Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z~4

9.4 MB·

by  Cristina Garcia-Vergara

Draft version January 6, 2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
STRONG CLUSTERING OF LYMAN BREAK GALAXIES AROUND LUMINOUS QUASARS AT Z ∼41,2
Cristina Garc´ıa-Vergara 3,4, Joseph F. Hennawi 4,5, L. Felipe Barrientos 3, and Hans-Walter Rix 4
Draft version January 6, 2017
ABSTRACT
In the standard picture of structure formation, the first massive galaxies are expected to form at
the highest peaks of the density field, which constitute the cores of massive proto-clusters. Luminous
quasars (QSOs) at z ∼ 4 are the most strongly clustered population known, and should thus reside
in massive dark matter halos surrounded by large overdensities of galaxies, implying a strong QSO-
7
galaxy cross-correlation function. We observed six z ∼ 4 QSO fields with VLT/FORS exploiting a
1
novel set of narrow band filters custom designed to select Lyman Break Galaxies (LBGs) in a thin
0
redshiftsliceof∆z ∼0.3,mitigatingtheprojectioneffectsthathavelimitedthesensitivityofprevious
2
searches for galaxies around z (cid:38) 4 QSOs. We find that LBGs are strongly clustered around QSOs,
n and present the first measurement of the QSO-LBG cross-correlation function at z ∼ 4, on scales
a of 0.1 (cid:46) R (cid:46) 9h−1Mpc (comoving). Assuming a power law form for the cross-correlation function
J
ξ = (r/rQG)γ, we measure rQG = 8.83+1.39h−1Mpc for a fixed slope of γ = 2.0. This result is in
4 0 0 −1.51
agreement with the expected cross-correlation length deduced from measurements of the QSO and

LBG auto-correlation function, and assuming a linear bias model. We also measure a strong auto-
]
A correlation of LBGs in our QSO fields finding rGG =21.59+1.72h−1Mpc for a fixed slope of γ =1.5,
0 −1.69
which is ∼ 4 times larger than the LBG auto-correlation length in random fields, providing further
G
evidencethatQSOsresideinoverdensitiesofLBGs. Ourresultsqualitativelysupportapicturewhere
h. luminous QSOs inhabit exceptionally massive (Mhalo >1012M(cid:12)) dark matter halos at z ∼4.
p Subject headings: cosmology: observations–earlyUniverse–large-scalestructureofuniverse–galax-
- ies: clusters: general – galaxies: high-redshift – quasars: general
o
r
t
s 1. INTRODUCTION search for these so-called proto-clusters around known
a
massive galaxies at high redshift.
[ Our understanding of structure formation suggests
Oneveryfruitfultechniquetofindhigh-redshiftproto-
that small inhomogeneities in the density field shortly
1 clusters has been to use the presence of an active su-
after the Big Bang grew over cosmic time via gravi-
v per massive black hole (BH) as a signpost for a massive
tational instability (e.g. Dodelson 2003; Padmanabhan
4 galaxyandhencemassivedarkmatterhalointhedistant
2006; Schneider 2015) into massive dark matter halos at
1 Universe (e.g. Venemans et al. 2007; Kashikawa et al.
z = 0. As clusters of galaxies are the most massive,
1 2007; Overzier et al. 2008; Morselli et al. 2014). This
gravitationally bound structures in the Universe, they
1 technique is motivated by several considerations. First,
musthaveformedfromthehighestdensitypeaksatearly
0
the masses of supermassive BHs (M ) are known to
. times. This make them ideal laboratories for studying BH
1 the formation and evolution of cosmic structure. tightlycorrelatewiththebulgemassoftheirhostgalaxy
0 (Magorrian et al. 1998; Ferrarese & Merritt 2000; Geb-
Because of the small areas of sky surveyed at high-
7 hardt et al. 2000), and possibly with the masses of their
redshift, and the low comoving number density ∼
1 10−7Mpc−3 oflocalclusters(Gioiaetal.2001;Vikhlinin host dark halos (Mhalo) (Ferrarese 2002, but see Kor-
: mendy & Bender 2011). Intriguingly, the most luminous
v et al. 2009), the evolutionary link between these low-
i redshiftclustersandhigh-redshiftgalaxieshasbeenchal- quasars (QSOs) at z > 3 have MBH ∼ 1−6×109M(cid:12)
X lenging to make. The progenitors of clusters are ex- (Shen et al. 2011), comparable to the most massive
r tremelydifficulttoidentifywhenthedensitycontrastbe- knownlocalBHs. IfthepresentdayMBH−Mhalorelation
a tween the forming cluster and its surroundings is small. holdsatearlytimes,suchBHsshouldresideinexception-
For this reason, a commonly adopted approach is to ally massive halos. Second, some studies have suggested
that the nuclear activity in active galactic nuclei (AGN)
is triggered by processes related to the environment
[email protected] where they reside. For example, galaxy mergers could
1Based on observations collected at the European Organi-
trigger the AGN activity (Bahcall et al. 1997; Wyithe &
zation for Astronomical Research in the Southern Hemisphere,
Chile. Data obtained from the ESO Archive, Normal program, Loeb2002;Hennawietal.2015),andgalaxymergersoc-
visitormode. ProgramID:079.A-0644. cur preferentially in dense environments (Lacey & Cole
2We dedicate this work to the memory of Josef Fried, who 1993). This would imply that the existence of an AGN
originallyobtainedandanalyzedthedataonwhichthisworkis
requiresadenseenvironmentaroundit. Finally,another
based.
3Instituto de Astrof´ısica, Pontificia Universidad Cat´olica de lineofevidencethatQSOstracetherarestenvironments
Chile,AvenidaVicun˜aMackenna4860,Santiago,Chile. at high redshift arises from their extremely strong clus-
4Max-PlanckInstitutfu¨rAstronomie(MPIA),K¨onigstuhl17, tering. Indeed,Shenetal.(2007)determinedthatQSOs
D-69117Heidelberg,Germany.
5DepartmentofPhysics,UniversityofCalifornia,SantaBar- at z > 3.5 have a comoving auto-correlation length of
bara,CA93106,USA r0 =24.3h−1Mpc (for a fixed correlation function slope
2 Garc´ıa-Vergara, C. et al.
of γ = 2.0), making them the most strongly clustered galaxies around QSOs at z ∼ 6−7. Kim et al. (2009)
population in the universe, and demanding that they re- studied five QSO fields at z ∼ 6 and reported a mix
side in the most massive M > 1012M dark matter of overdensities and underdensities, and Husband et al.
halo (cid:12)
halos at this epoch. Additionally, the Shen et al. (2007) (2013) find galaxy overdensities in z ∼5 QSOs environ-
correlationfunction,agreeswiththatrequiredtoexplain ments, but they note that even some randomly chosen
the abundance of binary QSOs at z > 3.5 (Hennawi patches of sky without AGN signposts (‘blank fields’)
et al. 2010; Shen et al. 2010), indicating that overdense at the same redshift contain similar galaxy overdensi-
structures around QSOs extend down to scales as small ties. Indeed, surveys of a few deg2 for z ∼ 6 LBGs or
as 100h−1kpc. Since in hierarchical clustering models, LAEs have identified comparable overdensities in blank
QSOs and galaxies trace the same underlying dark mat- field pointings (e.g. Ouchi et al. 2005; Ota et al. 2008;
ter density distribution, the generic prediction is that Toshikawa et al. 2012). These mixed results at z (cid:38)5 do
galaxies should be very strongly clustered around QSOs not yet provide compelling evidence QSOs inhabit mas-
at z (cid:38)3.5. Observationally this should be reflected as a sivedarkmatterhalosatthehighestredshifts,andmore
strong QSO-galaxy cross-correlation function. work is clearly required.
The QSO-galaxy cross-correlation function has been One complication of these studies is that the majority
measured at z < 4 in the past. At z (cid:46) 1 it is found to of them are focused on dropout selection, which selects
beingoodagreementwiththeauto-correlationofgalax- galaxiesoverabroadredshiftrangeof∆z ∼1(e.g.Ouchi
ies and QSOs, and it has been shown to be independent etal.2004a),correspondingto∼520h−1cMpcatz =4.
of the QSO luminosity, and weakly dependent on red- A large part of such a volume is unassociated with the
shift (e.g. Padmanabhan et al. 2009; Coil et al. 2007). QSO, which introduces projection effects that dilute the
Adelberger & Steidel (2005) measured the AGN-galaxy overdensity around the QSO making it much more dif-
cross-correlation function at higher redshifts (2(cid:46)z (cid:46)3) ficult to detect. Furthermore, most work at the highest
findingacross-correlationlengthofr ∼5h−1Mpcfora redshifts have focused their searches around a handful
0
slope of γ = 1.6 which is similar to the auto-correlation of individual QSOs, and given the poor statistics and
of Lyman Break Galaxies (LBGs) at z ∼ 3 (Adelberger large cosmic variance (which is typically not taken into
et al. 2003). They also claim an independence of the account), this could preclude the detection of an over-
cross-correlationlengthwiththeAGNluminosity,imply- density.
ing that both faint and bright AGNs should be found in In this paper we study the environs of QSOs at z ∼4.
haloswithsimilarmasses. Thehighestredshiftmeasure- There are several advantages to working at this redshift.
mentofQSOenvironmentsistheworkofTrainor&Stei- First, it is the highest redshift at which auto-correlation
del(2012),whoquantifiedtheclusteringofLBGsaround measurements exist for QSOs (Shen et al. 2007), estab-
15 hyper-luminous QSOs at z = 2.7. They find a QSO- lishing that they reside in massive dark matter halos.
LBG cross-correlation length of r = 7.3±1.3h−1Mpc Second, the luminosity function and clustering proper-
0
for a fixed slope of γ = 1.5 and claim that this mea- ties of z ∼ 4 galaxies are also well known (e.g. Shen
surement is in agreement with the Adelberger & Steidel etal.2007;Ouchietal.2004a,2008). Thewell-measured
(2005) results. Additionally, they compute a halo mass luminosity function allows us to accurately determine
for those QSOs of log(M /M )=12.3±0.5, which is the background number density, essential for a robust
halo (cid:12)
in agreement with the halos masses inferred for fainter clustering analysis. Furthermore, the fact that the auto-
QSOs at the same redshift (White et al. 2012). correlation of QSOs and galaxies are both known, gives
Theoretical considerations suggest that high-redshift us an idea of what the cross-correlation should be on
QSOs live in massive dark matter halos, but not nec- large scales where linear bias models apply. In practi-
essarily the most massive ones (Fanidakis et al. 2013). cal terms, redshift z ∼ 4 also represents a compromise
However,ahighsignaltonoiseclusteringanalysisisnec- since the dark matter halos hosting QSOs are still ex-
essary to confirm this hypothesis. pected to be massive (Shen et al. 2007), while at the
In addition to these statistical clustering analyses, same time the characteristic galaxy luminosity L can
∗
manystudiesofindividualAGNenvironmentshavebeen beimagedwithmuchshorterexposuretimesthangalax-
conducted. The population of AGNs whose environ- ies at z (cid:38) 5, allowing us to observe a larger statistical
ments have been studied most intensively are the high- sample of QSO fields. Note that at z ∼ 4 the universe
redshiftradiogalaxies(HzRGs)atz ∼2−4, whichhave was only ∼ 1.5Gyr old, and only 0.5Gyr has elapsed
beenshowntooftenresideinproto-clusterenvironments since the end of reionization. Thus, our QSO targets are
(e.g. Venemans et al. 2007; Intema et al. 2006; Overzier definitelyyoungobjectsresidinginlargescalestructures
etal.2008;Hennawietal.2015). Athigherredshiftsthe that are still forming.
environments of other classes of AGN, such as optically- HerewepresentVLT/FORSimagingofsixz ∼4lumi-
selected QSOs, are currently less well constrained. Most nousQSOsfields. Usinganovelnarrowband(NB)filter
previous work focuses on searching for galaxies around technique designed to select LBGs in a narrow redshift
the most distant z (cid:38) 5 QSOs, and these results paint range(∆z ∼0.3)aroundQSOs. Thisminimizestheline-
a diverse and rather confusing picture: Stiavelli et al. of-sightcontamination,dramaticallyreducingtheprojec-
(2005), Zheng et al. (2006), Kashikawa et al. (2007), tion effects which are inherent in broad-band selection.
Utsumi et al. (2010), and Morselli et al. (2014) find a We measure the QSO-LBG cross-correlation function at
quite strong enhancement of galaxies compared to con- z ∼ 4 for the first time, to determine whether luminous
trol fields around z ∼5−6 QSOs, whereas Willott et al. QSOs at z ∼4 are surrounded by overdensities of galax-
(2005) Ban˜ados et al. (2013),Simpson et al. (2014) and ies. The large sample of QSOs studied allows us to beat
Mazzucchelli et al. (2016), find no significant excess of downthenoisefromlimitednumbersofgalaxiesandcos-
Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z ∼4 3
mic variance. Shen et al. 2009). A summary of the QSO properties
Theoutlineofthispaperisasfollows. Insection§2we are listed in Table 1, where we show more recent M
BH
describe the QSO target selection, we explain the novel estimates taken from Shen et al. (2011).
NB imaging technique used to select LBGs, and we give
details of the imaging observations, data reduction, and 2.2. A Novel Method to Select LBGs
photometry. We present the color criteria used to select
The traditional Lyman break technique used to select
LBGs and compute the redshift selection function of the high-redshift galaxies relies on the detection of the 912˚A
sampleinsection§3. ThemeasurementoftheQSO-LBG
flux break (the so-called Lyman limit break) observed in
cross-correlation function and LBG auto-correlation in
galaxiesduetotheabsorptionofphotonswithλ<912˚A
QSO fields are presented in section § 4, where we also
by neutral hydrogen in their interstellar and circum-
estimate the power law correlation function ξ(r) = (r/
galactic media. For this selection method, two bands
r )−γ parameters r and γ. We test the robustness of
0 0 are typically used bracketing the break, one located at
our results in section § 5, and summarize and conclude
λ<912(1+z)˚A,andtheotheratλ>912(1+z)˚A,where
in section § 6.
z is the redshift of the galaxies in question. Given this
ThroughoutthispapermagnitudesaregivenintheAB
configuration, a non-detection is expected in the band
system (Oke 1974; Fukugita et al. 1995) and we adopt
blueward of the break, whereas a clear detection is ex-
a cosmology with H = 70kms−1Mpc−1, Ω = 0.26
0 m pected redward of it, such that a very red color will be
and Ω = 0.74 which is consistent with the nine-year
Λ measured. Additionally, a third band is added at longer
Wilkinson Microwave Anisotropy Probe (WMAP) Ob-
wavelengthsinordertoeliminatepossiblecontaminants.
servations (Hinshaw et al. 2013). Comoving and proper
This method was originally explored using the UGR fil-
Mpc are denoted as “cMpc” and “pMpc”, respectively.
tersystemtodetectgalaxiesatz ∼3(Steideletal.1995,
2. OBSERVATIONSANDDATAREDUCTION 1996, 2003), however, it was subsequently generalized to
higher redshift (z ∼ 4−5) by using a filter set shifted
The dataset presented in this section was obtained
to longer wavelengths (Steidel et al. 1999; Ouchi et al.
from the ESO Archive (Program ID: 079.A-0644, P.I:
2004a).
Rix). This program was designed to search for LBGs in
At higher redshifts (z (cid:38) 4), a second break in galaxy
z ∼ 4 QSOs environments using a novel NB filter tech-
spectra becomes important. The Lyα opacity of the in-
nique. TheaimwastotestwhetherQSOswiththemost
tergalactic medium (IGM) rapidly increases with red-
massiveBHsatz ∼4liveinthemostmassivedarkmat-
shift, such that a large fraction of photons emitted by
terhalos. Inthissectionwesummarizethestrategyused
toselectthetargetedQSOs,weexplaintheNBtechnique galaxies with λ<1216˚A are absorbed by neutral hydro-
used to select LBGs, and we provide details of the imag- gen. This implies a break at λ = 1216˚A (the so-called
ing observations, reduction process, and photometry. Lymanalphabreak),whichcanbeusedtoselectgalaxies
analogous to the traditional Lyman break technique de-
2.1. QSO Target Selection scribed above. This Lyα break detection technique has
ThePIofthisprogramdesignedacustomsetoffilters been used to successfully identify galaxies and QSOs at
(see § 2.2 for details) to search for LBGs in QSO envi- z (cid:38)6 (Fan et al. 2000; Bouwens et al. 2007, 2010; Oesch
ronments. Using experiments with mock-catalogs, they et al. 2010; Ban˜ados et al. 2016).
showed that this filter set allowed one to select galaxies In order to achieve our goal of selecting galaxies phys-
with z = 3.78±0.08. Given this small redshift interval, ically associated with high-redshift QSOs, we need to
and with the goal of stacking the galaxy number counts select LBGs within a narrow redshift range centered on
from several QSO fields, the QSO targets were selected the QSO. However, the Lyman break method (using ei-
to span a narrow redshift range of ∆z = 0.04, centered ther the Lyman limit or Lyα breaks) efficiently selects
at z =3.78. LBGs in a broad redshift slice of ∆z ∼ 1 (e.g. Ouchi
Taking advantage of the large sample of QSOs from et al. 2004a; Bouwens et al. 2007, 2010), corresponding
the Sloan Digital Sky Survey (SDSS; York et al. 2000), to ∼ 520h−1cMpc at z = 4. For such a broad redshift
they first selected all QSOs in this redshift range. Given range,theoverdensitysignalaroundtheQSOwillbesig-
the goal of studying the most massive dark matter ha- nificantly diluted by the projection of galaxies at much
los at z ∼ 4, believed to be correlated with the most larger distances, hundreds of comoving Mpc away.
massive BHs, only QSOs with M (cid:38) 109 M were se- In order to address this problem, the PI proposed a
BH (cid:12)
lected. As is typical, the M was estimated from the novel selection technique analogous to the Lyα break
BH
emission line widths and continuum luminosities using method, but with the difference that the selection of
the so-called single-epoch reverberation mapping tech- LBGsisperformedusingtwoNBfilterslocatedveryclose
nique (Vestergaard 2002). One of the targeted QSOs to each other, instead of using broad bands. These filter
was not selected from SDSS, but it was added to the curves are compared to those used for traditional LBG
samplebecauseitbelongstotheredshiftandM range selection in Fig. 1. The advantage of using NB filters is
BH
of interest. The final sample is comprised of six bright that they allow one to select LBGs in a much narrower
QSOs with i<20.2 mag. redshiftrangeof∆z ∼0.3(∼167cMpcatz =3.78)(see
We verified that none of the QSOs had a detected ra- section § 3.4), which is ∼3.3 times smaller than the red-
dio emission counterpart at 20cm by checking the Faint shift range covered when broad bands are used, allowing
Images of the Radio Sky at Twenty-centimeters (FIRST one to minimize line-of-sight projections from physically
Becker et al. 1995) catalog, since it is known that radio unassociated galaxies.
emissioncouldstronglyaffectthegalaxyclusteringprop- This method has never been used before to select
erties in AGN environments (e.g. Venemans et al. 2007; LBGs, and the filters used to perform the observations
4 Garc´ıa-Vergara, C. et al.
Table 1
TargetedQSOsproperties.
Field RA(J2000) DEC(J2000) Redshift i log(MBH/M(cid:12))a
SDSSJ0124+0044 01:24:03.78 00:44:32.67 3.834 17.99 10.15±0.03
SDSSJ0213–0904 02:13:18.98 -09:04:58.28 3.794 19.03 9.57±0.18
J2003–3300b 20:03:24.12 -32:51:45.02 3.773 17.04 9.7
SDSSJ2207+0043 22:07:30.48 00:43:29.37 3.767 19.47 9.13±0.16
SDSSJ2311–0844 23:11:37.05 -08:44:09.56 3.745 20.18 9.41±0.24
SDSSJ2301+0112 23:01:11.23 01:12:43.34 3.788 19.44 8.55±0.80
a VirialBHmassesfromShenetal.(2011).
b ThisQSOwasnotselectedfromSDSS,butitwastargetedbecauseitbelongstotheredshiftrangeofinterest. The
propertiesshownherearefrom(McLeod&Bechtold2009),whodonotreporttheerrorfortheBHmassmeasurement.
8000s, 4000s, and 1800s for NB , NB , and r
571 596 GUNN
respectively. Observations were acquired in shorter indi-
1.0 Ly alpha z=3.78 vidualditheredexposures,inordertofillthegapbetween
NB NB
0.8 571 596 the CCDs and to facilitate the data reduction process
r
0.6 GUNN (cosmicrayandbadpixelrejection, buildingasuperflat,
etc). A spectrophotometric standard star was observed
0.4
units) 00..02 Ly limit odnulryinigntthheethserceoenndigahntds wthaisrd0.6ni-gh0t.8. aTrchseect.ypical seeing
bitrary 1.0 Ly alph a z=3.78 tasSkcsienancediomuargoews nwecruestroemduccoeddesuswinrgittsetnanidnartdheIRInAteFr6-
F (arλ00..68 B R i aclcutdiveedDbaiatsasLuabntgraucatgioen(IaDnLd)fl.aTthfieerldedinugc.tiAons opurorciemssagines-
Fshi ogwun000r...4e0240o01n0.aLUyL lpiBmpiGet5r00sp0iamnuella:teFd6i0lt0se0preλcc(toÅrnu)fimg7u0ar0a0ttizon=us38e0.d7080in(steheiss9se0tc0ut0idoyn, efiioasxbnetShlejdaeEribicvenxtdietgtsrerasadowcgcuieietittolnhslrauicgnesm(mudBfipranetae-arhmcrttelfliiinenopasntp.&cioinpFmmAgaoatrbratgnitleengohrseouna,drtstcis,,ttrhhwe1wmae9eet9.esfi6pcdr)ieseurwtnfsocamiernsmagfusrekstadehemddetehtausoelnlwrcflteirhtagehet--
ate a source catalog for each individual image and then
§ 3.1 for the simulated spectra details). The NBs were designed
speciallyforthisprogram,inordertoidentifyLBGsatz∼3.78by SCAMP(Bertin2006)wasusedtocomputeanastromet-
detectingtheLymanalphabreak. Thisfilterconfigurationselects ricsolution,usingtheSDSS-DR7r-bandstarcatalogsas
galaxiesinaquietnarrowredshiftsliceof∆z∼0.3. Lower panel: the astrometric reference. Finally, the individual images
Exampleofafiltersetusedtoidentifygalaxieswiththestandard
were sky-subtracted, re-sampled, and median-combined
LymanbreaktechniquewhichisbasedinthedetectionoftheLy-
manlimitbreak. ThefiltercurvesshownarethoseusedbyOuchi using SWarp (Bertin et al. 2002), and then the noisy
etal.(2004a)tofindLBGsatz∼4overaredshiftsliceof∆z∼1.0 edges of the combined images were trimmed.
For the flux calibration, we only had observations of
were custom designed to select LBGs at z ∼ 3.78 cen- the spectrophotometric standard star SA109-949 at the
tered on the redshift of our six QSO targets. The two beginning of the last two nights. The tabulated spec-
NB filters used in this study are NB571 (λeff = 5657˚A, trum of this star has a coarse sampling of 25˚A(Stone
FWHM = 187˚A), and NB (λ = 5947˚A, FWHM = 1996) which is not suitable when NB filters are used.
596 eff
116˚A),whichwere designedto havea gapbetweenthem For the first night, spectrophotometric standard stars
to exclude the Lyα emission line at z = 3.78. Then werenotobserved,butwetookadvantageoftwoexisting
the galaxy selection is not influenced by the Lyα line- SDSS star spectra in one of the fields taken during that
strength , but rather is sensitive to the Lyα break. Ad- night. The coordinates of the stars with available SDSS
ditionallydatawasalsocollectedinthebroadbandfilter spectra are RAstar1 = 21.014, DECstar1 = 0.740872 and
r (λ = 6490˚A) to help remove low-redshift inter- RAstar2 = 21.057, DECstar2 = 0.686577 and the median
GUNN eff
signal-to-noise ratio per angstrom of their spectra at the
lopers.
wavelengths of interest is 13.3 and 8.5 respectively.
2.3. VLT Imaging and Data Reduction The flux calibration process was as follows. For the
first night calibration we convolved the SDSS star spec-
Imaging observations were acquired on three con-
tra with the three filters curves in order to obtain stan-
secutive nights during 2007 September 9 - 11, using
dardmagnitudes. Thesemagnitudeswerecomparedwith
the FOcal Reducer and low dispersion Spectrograph 1
the stars instrumental magnitude (obtained using the
(FORS1; Appenzeller & Rupprecht 1992) instrument
MAG AUTO of SExtractor on the combined science im-
on the Very Large Telescope (VLT). The field-of-view
ages) to obtain the zero-points (ZPs) for each filter. A
(FOV) of FORS1 is 6.8×6.8 arcmin2 which corresponds mean final ZP was computed from the two stars and the
to ∼ 3.0×3.0pMpc2 at z = 3.78. The instrument pixel typical error for this ZP measurement was ∼ 0.08 mag.
scale is 0.251 arcsec/pix for images binned 2×2. For the second and third night calibration, we used the
EachQSOfieldwasobservedinthethreefiltersshown
in Fig. 1. The total exposure time for the filters was 6 ImageReductionandAnalysisFacility
Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z ∼4 5
spectrumoftheobservedspectrophotometricstartocon-
volve it only with the broad-band filter curve to obtain Table 2
4σ limitmagnitudesperfieldmeasuredina2(cid:48)(cid:48) diameteraperture
ther ZP.Theerrorinthiscomputationwas∼0.02
GUNN andseeingmeasuredontherGUNN images.
mag. After that, the differential ZPs from the first night
wereusedtodeterminetheNBzero-pointsforthesecond
Field NB571 NB596 rGUNN Seeing[(cid:48)(cid:48)]
and third nights for which we obtained a typical error of
∼0.11 mag. SDSSJ0124+0044 26.04 25.51 25.86 0.83
SDSSJ0213–0904 26.18 25.71 25.92 0.89
2.4. Photometric Catalogs J2003–3300 26.05 25.44 25.62 0.45
SDSSJ2207+0043 26.03 25.38 25.78 0.53
Object detection and photometry were performed us- SDSSJ2311–0844 26.02 25.60 25.84 0.76
ing SExtractor in dual mode, with the r image as SDSSJ2301+0112 26.04 25.55 25.91 0.70
GUNN
thedetectionimage. WesettheparametersBACK SIZE
and BACKPHOTO THICK such that the background
was calculated in regions of 64 pixels in size and then where the photometric catalogs are assumed to be 100%
recomputed locally in an annulus area of 24 pixels of complete. We extrapolated the linear fit to fainter mag-
thickness centered around the object. The parameters nitudes and we measured the completeness as a function
DETECT MINAREA and DETECT THRESH were set ofmagnitudeastheratioofthehistogramrelativetothat
such that every group of at least five contiguous pixels linearfit. Wefindthatatour4σ limitingmagnitudethe
havingavalueabove1.5σ (withσ thebackgroundRMS) completeness is on average ∼12%.
was considered as an object.
3. LBGSELECTIONATZ=3.78
In order to ensure an adequate color measurement
we need to carry out photometry in the same object LBG candidates at z = 3.78 were selected using the
area for the three different filters. Therefore, we con- Lyαbreaktechniqueadaptedtoourcustomfilters,which
volved our images with a Gaussian kernel to degrade its target the Lyα break at λ =(1+z)1216˚A. Our
rest−frame
PSF to match it with the worst seeing image for each twoNBfilterswerechosentobracketthisbreak,andthus
field. Then, the object magnitudes were estimated by we expect that LBGs at z =3.78 will have red colors in
the MAG APER parameter of SExtractor using a fixed NB −NB . Butifweusedonlythiscolorcriteria,we
571 596
aperture of 2(cid:48)(cid:48) diameter. This magnitude is not neces- could be including some low-redshift galaxy interlopers
sarily the total magnitude of the object, but is used to in the sample. In order to remove them, a third filter is
computethecolorsofgalaxies. Withthischoice,ifgalax- usedtogiveameasurementoftheLBGcontinuumslope
ies at z ∼4 are unresolved by the PSF, we are including using the NB −r color.
596 GUNN
the flux out to ∼ 3σ of the object’s PSF (for a seeing Sincethefiltersusedinthisstudyarenotstandard,the
of 0.8(cid:48)(cid:48)). This ensures that we measure the majority of colorcriteriatoselectLBGsisunknown. Wealsodonot
the object’s flux, as well as avoid contamination from know what colorslow-redshift galaxy contaminants have
other close sources. Magnitudes of objects not detected in this filter system. For this reason, we must explore
or detected with a signal-to-noise ratio (S/N) <2 either howgalaxiespopulatethecolorspaceinordertoselecta
in NB or NB were assigned the value of the corre- completeLBGssamplewhileavoidinglow-redshiftinter-
571 596
sponding 2σ limiting magnitude. lopers. Furthermore,inordertoperformaLBGscluster-
Here, the S/N of each object is defined as the ratio ing analysis in QSO fields we need to know the number
of counts in the 2(cid:48)(cid:48) aperture, given by SExtractor, to density of LBGs expected at random locations in the
the rms sky noise in the aperture. This rms sky noise universe. When a standard filter set is used (e.g. LBG
is calculated using an IDL procedure which performs 2(cid:48)(cid:48) selection using broad band filters), this number density
aperture photometry in ∼ 5000 different random posi- canbecomputeddirectlyfromtheLBGluminosityfunc-
tions in the image (avoiding the locations of objects) to tion measured from work using similar filters. However,
compute a robust measurement of the mean sky noise. in our case if we compute the number density from this
Thermsskynoiseiscalculatedasthestandarddeviation LBG luminosity function, we have to correct this quan-
of the distribution of mean values. tity to take into account the fact that our filter system
Magnitudes were corrected for extinction due to air- is mapping a different survey volume and does not nec-
mass using the atmospheric extinction curve for Cerro essarily identify all of the LBGs selected by broad-band
Paranal (Patat et al. 2011), and by galactic extinction selection. Specifically,weneedtoa)determinewhatfrac-
calculatedusingtheSchlegeletal.(1998)dustmapsand tion of LBGs we are detecting at any redshift (i.e. the
extinction laws of Cardelli et al. (1989) with R = 3.1. completeness) and b) determine the redshift range over
V
The error in the measured magnitude was computed by which we are selecting LBGs (∆z). Both of these goals
errorpropagation,withtheobjectfluxerrorgivenbythe can be achieved by performing an accurate computation
rms noise N in the aperture computed as we described of the redshift selection function φ (z), defined as the
z
above. LBG completeness as a function of redshift.
The mean 4σ limiting magnitude of the reduced im- In order to perform the optimal LBG selection and
ages was of 26.06 for NB , 25.53 for NB and 25.82 compute φ (z), we conducted detailed simulations to
571 596 z
forr for2(cid:48)(cid:48)diameterapertures. Theselimitingmag- model the distribution of LBG colors in the color-space.
GUNN
nitudes are listed in Table 2 for each field. Inthissectionwedetailhowthecolormodelingwasper-
For each field, we computed the completeness of the formed, we study what contaminants could be affecting
photometriccatalogsfortheimagedetectionr . For our LBGs selection, and we define a color criteria to se-
GUNN
that, we linearly fitted the logarithmic magnitude distri- lect LBGs at z = 3.78. Finally, we present the redshift
bution in the magnitude range 21.0 < r < 24.5 selection function providing the completeness as a func-
GUNN
6 Garc´ıa-Vergara, C. et al.
tion of redshift for the sample.
1.0
3.1. LBG Color Modeling
We performed a Monte Carlo simulation of 1000 LBG 0.8
spectra at each redshift, that were created to have dif-
ferent UV continuum slopes and Lyα equivalent widths
L(EBWGLsypαe)c,tsruachintfhoramttehdeybyreopurrodkuncoewtlhedegsepaocfeLoBfGpospsriobple- W )αLy0.6
E
erties. P ( 0.4
Eachsimulatedrest-framespectrumwascreatedinthe
following way. As a starting point, we considered a tem-
plate galaxy spectrum generated from Bruzual & Char- 0.2
lot (2003) population synthesis models7, corresponding
to an instantaneous burst model with an age of 70Myr, 0.0
a Chabrier (2003) IMF, and a metallicity of 0.4Z , as −300 −200 −100 0
(cid:12)
expected for LBGs at z ∼ 4 (Jones et al. 2012). We as- EWLyα
sumedapowerlawUVcontinuumforthistemplatewith
Figure 2. Normalized probability distribution function of
amplitude A and a slope α , such that we modeled its
flux as FBC(λ) = AλαBC. WBCe fit this model to the tem- cEoWrrLesypαonudsetdoefomristshioensliimneusl.atEeWd Lsypαecwtraas,cwhohseernefrnoemgataivGeauvassluiaens
plate spectrum over the UV continuum range (here de- distribution with rest-frame mean µ = −25˚A and σ = 40˚A
fined as 1300˚A< λ <2000˚A) by least-squares minimiza- (Shapley et al. 2003) plus an exponential tail of high EWLyα
tion to obtain the best fit A and α parameters. valueswithscalelengthofW0=−64˚A(Ciardulloetal.2012).
BC
First, we modified the UV slope of this template by
multiplyingitsfluxbyλα−αBC inordertoobtainaspec- amplitude B, as we described above, and Fcont is the
trum with a power law UV continuum given by Aλα. flux of the continuum given by Aλα. Note that we de-
The new slope α was chosen as a value taken randomly fined negative values of EWLyα for emission lines and
fromaGaussiandistributionwithmeanµ=−1.676and positive for absorption lines.
σ =0.39. These values are motivated by Bouwens et al. Once α and EWLyα were chosen for a given simulated
(2009), whopresented the UVcontinuum slopedistribu- spectrum, we dust-attenuated it using the starburst red-
tion of LBGs at z ∼ 4 for samples selected in different dening curve from Calzetti et al. (2000) and adopted a
magnitude ranges. color excess value of E(B−V) = 0.16 according to the
Second,weaddedaGaussianLyαlinewithrest-frame valuesestimatedforLBGsatz ∼3(Shapleyetal.2003).
central wavelength λ = 1215.7˚A, standard deviation After the dust-attenuation is applied, we model the
Lyα
σ andamplitudeB whichadjuststheintensityofthe fact that only a small fraction of Lyman limit pho-
Lyα
line. For all the simulated spectrum we used a fixed tons escape LBGs with an escape fraction parameter
σLyα =1˚A which agrees with the σLyα of the composite feλs<c912. Although this value is observationally poorly
constrained, studies suggest it is in the range 0.04-0.14
spectrum of LBGs at z ∼ 4 (Jones et al. 2012). The B
(Fern´andez-Soto et al. 2003; Shapley et al. 2006; Ouchi
value was adjusted in order to model a Lyα line with a
EWLyα value drawn randomly from a distribution cho- etal.2004a). Weassumedafixedvalueoffeλs<c912 =0.05,
sen to agree with observations of LBGs. The EW and multiplied the spectrum at λ ≤ 912˚A by this
Lyα
distribution was given by a Gaussian core plus a tail value. Wealsotestedourresultsusingdifferentvaluesof
to large negative equivalent widths to represent strong fλ<912, finding that the colors of simulated galaxies are
esc
line emitters. For the Gaussian core we adopted a mean relatively insensitive to the exact value of fλ<912 used,
esc
µ=−25˚A andstandarddeviationσ =40˚A(rest-frame), because these wavelengths are subsequently significantly
basedonthemeasurementsofShapleyetal.(2003),who attenuated by the IGM transmission function (see be-
studied the spectra of 811 LBGs at z ∼ 3. We thus as- low).
sume that the Gaussian core of the LBG EW distri- Finally,weredshiftedeachmodelspectrumtodifferent
Lyα
bution does not evolve significantly from z ∼3 to z ∼4. redshifts on a grid with a grid spacing of 0.02 and rang-
For the tail representing strong line-emitters, we modi- ing from z = 3.2 to z = 4.4. In the redshifting process
fiedtheGaussianbyaddinganexponentialfunctionwith we used the IGM transmission model T (λ) for the cor-
z
rest-frame EW scale length of W = −64˚A, as pre- responding redshift z from Worseck & Prochaska (2011)
Lyα 0
sentedinCiardulloetal.(2012). Inthiswayourmodelof to attenuate the flux blueward of the Lyα line8. Note
line emission encompasses both LBG and LAE spectra. thatinprincipleweshouldattenuateboththecontinuum
Fig. 2 shows the EW probability distribution func- bluewardoftheLyαlineandthelineitself,however,the
Lyα
tion used to simulate our spectral models. The EW EW valuesusedinthissimulationaretakenfromthe
Lyα Lyα
are defined as: literature, which are observed values that are not cor-
(cid:90) F rected for IGM attenuation, such that this line emission
EW =− Lyαdλ, (1) iseffectivelyalreadyattenuated. InFig.3weshowsome
Lyα F
cont examplesofourrest-framesimulatedspectra,whichhave
where F is the flux of the Lyα line (with the con- been normalized to have the same flux at λ=1245˚A.
Lyα
tinuum subtracted), which is given by a Gaussian with Ateachredshift,weintegratedthespectraagainstour
7 Obtainedfromhttp://bruzual.org/ 8 KindlyprovidedtousbyG.Worseck.
Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z ∼4 7
0.16. However,ifweconsidertheintrinsicscatterinLBG
3.0
properties(continuumslopeandEW )andphotomet-
150 Lyα
nits) 22..05 F (arbitrary units)λ15000 rp0staih.oc5ioinnuuatnlansdc)dhessrie−gptlhaea0icln.nyt6taciL(cid:46)eoBwsm,NGidtpBhseleer5it9ncze6ots(cid:39)−lhaoimr3rsG.rpb7aUl8renNo,gLNahedBo(cid:46)wGwseise0tlvhe.(8cein.tNri,doBIwinnc5ea7rp1teareg−lidsnioocNbninypBetlg5eoe9r,d6eowetb(cid:38)noe-
u
ry 10210 1215 1220 take into account the colors of low-redshift galaxies in
ra 1.5 λ(Å) our filter system to define a final selection criteria. We
bit perform this analysis in § 3.2, where we also test our
r
F (aλ1.0 LarByGtrcaoclkorpmreosednetliendgibnyprreepvriooduuscwinogrkthuesiLnBgGbreovaodlubtiaonnd-
LBG selection.
0.5
3.2. Low-Redshift Galaxy Colors
0.0
500 1000 1500 2000 2500 3000 We use template galaxy spectra to develop a basic un-
λ(Å) derstanding of how low-redshift galaxies populate the
color-color diagram in our new filters. We used a set of
Figure 3. Example of ten rest-frame simulated spectra using fivecommonlyusedtemplatesforestimatingphotometric
ourMonteCarlosimulation. Thespectrahavebeennormalizedto redshifts, such that they span the range of galaxy spec-
havethesamefluxvalueatλ=1245˚A.Thesubplotintheupper
tralenergydistributions(SEDs). Thetemplatesarefrom
rightcornershowsazoom-inoftheregionoftheLyαline.
thephoto-zcodeEASY(Brammeretal.2008),whichare
distilled from the PEGASE spectral synthesis models.
three filter transmission curves to obtain the fluxes and
We redshifted these template spectra from z = 0 to
then the LBG colors. In order to model the impact of
z = 3, and integrated them over our filter transmission
noise,weaddedphotometricerrorstothesimulatedLBG
curves to generate their evolutionary track. Note that
photometry. Tothisendwefirstassignedanr mag-
GUNN we need not attenuate these spectra by the IGM trans-
nitude to each simulated object by randomly drawing a
mission function T (λ), since our NB filters never cover
value from the z ∼ 4 LBG luminosity function, inte- z
rest-framewavelengthslowerthan1216˚A forthelowred-
grated over the same magnitude range as our LBG sam-
shifts considered. In Fig. 5 we show the evolutionary
ple (24.0 ≤ r ≤ 25.6 or 0.76 ≤ L/L ≤ 3.5; see
GUNN ∗ tracks for different galaxy types together with the me-
§3.3)9. Wealsoweightedtheluminosityfunctionbythe
dian LBG evolutionary track that we computed in § 3.1.
completeness of the source detection at each apparent
In order to test our Monte Carlo simulation as well as
magnitude and for each field (computed in § 2.4), which
theevolutionarytracksforlow-redshiftgalaxies,wehave
takes into account the fact that the fraction of sources
usedour1000simulatedspectraateachredshifttocom-
detecteddependsontheirmagnitude,suchthatthepho-
putethemedianLBGevolutionarytrackinthestandard
tometric catalog is complete for bright sources but less
BRifiltersetusedtoselectLBGsatz ∼4(seeFig.1)by
complete at the faint end. In this way the incomplete-
Ouchietal.(2004a). Wealsocomputedtheevolutionary
ness of our photometry is also factored into our color
track of these low-redshift galaxies in the standard LBG
modeling.
filtersinthesamewayasdescribedabove. Theseresults
Based on the simulated LBG colors the chosen r
GUNN are shown in Fig. 7, where we also overplot the selec-
value, we then determined the magnitude in the other
tion region used by Ouchi et al. (2004a) to select z ∼ 4
two filters NB and NB for each spectrum in each
571 596 LBGs. WefindthatthemedianLBGevolutionarytrack
redshift bin. In order to construct a noise model , we
from our Monte Carlo model lies within the Ouchi et al.
selected a galaxy sample from our photometric catalogs,
(2004a) selection region, and selects LBGs at z (cid:38) 3.5
andwecomputedthemedianmagnitudeerrorasafunc-
as claimed. Note also that our LBG evolutionary track
tionofthemagnitudeforeachfilter(withthemagnitude
agrees well with the Ouchi et al. (2004a) evolutionary
error computed as we explained in § 2.4). Finally, we
track(seeFig.4oftheirpaper)determinedfromamuch
assigned random Gaussian distributed magnitude errors
simpler model of LBG spectra and IGM transmission.
using our median relations, and then added this noise to
In addition we see that the evolutionary tracks of low-
the model photometry which defined the final photome-
redshift galaxies lie comfortably outside the BRi LBG
tryofthesimulatedspectra. Thecolorsforthe1000sim-
selection region as claimed by Ouchi et al. (2004a).
ulated spectra at each redshift are shown in Fig. 4. We
HoweverFig.5showsthatinourNBfilterset,someof
also computed the median of our 1000 rest-frame Monte
the low-redshift galaxies have similar colors as z = 3.78
Carlo spectra, redshifted it, and obtained the colors at
LBGs, which suggests that our new filter configuration
each redshift to compute the median evolutionary track
could make it challenging to select a sample of LBGs at
of LBG colors, shown as the black solid line in Fig. 4.
z = 3.78 with high completeness and at the same time
Fig. 4 indicates that the median colors of LBGs at
high purity. When we use NB filters the low-redshift
z =3.78areNB −NB =1.05andNB −r =
571 596 596 GUNN galaxy colors are located in a wider region in the color-
color plot in comparison with the location of the color
9 Giventhatforeachfieldwereachedslightlydifferentlimiting
locus of contaminants when broad band filters are used.
magnitudes, we simulated the LBG photometry field by field ac-
cordingtotheirrespectiverGUNNlimitingmagnitude. Thisresults We attribute this to sensitivity of the NB filters to fea-
inaslightlydifferentredshiftselectionfunctionforeachfield. turesinthegalaxyspectrasuchasemissionorabsorption
8 Garc´ıa-Vergara, C. et al.
Figure 4. Color-color diagram showing the simulated colors for 1000 LBGs spectra, plotted as redshift color-coded points according to
thecolorbar. ThemedianLBGevolutionarytrackisplottedasablackcurve. ThefilledpointsoverthiscurveindicatethemedianLBGs
colors at different redshift ranging from 3.6 to 4.2. The largest circle shows the exact position of the median z =3.78 LBG colors. The
dashedlineindicatestheselectionregionusedtoselectLBGsaccordingtotheeqn.(2).
lines. In the case of broad bands these features are di- binationwiththeλ ∼2900˚A break. WhentheNB
RF 571
luted by averaging over large regions of spectra, but for is located over this absorption the filter NB falls on
596
NB the features result in large excursions in color with the continuum, then, red colors are detected (points E
changing redshift, making the low-redshift galaxy locus andGonthemagentaandbrowncurves,respectively,in
extend over a larger region of color space that overlaps Fig. 5). Other interlopers are galaxies with strong flux
with the colors of z =3.78 LBGs. breaks redshifted just between our NB filters. One ex-
Given that LBG colors at z = 3.78 span the range amplearegalaxiesatz ∼1.23withalargeλ ∼2640˚A
RF
NB571−NB596 (cid:38) 0.5 and −0.6 (cid:46) NB596−rGUNN (cid:46) 0.8 break(pointsDandFonthemagentaandbrowncurves,
(seeFig.4), thereareseveraltypesofcontaminantsthat respectively, in Fig. 5) and galaxies at z ∼ 1.83 with a
could be affecting our LBG selection. Their colors are strong break at λ ∼ 2085˚A (point B on the brown
RF
indicatedbypointsontherespectivelow-redshiftgalaxy curve in Fig. 5).
evolutionary tracks are labeled by with letters in Fig. 5,
and some examples are shown in Fig. 6. The first type 3.3. Selection Region and LBG Sample
are red galaxies at z ∼0.45 having a large λ ∼4000˚A
RF As we are interested in measuring the clustering prop-
Balmer break and strong Calcium H & K absorption.
erties of LBGs at z = 3.78, we need to select a sample
This break is located just between our two NBs, so they
withhighcompletenessandpurity. Inordertoavoidlow-
present red colors (point C in brown curve in Fig. 5).
redshiftcontaminants,wewereforcedtochooseasmaller
The second type of interlopers are star-forming galaxies
selection region in the color-color diagram, which results
atz ∼0.60withstrong[OII]3727˚A emissionlines. Ifthe
in relatively low completeness, but it ensures that the
NB is located just over this line, and NB over the
596 571 sample is not highly contaminated.
continuum, we again detect red colors (point A on green
First, we defined two vertical color cuts in Fig. 4, one
curveinFig.5). Thethirdtypeofinterlopersaregalaxies
to the left of the median LBG colors at z = 3.78 and
at z ∼ 1.04 with strong MgI and MgII absorption lines
one to the right. The first cut is meant to exclude LBGs
atλ =2852˚A,andλ =2799˚A respectivelyincom-
RF RF located in the upper left region of the diagram, which
Strong Clustering of Lyman Break Galaxies around Luminous Quasars at z ∼4 9
22..55 44
LBG 3.9
Elliptical
22..00 SSba 33 3.8 1
Sc 3.7
Irregular
11..55 3.6 3 1
B596 G 22 33..54 3 2
B− N571 11..00 3.7 3B.8CDFE B - R 11 33..23 00032 2 1
N 00..55 A 3.9 2 1
3.6 30 3 LBG
00..00 00 0 2 1 EllipticSaal
4.0 Sb
Sc
Irregular
−−00..55 --11
−−11..00 −−00..55 00..00 00..55 11..00 11..55 --00..55 00..00 00..55 11..00 11..55 22..00
NB − r R - i
596 GUNN
Figure 5. Evolutionarytracksoflow-redshiftgalaxiesredshifted Figure 7. Same as Fig. 5 but using the filter system used by
from z = 0 to z = 3. We plot as brown, magenta, orange, blue, Ouchi et al. (2004a) to select LBGs at z ∼ 4 (broad band filters
and red curves the evolutionary track of elliptical, Sa, Sb, Sc, B, R, i). Filled circles over the black curve indicate colors of
and Irregular galaxies, respectively. We overplotted the track of LBGsfromredshift3.2to3.9. Filledcirclesoverthecurveofthe
LBGscomputedaswasexplainedinsection§3.1asablackcurve. low-redshift galaxies indicate colors from redshift 0.0 to 3.0. The
Filled circles over the black curve indicate colors of LBGs from dashed line is indicating the region used Ouchi et al. (2004a) to
redshift3.6to4.0,andthelargestblackpointindicatestheexact selectLBGsintheirwork.
position of the color of LBGs at z = 3.78. Filled circles labeled
with letters over the low-redshift galaxies evolutionary tracks are
indicatingthecolorsofsomecontaminantsthatcouldbeaffecting maintaining the highest completeness possible.
ourselection: galaxiesatz=0.60(A),z=1.83(B),z=0.45(C),
We also tested several different color criteria to select
z=1.23(DandF)andz=1.04(EandG).
LBGs. In section § 5.2 we will further discuss our color
selection,contaminationbylow-redshiftgalaxies,andthe
z=0.45 z=0.60 impact that contamination can have on our clustering
1.0 1.0
measurements. There we argue that the choice of color
0.8 0.8 selection that we present here selects a reasonably com-
F (arbitrary units)✁000...246 F (arbitrary units)✄000...246 pctiuloetntses:aLrBeGshsoawmnpilnew4i,thanhdigdhepfiunreidty.byOuthrefinfoallloswetinogfcroelloar-
NB −NB >1.2
0.0 0.0 571 596
3000 4000 5000 6000 7000 8000 3000 4000 5000 6000 7000 8000
z=(cid:0)(1Å.0)4 z=✂(1Å.2)3 −0.6<NB596−rGUNN <0.8
1.0 1.0 NB −NB >0.7(NB −r )+0.9 (2)
571 596 596 GUNN
0.8 0.8
We selected LBGs based on our galaxy photometry,
F (arbitrary units)✆000...246 F (arbitrary units)✞000...246 btbNhyuBetf5aL9rl6eBsqeaGudniredcetoedrncGttsUiionoNuunNrusc,mefiws.lteteIoornsn,hloyatrvodceeoernnastsioSud/rereNreedadu≥scooeb4lij.cde0ocndtinsteattmbehcoaitnttihoahntatiohvoneef
0.0 0.0 FLAGS= 0 in SExtractor, which excluded objects that
3000 4000 5000 6000 7000 8000 3000 4000 5000 6000 7000 8000
(Å) (Å) were blended, saturated, truncated (too close to an im-
☎ ✝
Figure 6. Examples of interlopers that could affect our LBGs age boundary), or affected by very bright neighboring
selection. Weshowthegalaxyspectraandthepositionofourthree objects. Brightstarsinourimagesweremaskedinorder
filters over it. Top left panel: The spectra of a elliptical galaxy
to avoid spurious object detection due to contamination
at z = 0.45, with strong Balmer break located at λ = 5840˚A
obs from their stellar flux. This procedure results in a set of
and intense Calcium H & K absorption. Top right panel: The
spectra of a galaxy at z = 0.60, with intense OII emission line masks indicating where we were able to detect galaxies,
at λobs = 5925˚A. Bottom left panel: The spectra of a galaxy at which we use later in our clustering analysis to compute
z=1.04,withMgIandMgIIabsorptionatλobs∼5650˚A.Bottom the effective area of our survey.
right panel: The spectra of a galaxy at z = 1.23, with a large
We also imposed a lower limit on the magnitude in
breakatλ =5887˚A.
obs order to exclude bright low-redshift interloper galaxies
fromourselection. Thusweonlyconsideredobjectswith
mostly corresponds to LBGs at z ∼3.9 with strong Lyα magnitudes fainter than r = 23.97, corresponding
GUNN
lineemission. ThesecondcutavoidsLBGsatz >3.9. A to LBGs with L ∼ 3.5L . We chose this value by com-
∗
third color cut defines a lower limit for NB −NB , putingtheLBGluminosityfunctionatz ∼4,andfinding
571 596
which ensures we are detecting the Lyα break, while at the bright end cut at which we would lose no more than
the same time avoiding LBGs at z (cid:46) 3.7. We used a 1% of the galaxies. In other words, 99% of the total
diagonal color cut, to most effectively avoid the contam- number of LBGs have magnitudes between our bright
ination of low-redshift galaxies (see Fig. 5), while at the end cut of r = 24.0 and the limiting magnitude
GUNN
same time including most of the LBGs at z =3.78, thus r = 25.82 (mean limit magnitude at 4σ for a 2(cid:48)(cid:48)
GUNN
10 Garc´ıa-Vergara, C. et al.
Figure 8. Color-color diagram for the six stacked QSO fields.
Here the evolutionary track showed in Fig. 5 is plotted as
redshift color-coded track according to the color bar. We have
highlighted the selected LBGs as red points. The magenta
points indicate the color of each QSO in the filters. Arrows
indicate lower limits for NB571 −NB596 color. These are cases
in which the object was not detected in NB571 filter at 2σ level
andmagnitudewasreplacedbythecorrespondinglimitmagnitude.
diameter aperture) of our images, which corresponds to
L=0.76L . Inthiswaywecansafelyassumeweareex-
∗
cluding only extremely rare bright LBGs. For the LBG
luminosity function we used the Schechter parameters
from Ouchi et al. (2004a) who studied the photometric
properties based on a large sample of ∼ 2200 LBGs at
z ∼ 4. The values used are φ∗ = 2.8×10−3h3 Mpc−3,
70
M∗ =−20.6 mag, and α=−1.6.
1700
Given all of these selection criteria and the color cuts
definedineqn.(2),weselectedLBGsineachofourfields.
We compute the total area of our survey by adding the
effective area of each individual field, which is defined
by subtracting the masked area from the total area of
the image. The the total area of our survey is 232.7
arcmin2 corresponding to an average area per image of
38.79 arcmin2 (recall the FOV of FORS1 is 6.8 × 6.8
arcmin2 or 46.24 arcmin2). We show color-color dia-
gramsofobjectsdetectedinallsixofourfieldsinFig.8.
Wefoundatotalof44LBGs(seeTable3)corresponding
to a mean number density of 0.19 LBGs arcmin−2. Im-
age cutouts in our three filters for several of our selected
LBGsareshowninFig.9. InFig.10weshowthespatial
distributionoftheLBGsrelativetotheQSO(reddotat
zero)foroursixfields. Wealsoshowtheindividualcolor-
colordiagramsandindicatethenumberofLBGsfoundin
each individual field in Fig. 11. Note that the number of
LBGs in the fields cannot be directly compared because
each image has different limiting magnitude and differ-
Figure 9. Images of some selected LBGs. From left to right we
ent effective area (different reduced image size, masked show the NB571, NB596 and rGUNN images. Each panel is 7.5(cid:48)(cid:48)
region, etc). In Fig. 12 we show a false color image of onaside. Theredcircleshowthepositionofthedetectedobject,
the field around QSO SDSS J2301+0112 with the LBG anditssizecorrespondtotheregioninwhichthephotometrywas
done(2(cid:48)(cid:48)indiameter). Themagnitudesareindicatedineachpanel.
candidate positions indicated.
3.4. Redshift Selection Function
nosityfunction,computemagnitudesandcolors,andadd
WeusedtheLBGcolormodelingmachinerydescribed photometric errors. We then compute the completeness
in § 3.1 to compute the redshift selection function φ (z) at each redshift by calculating the fraction of simulated
z
ofourLBGcolor-selectioncriteria. Ateachredshiftstep, LBGs that satisfy the selection criteria defined in § 3.3,
we redshift the 1000 rest-frame simulated LBG spectra namely: fulfillthecolorcriteriaineqn.(2),andfulfillthe
intotheobservedframe,drawluminositiesfromthelumi- magnitude constraints (given by the 4σ limiting magni-