is moreradially extended, with the 1 + δLAE > 2 level extending
more than 12 h−1 comoving Mpc. Another two peaks are
c 2013 RAS, MNRAS 000, 1–17⃝

13

relatively isolated, unlike Peak 1, but neither peak simultaneously reproduces the amplitude and the width observed
for TNJ1338. If the normalization were diﬀerent, these peaks
might resemble the observed high-density region. Since we
do not know the true mean LAE density of the universe, it
is possible that the normalization is not correct. Even the
SXDS field might be overdense, as the average density isalmost the same as that in the TNJ1338 field. To evaluate
this possibility, further wide-field observations, such as theHyper Suprime-Cam survey, are needed especially for thecontrol sample in blank fields.
There are at least three factors which might explain thediﬃculties in reproducing the density distribution observedin the TNJ1338 field. First, the selection of LAEs in thesimulation does not exactly match the observational one.
Especially for the broadband colours, we did not put any
constraints to select the LAEs from the mock catalogue, possibly causing the diﬀerence in the selection function. However, this eﬀect is unlikely to significantly change the resulting density distribution. Our mock LAE sample reproduces
both the LF and the density distribution of the SXDS control sample quite well. Our selection of LAEs is thus thought
to be working well at least for the faint end of the LF, where
the TNJ1338 and the mock samples agree with each other.
The second possibility is that the LAE model itself is not
suﬃciently realistic. For example, the escape fraction of Ly α
photons is assumed to be constant for all the LAEs. If theescape fraction is changed in highly overdense regions by e.g.
galaxy-galaxy interactions or AGN feedback, the spatial distribution of LAEs may significantly change in the field. Thisis also related to the third factor, i.e., the observations might
include a significant contribution of Ly α coming from AGN,
which is not included in the model. AGN activity may aﬀect
the galaxy-formation processes of the surroundings through,e.g., induced star formation (Zirm et al. 2005). Such AGN
activity may be enhanced in overdense environments (e.g.
Pentericci et al. 2002; Croft et al. 2005; Lehmer et al. 2009;
Digby-North et al. 2010). If the bright LAEs in our TNJ1338
sample are predominantly AGN, this could lead to significant enhancement of the LAE number density, emphasizing
the density contrast.
Another, much more naive interpretation is that theMillennium Simulation is not large enough to reproduce thiskind of overdensity. This is in case if the halo mass of theoverdensity is significantly larger than the maximum halo
mass of the Millennium Simulation. Even if the SXDS field
is suﬀering from overdensities and our density normalisation is not correct, such a steep and high density peak withlarge density contrast is not reproduced in the current simulation. The disagreement may be overcome by carrying out
even larger simulations. The density profiles around massive
haloes in such a large simulation may be diﬀerent from thosearound less massive haloes: extremely massive haloes possibly form very high density peaks without significant growthin size of the overdense-regions.
In any case, more precise measurement of the density
field and constraints on the AGN activity in our LAEs areneeded to test the possibilities described here.

T. Saito et al.
TN J1338-1942

Relative density (1+δLAE)

4.0

Peak
Radio galaxy

1.0 4.0
0.8

3.0
Half Max.

2.0
1.0

Peak 1

0.6
0.4

3.0
2.0

0.0

0.2 1.0
0.0 0.0

4.0

1.0 4.0

Mean

Peak 13
1.2 4.0
1.0
3.0
0.8
0.6 2.0
0.4
1.0
0.2
0.0 0.0
1.0
4.0
0.8
3.0
0.6
0.4 2.0

Peak 21
1.2 4.0
1.0
0.8 3.0
0.6 2.0
0.4
1.0
0.2
0.0 0.0
1.2
1.0 4.0

1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.0

0.8
0.8 3.0
0.6
0.6
0.6
2.0
2.0
2.0
0.4
0.4
0.4
1.0
0.2
0.2 1.0
0.2 1.0
0.2 1.0(normalized w/ SXDS)(normalized
w/
whole
map)
(normalized
w/
whole
map)
(normalized
w/
whole
map)
0.0
0.0
0.0
0.0
0.0 0.0
0.0
0.0
0
4
8
12
0
4
8
12
0
4
8
12
0
4
8
12
3.0

0.8

3.0

(normalized with the peak)

14

Radius [h−1 Mpc]
Figure 8. Overdensity profiles around density peaks. Relative overdensity is plotted as a function of the comoving distance from thepeak. The leftmost column shows the observed density profile centered at the density peak observed in the TNJ1338 field. The profilein the top panel is based on the density normalised with the average over the FoV of Suprime-Cam in the same field. The density
measured at the radio-galaxy position is shown with the blue cross. The bottom panel is based on that normalised with the average of
the SXDS field. The remaining columns show the profiles of the density peaks found in the simulated map. For each panel, each black
point corresponds to the measurement at a single grid point. The LAE positions are marked with cyan diamonds, with the symbol sizes
representing the Ly α line luminosities. The mean density is shown by the dotted line, and the peak- and the half-maximum densities
are shown by the black dashed lines. The density and the distance measured at the position of the radio galaxy are marked with themagenta dot-dashed lines. The right axis shows the density normalised with the peak value.

4.3.4

Luminosity function

Fig. 6 also shows the LF of the mock LAE sample. Again thissample is selected with the same colour constraints as the
TNJ1338 sample. The mock sample has been already shownto have a Ly α LF reproducing well that of O08’s sample(Orsi et al. 2008). This means that the mock sample is expected to reproduce the LF of our control sample. The LF of
the mock sample agrees quite well with the control sample
except for the bright end (log LLyα ≳ 43.6). The small difference from the O08’s sample at the faint end is thought tocome from the diﬀerence of the filter and the depth: oursample is selected based on the intermediate-band imaging, while O08 is based on the narrowband imaging. The
colour constraints of our sample roughly corresponds to therest-frame EW of ≳ 70Å, while that of O08 corresponds to≳ 44Å. The diﬀerences in the band, as well as the exposure
time, also lead to the diﬀerence in the sensitivities to the
Ly α line. O08’s sample is a factor of ∼ 2 deeper than ours,
so that the mock LF comes slightly lower than the O08’s LF,
as is also true for our control sample. The bright end of the
LF was determined from a single source, and thus the LF of
the mock sample is still consistent with that of the control
sample within the large errors. Since the number of sources
is much larger in the mock catalogue than in the SXDS
sample, the mock LF may be correctly reproducing the LF
of normal star-forming galaxies at this redshift, excluding
AGN. The bright end of the LF is likely to be dominatedby AGN as suggested in O08, and the single source found in
the highest luminosity bin in the SXDS field is possibly an
AGN host.
Similarly to the comparison with the blank fields, the
LF in the whole TNJ1338 field is a factor of ∼ 2 higher
than the mock LAE LF at log LLyα ∼ 43.6. For the fainterrange, the TNJ1338 LF comes below that of mock LAEs at
log LLyα ∼ 43.3. The crossing point is in between these two,i.e., the number of LAEs fainter than log LLyα ∼ 43.3 − 43.6
seems to be suppressed in this field. The faint end of the
LF agrees with the mock, when we look at the LF of theoverdense regions in the TNJ1338 field. While the faint-end
LF of this field does not show any enhancement comparedto the mock LF, the bright end, log LLyα ∼ 43.9, shows alarge enhancement by one order of magnitude. This again
suggests that the TNJ1338 field is a peculiar field dominatedby bright LAEs, or AGN including the host of the radiogalaxy. There are four bright LAEs contained in the twohighest-luminosity bins (43.8 ⩽ log LLyα ⩽ 44.4) in thisfield, and such bright sources are likely to be hosting AGN,
as suggested by O08. Such a population of bright LAEs, aswell as the unusually high galaxy overdensity, should largely
aﬀect the galaxy-formation within this field.
The main diﬀerences between the TNJ1338 and themock LAE samples in terms of LFs are then thought tobe (1) the presence of the AGN, (2) the high-density peakas high as 1 + δLAE ∼ 4, and (3) the large density contrast
within a single FoV of the Suprime-Cam. Of these three,(2) can be partly reproduced with the mock sample as described in §4.3.1 and §4.3.3. We then tested how the LF
diﬀers from the observed one when one of these three main
discrepancies are partly solved, by computing the LF within
the peak regions seen in the simulated map. The resulting
LFs in overdense regions show almost the same shape as the
LF from the whole mock sample, and the amplitude of the
LF becomes a factor of 0.2 − 0.4 dex higher. We can see in
Fig. 6 that only five out of the 25 high-density fields contain
LAEs with log LLyα ∼ 43.9. Even these five fields contain
only one source each, but we can estimate the bright end ofc 2013 RAS, MNRAS 000, 1–17⃝

The environment of Ly α blobthe LF by averaging the 25 fields, log nLAE = −5.41 at thebright end. This value is only 0.27 dex higher value than the
total mock sample. This means that there are no significant
enhancements of the number (fraction) of bright LAEs suchas we found in the TNJ1338 field. While the enhancementsof the total number density of LAEs are relatively well reproduced in these high-density fields, the LF shape remains
almost unchanged from that of the whole mock sample, i.e.,
not biased to bright sources.
Note that none of the three peaks described in §4.3.3,
nor the G478 field described in §4.3.2, are included in thefive fields containing the brightest LAEs. These five fields
do not have extremely high G’s, only one of which exceeds
0.3. This simply means that the brightest LAEs are likely
to be found in fields with high average density. This is also
expected from the properties of the mock LAEs: the galaxy
bias positively correlates with the Ly α luminosity LLyα , butchanges by only a factor of ∼ 2 − 3 (Le Delliou et al. 2006;
Orsi et al. 2008). On the other hand, the LFs of our observed samples suggest that the bias depends more strongly
on LLyα . The mock LAE sample does not contain AGN atall, so that it can reproduce only the properties of “normal”
LAEs, not LAEs hosting AGNs, nor AGN-induced star formation. Activity related to such AGN, e.g., AGN-induced
star formation in the vicinity of the radio galaxy (Zirm etal. 2005), may lead to enhancements of star-formation inthis high-density region. Such interactions between the AGN
and the surrounding environment may also occur further out
from the central radio galaxy, as the extended Ly α nebula isobserved up to ∼ 100 kpc (Venemans et al. 2002), and some
Ly α nebulae are aligned with the surrounding large-scale
structure up to ∼ 10 h−1 comoving Mpc (Erb et al. 2011).
Furthermore, three out of the four LAEs mentioned abovein the highest luminosity bins, as well as the radio galaxy,lie within the overdense (1 + δLAE > 1) regions. These may
together suggest that star-formation / AGN activity is enhanced by the presence of AGN in the overdense regions,while there are no such sources of enhancement in the underdense regions.
Such an enhancement is expected from the high galaxy
density, leading to frequent galaxy mergers. The high density
may also lead to high gas accretion rates, which enhances
the star-formation / AGN activity resulting in bright LAEs.
These mechanisms will result in a large bias of the brightLAEs, dominating the bright end of the LF. Such a large
bias for bright LAEs results in the large density contrast ofbright LAEs described in §4.1.2. In order to see how such anenhancement aﬀects the LF of normal star-forming galaxies
in the overdense environment, we need to take deeper images
to construct a sample of much fainter LAEs. We still havediﬃculties to make a meaningful comparison with the simulation, due to the shallowness of the data: the luminosity
range of our observed samples corresponds to the very brightend of the mock LAEs. Constructing a sample of fainterLAEs (log(LLyα ) ≲ 43: ≲ 42.7 when h = 0.7 is assumed),
which is less likely to be contaminated by AGN, is essential to probe the LF and its environmental dependence. The
uncertainty in the redshifts is also a problem in computing
the galaxy density and the luminosities, as well as evaluating
the contamination of AGN and foreground galaxies. Further
deep imaging to construct a deeper sample, and subsequentc 2013 RAS, MNRAS 000, 1–17⃝

15

follow-up spectroscopy, are needed to draw further information from this comparison.

5

CONCLUSIONS

We have carried out intermediate-band and broadband
imaging observations with Suprime-Cam on the Subaru
Telescope of a z = 4.1 radio galaxy associated with a giant
Ly α nebula to probe its environment on a ∼ 50 h−1 Mpc
scale. In order to quantify the environment with a control
sample, we utilized the existing data from a blank field,
SXDS, taken with the same instrument and similar filters.
We also used a mock LAE catalogue generated with a semianalytical galaxy formation model based on the Millennium
Simulation.
We confirmed that the radio galaxy lies in a region withpeak LAE number density of 1 + δLAE = 4.1 ± 0.5 at theradio galaxy position, even after taking account of the relatively large redshift range covered by the IA624 filter. The
average density over the Suprime-Cam FoV is almost thesame as that of the blank field within 2.5 percent, showingthat the density contrast in this field is very high. These results suggest that radio galaxies associated with Ly α nebulae emerge in extreme overdensity environments. Comparing
these with the mock LAEs, we found that such high-density
regions are quite rare, 25 peaks in the whole simulation volume of (500 h−1 Mpc)3 , and correspond to the densest > 0.1
percentile. The corresponding number density is comparable to that of Coma-type protoclusters found in the same
simulation, and known radio galaxies at z > 2. The overdensity associated with the radio galaxy can be traced up
to ∼ 10 − 20 h−1 comoving Mpc, facing the large void region
just adjacent to it. Only one of the 25 density peaks havesuch a large density contrast on this scale, and even thispeak cannot fully reproduce the density peak profile.
We found the density dependence of the luminosity
functions (LFs). The Ly α LF of the TNJ1338 field shows enhancement at the bright end (log(LLyα [h2 erg s−1 ]) ≳ 43.6)
by an order of magnitude or more, while the faint end almost agrees with that in the blank field. We compared the
LFs with the mock LAEs to conclude that star-formation
and/or AGN activities aﬀecting the bright end of the LF arehighly enhanced within overdense regions. We pointed out
the possibilities that frequent galaxy mergers or high gasaccretion rate enhance the star-formation / AGN activity,
or AGN-induced star formation in this field. The presence ofa powerful radio galaxy showing a giant Ly α nebula is thus
a possible signpost of changes in galaxy formation activity
on scales of ∼ 10 − 20 h−1 comoving Mpc.

ACKNOWLEDGEMENTS
We thank Masami Ouchi for providing the data of luminosity functions, and giving us useful comments. We thank YiKuan Chiang, Surhud More and John Silverman for having
discussion over this work, and giving us valuable comments.
This work was supported by the FIRST programme “Subaru
Measurements of Images and Redshifts (SuMIRe)”, World
Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. This work was supported in part by

16

T. Saito et al.

the Science and Technology Facilities Council rolling grant
ST/I001166/1 to the ICC. Calculations were partly performed on the ICC Cosmology Machine, which is part of the
DiRAC Facility jointly funded by STFC and Durham University. YM acknowledges support from JSPS KAKENHI
Grant Number 20647268. IRS acknowledges support from
STFC (ST/I001573/1), the ERC Advanced Investigator programme DUSTYGAL 321334 and a Royal Society/Wolfson
Merit Award. The data were in part obtained from SMOKA,
which is operated by the Astronomy Data Center, National
Astronomical Observatory of Japan.

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APPENDIX A: THREE-DIMENSIONALDENSITY PROFILESAs discussed in the §4.3.2, such a high density peak anda large void region within a single FoV as we found in
the TNJ1338 field is likely to be reproduced by fields withlarge G’s, like the G478 field. However, although the G478
field has very large G, the peak density is only ∼ 3.2 whennormalised within the field, since the G478 field has large
plateau of the density. Unlike the G478 field, the three fields
shown here have relatively steep peaks on their centres. They
also have relatively large G’s: two of these are the fields withthe second- and third largest G. The G’s for these three fields
are 0.371, 0.349, and 0.307 for Peak 1, 13, and 21, respectively. This kind of diﬀerences becomes clearer when we look
into the three-dimentional (3-D) densities. We calculated the
local- and global densities using the 3-D spatial distributionof the mock LAEs within these fields. The density at the position of each source was calculated based on the distance tothe 5th-, 10th- and 20th-nearest neighbour. We normalised
the density with the average over the same field, and calculated the overdensity δ5th , δ10th , and δ20th . Then we counted
the LAEs residing in the density greater than the average.
c 2013 RAS, MNRAS 000, 1–17⃝

17

Table A1 summarizes the results of the density measurements of these four high-density fields, comparing with theobserved data.
Among the four high-density fields shown here, theG478 field has the largest fraction of LAEs lying within theoverdensities in terms of δ5th and δ10th . However, this field
does not have regions of δ20th > 0. On the other hand, thePeak 21 field does not have such a high fraction of δ5th > 0
and δ10th , but has three sources lying within δ20th > 0 regions. The remaining two fields, Peak 1 and 13, show theclustering signals which are in between the G478 and thePeak 21 fields. The average 3-D density corresponds to the
distance of the 5th-, 10th- and 20th-nearest neighbour of 8.5,
12 and 19 h−1 comoving Mpc, respectively. Comparing thetwo fields, the overdensities spread more widely in the G478
field than in the Peak 21 field. The high-density regions areconcentrated along the line of sight at 340 ≲ z ≲ 390 h−1
Mpc in the Peak 21, and seems to spread more widely overthe sky than in the G478 field (Fig. A1).
The high surface-density peak seen at the centre of
G478 field is thus likely to be clumps of LAEs forming a filamentary structure elongated toward the line of sight, rather
than a single extremely overdense region. If radio galaxies
are formed within extremely overdense regions, the Peak 21
is more likely to be reproducing the environment of radiogalaxies. However, as expected from the relatively small G’s
compared with the TNJ1338 field, the Peak 21 field do nothave such a large fraction of void regions as seen in the
TNJ1338 or G478 fields. The Peak 21 seems to be rather
evolved protocluster, in which LAEs are clustered up to a
few tens of comoving Mpc, but such evolved protocluster
cannot reproduce the large fraction of void regions. Similarly, overdense regions containing very massive dark haloes(the maximum halo mass in the simulation, 9.4 × 1012 M⊙ )do not reproduce the high peak density and the large density
contrast. One of the 25 peaks described above contains sucha massive dark halo, but the field around this peak have thepeak density only up to 1 + δLAE = 2.90 when normalised
within the same field, and have relatively small void fraction
leading to G = 0.289.
These analyses together suggest that the simulation
cannot fully reproduce the density distribution of the
TNJ1338 field. The environment of this field is thus extremely rare, more than an order of magnitude lower density
than known radio galaxies at z > 2.

18

T. Saito et al.
Table A1. Density measurements around the high-density peaks
Field

Ntot amax(1 + δLAE )b

N (δLAE > 0)c

N (δ5th > 0)d

N (δ10th > 0)d

N (δ20th > 0)d

G478
Peak 1
Peak 13
Peak 21

72
84
79
83

3.2
3.5
3.5
3.5

51
56
43
42

22
13
3
13

13
3
0
8

0
0
0
3

TN J1338-1942(SXDS)e

31
34

4.1
2.4

27
29

-

-

-

a Total number of LAEs within the field.
b The peak (maximum) surface density within the field.
c The number of LAEs with the surface density greater than the average.
d The number of LAEs with the 3-D densities greater than the average. The densities were calculated from the 5th-, 10th-and 20th-nearest neighbours for δ5th , δrm10th and δ20th , respectively.
e Control field (not a high-density peak).

xz

G478
yz

xz

Peak 21yz

150

z [h−1 Mpc]

450
100

400
50

350
200 220 240 430 450
x [h−1 Mpc] y [h−1 Mpc]

210 230 250
180 200−1x [h Mpc] y [h−1 Mpc]

Figure A1. LAE density maps of the two fields with high-density peaks, generated with the mock LAEs projected onto the xz- and yz
planes, instead of the xy plane shown in Fig. 4. The left two panels are the maps for the G478 field, projected on the xz- (left) and theyz plane (right). The right two panels are for the Peak 21 field. The overdense region in the G478 field emerged on the xy-plane density
map seems to have sub-clumps that are distributed over a wide range along the z axis. On the other hand, the density distribution in
the Peak 21 is relatively concentrated at z ∼ 340 − 390 h−1 Mpc, except for the minor clump at z ∼ 480. All the coordinates shown here
are in the comoving scales. The maps are drawn with the same manner as in Fig. 4, except for the use of smoothing radius of 8 h−1 Mpc.

c 2013 RAS, MNRAS 000, 1–17⃝