Galaxy Alignments in Very X-ray Luminous Clusters at z>0.5

0.74 MB·English

by  Chao-Ling Hung

Mon.Not.R.Astron.Soc.000,1–??(2002) Printed16January2012 (MNLATEXstylefilev2.2)
Galaxy Alignments in Very X-ray Luminous Clusters at
z > 0.5
2
Chao-Ling Hung1⋆ & Harald Ebeling1
1
0 1Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
2

n
a Accepted 2012January12.Received2012January11;inoriginalform2011December10
J

3
1 ABSTRACT
We present the results of a search for galaxy alignments in 12 galaxy clusters at

] z > 0.5, a statistically complete subset of the very X-ray luminous clusters from the
O
MAssive Cluster Survey (MACS). Using high-quality images taken with the Hubble
C Space Telescope (HST) that render measurement errors negligible, we find no radial
. galaxy alignments within 500 kpc of the cluster centres for a sample of 545 spec-
h
troscopically confirmed cluster members. A mild, but statistically insignificant trend
p
- favouringradialalignmentsisobservedwithinaradiusof200kpcandtracedtogalax-
o iesonthe clusterredsequence.Ourresultsformassiveclustersatz >0.5areinstark
r contrast to the findings of previous studies which find highly significant radial align-
t
s ments of galaxies in nearby clusters at z ∼ 0.1 out to at least half the virial radius
a
using imaging data from the SDSS. The discrepancy becomes even more startling if
[
radialalignmentbecomesmoreprevalentatdecreasingclustercentricdistance,assug-

1 gestedbybothourandpreviouswork.We investigateanddiscusspotentialcausesfor
v the disparity between our findings based on HST images of clusters at z > 0.5 and
7 those obtained using groundbased images of systems at z ∼ 0.1. We conclude that
2
the most likely explanation is either dramatic evolution with redshift (in the sense
7
that radial alignments are less pronounced in dynamically younger systems) or the
2
presenceofsystematicbiasesin the analysisofSDSS imagingdata thatcauseatleast
.
1 partly spurious alignment signals.
0
2 Key words: galaxies:clusters: general; galaxies:evolution; galaxies:kinematics and
1 dynamics
:
v
i
X
r 1 INTRODUCTION In dense cluster environments, extensive evidence is
a
found of alignments between the brightest cluster galax-
Galaxyandclusterorientationsprovidecrucialinsightsinto
ies (BCGs) and their host-cluster halos (Binggeli 1982),
the processes governing cluster formation and evolution.
an effect that is again caused by dynamical connections
On large scales, the distributions of galaxies in clusters are
to large-scale filamentary structures. For cluster members
found to align with the direction toward their neighbours
other than the BCGs, any intrinsic alignment might be ex-
within distancesoftensof Mpc(Binggeli 1982),atendency
pected to be destroyed by their gravitational interaction
thatisexplainedbyapreferenceforclusteringandmerging
with the host-cluster halos on a time scale of a few or-
along large-scale filamentary structures (West et al. 1995).
bits (Coutts 1996). However, using Sloan Digital Sky Sur-
Onsmallerscales,intrinsicgalaxyalignmentsgenerateddur-
vey (SDSS) data in a study of a sample of 85 X-ray se-
ing galaxy formation are observed on scales of a few Mpc
lected clusters at 0.02 < z < 0.23, Pereira & Kuhn (2005)
(Lee & Pen2007)withdifferentorigins,however,forellipti-
(hereafterPK05)findatendencyforthemajoraxesofclus-
cal and spiral galaxies. Similar to the physical mechanisms
ter galaxies to be aligned with the radius vector pointing
behindcluster alignments, anisotropic accretion of material
toward the cluster centre. They propose that this radial
ontogalaxy halosalong filamentarystructurescan resultin
alignment istheresult oftidaltorquingexertedbythehost
thealignmentofellipticalgalaxies(West1994).Bycontrast,
cluster halo (Pereira, Bryan, & Gill 2008; Pereira & Bryan
the alignment of spiral galaxies is believed to be caused by
2010).Faltenbacheret al.(2007)(hereafterF07)confirmthe
correlations between their spin axes originating from initial
radial alignment signal for a sample of galaxy groups at
large-scale tidal fields (Pen et al. 2000).
0.02 < z < 0.2 selected from the SDSS group catalogue,
andfurtherfindatrendforthesignaltobemoresignificant
⋆ Email:[email protected] near thecluster centreand for redder galaxies.
2 Chao-Ling Hung & Harald Ebeling
So far almost all searches for galaxy alignments have
Table 1. Numbers of cluster members inthe 12 MACSclusters
been conducted for relatively nearby clusters owing to the withintheACSfieldofviewforvarioussubsamples:spectroscopi-
limited depth of readily available ground-based imaging callyconfirmed(A),red-sequenceselected(B),bothspectroscop-
data. If a study akin to PK05 could be conducted at sig- ically and colour-selected (A+B) and spectroscopically but not
nificantly higherredshift, thepresence or absence of galaxy colourselected (A-B).
alignments in distant clusters could shed light on the tem-
poral evolution of the effect and thus on the dynamical MACSname n(A) n(B) n(A+B) n(A-B)
timescales of the physical mechanisms at work. Unfortu-
MACSJ0018.5+1626 100 233 62 38
nately, measuring galaxy orientations from SDSS data is
MACSJ0025.4−1222 74 223 62 12
extremely challenging already at low to moderate redshifts
MACSJ0257.1−2325 50 142 33 17
duetothepoorseeingandinsufficientpixelsampling.High-
MACSJ0454.1−0300 75 159 52 23
qualityimagesarethusessentialinobtainingprecisegalaxy
MACSJ0647.7+7015 30 71 12 18
orientation measurements, specifically at high redshift. MACSJ0717.5+3745 120 316 97 23
Inthispaper,wediscussourstudyofgalaxyalignments MACSJ0744.8+3927 65 160 46 19
in 12 X-ray luminous clusters at z > 0.5 from the Massive MACSJ0911.2+1746 63 162 46 17
Cluster Survey (MACS; Ebeling et al. 2007) as a first step MACSJ1149.5+2223 80 267 58 22
towardinvestigatingtheevolutionofgalaxyalignmentswith MACSJ1423.8+2404 47 127 38 9
lookback time. All 12 clusters were observed with the Ad- MACSJ2129.4−0741 82 173 54 28
MACSJ2214.9−1359 86 209 67 19
vancedCameraforSurveys(ACS)aboardtheHubbleSpace
Telescope (HST).We describe our target clusters, the HST Total 872 2242 627 245
observations, and image reduction procedures in 2. Clus-
§
ter membership determination and galaxy shape measure-
mentsaredescribedin 3.Resultsongalaxyalignmentsare about 4500 seconds. Bad-pixel masking, geometric distor-
§
presented in 4.1 and 4.2, and possible systematics are ex- tion correction, cosmic ray rejection, image stacking and
§ §
amined in 4.3. Weinterpret ourresults and compare them resampling were performed on the flat-fielded images us-
§
with those of studies in nearby clusters in 5; a conclusion ing the MultiDrizzle program (Koekemoer et al. 2002). For
§
is given in 6. MACSJ0018.5+1626, observed in November 2010, addi-
§
ABmagnitudesareusedthroughout.Weadoptthecon- tional Charge Transfer Efficiency (CTE) corrections were
cordance ΛCDM cosmology with H0 = 70 km s−1 Mpc−1, applied to the data using the pixel-based CTE correc-
ΩM =0.3 and ΩΛ =0.7. tioncode(Anderson & Bedin2010)beforefurtherreduction
with the MultiDrizzle program. We applied the optimized
resampling scales of 0.03′′, a Gaussian drizzle kernel, and
2 TWELVE MACS CLUSTERS AT Z >0.5 pixfrac=0.8toavoidaliasing inthePointSpreadFunction
(Rhodeset al. 2007). Pseudo-color HST/ACS images of all
MACS provides a statistically complete sample of themost
12clustersareshowninFigure1.Objectdetectionandpho-
X-ray luminous clusters at z > 0.3 (Ebeling et al. 2001).
tometry were performed on the reduced ACS images using
Ebeling et al. (2007) present a subsample of the 12 most
SExtractor (Bertin & Arnouts 1996). We removed the ob-
distant MACSclusters at z>0.5, with 11of themat 0.5<
jectswithSExtractorFLAGSlargerthan4aswellaspoint-
z < 0.6 and MACS J0744.8+3927 at z = 0.698. Like all
likeandspurioussourcesidentifiedfromtheirlocationinthe
MACSclusters,thesesystemsareverymassive(M 1014
1015M⊙; Mantz et al. 2010). Being purely X-ray ∼selected−, distribution of peak surface brightness versusmagnitude.
this sample is highly diverse with respect to optical ap-
pearanceanddynamicalstate.Forexample,MACSJ0025.4–
1222consistsoftwosubstructuresofnearlyequalmasswith 3 ANALYSIS
the hot gas residing in between them, showing it to be a
3.1 Cluster Membership Determination
post-collision merger(Bradaˇc et al. 2008; Mann & Ebeling
2011). Similarly, in-depth analyses of MACSJ0717.5+3745
The most accurate way to determine cluster membership
and MACSJ1149.5+222 show highly complex structures
is via spectroscopic observations of galaxies in our target
and dynamics (Ma et al. 2009; Smith et al. 2009). On the
fields. Spectroscopically determined redshifts are available
otherhand,MACSJ1423.8+2404 features aprominentcool
for 1150 objects from C.-J. Ma et al. (2011, in prepara-
core and a single dominant cD galaxy, implying that it is ∼
tion), Ma et al. (2008) and the NASA/IPAC Extragalactic
close to fully virialized (Limousin et al. 2010).
Database. Galaxies with a radial velocity within 3σ (where
σ indicates the dispersion in the velocity distribution) of
the systemic cluster velocity are taken to be cluster mem-
2.1 HST Imaging
bers(hereaftersampleA),whilethosewitharadialvelocity
All 12 target clusters were imaged with the ACS (Wide aboveorbelowthe3σ thresholdareselected asbackground
Field Channel) on HST (PID: 9722, 10703, 11560, PI: and foreground galaxies, respectively.
H. Ebeling; PID: 10493, PI: A. Gal-Yam). The field of Toincreasethesamplesize,wealternativelyselectclus-
view of ACS/WFC (3.5 3.5 arcmin2) corresponds to ap- ter members based on galaxy colour. For each cluster we
proximately 1.23 1.23×Mpc2 at z 0.55 and is thus well identify the red sequence from a colour-magnitude diagram
× ∼
matchedtothephysicalsize oftheclustercores. Eachclus- (F555W–F814W versus F814W; see Figure 2 for an exam-
ter field was imaged in the F555W and F814W filters for ple). The red sequence is formed by old elliptical galaxies
Galaxy Alignments in Clusters at z > 0.5 3
Figure 1.Three-colorimagesofour12MACSclusterswithF555W,(F555W+F814W)/2 andF814Wusedfortheblue,greenandred
channel,respectively.Clustersareshowninorderofascendingrightascensionfromlefttorightandtoptobottom.Ineachclusterfield,
theredcrossindicates thelocationofthepeakoftheX-raysurfacebrightness,whiletheyellowboxmarksthechosenBCG.Theinner
andouterwhitecircleshavearadiusof200and400kpcattheclusterredshift,respectively.
4 Chao-Ling Hung & Harald Ebeling
3.0
2.5
g)
a
m 2.0
W (
1.5
4
1
8
F 1.0
W-
5 0.5
5
5
F 0.0
-0.5 Figure 3.Definitionofθ,ξ,andφ.
18 20 22 24 26 28
F814W (mag)
3.3 Cluster Centre Determination
Figure 2. Colour magnitude diagram of MACSJ0717.3+3745. The location of the cluster centre would ideally be defined
The grey dots represent all galaxies in the field, and the black as the position of the peak of the dark-matter distribution.
dotsarered-sequenceselectedclustermembers.Thecrossesmark Since, however, maps of the dark-matter distribution are
galaxieswithredshiftinformationwheregreen,blue,andredindi- not available for the majority of our clusters, we use two
catespectroscopicallyconfirmedmembers,foreground,andback-
alternative estimators for the cluster centre: the location of
groundgalaxies,respectively.
the X-ray surface-brightness peak and the position of the
BCG. We will further discuss the impact of the choice of
cluster centrein some detail in 4.1.2.
whosespectrashowsimilarD4000breaksresultingfrompho- §
Seven out of the 12 clusters feature a single
tosphericabsorptionsofheavyelements(Bower et al.1992).
dominant BCG in the cluster centre; their aver-
Galaxies falling within 2σ of the red sequence (here σ
± age offset between from the X-ray surface-brightness
is the dispersion in the red sequence along the F555W–
peak is 5′′.7 ( 35 kpc). The remaining five clusters
F814Waxis)andfeaturingmagnitudesofF814W <24mag ∼ ∼
(MACSJ0018.5+1626, MACSJ0025.4–1222, MACSJ0454.1–
are classified as clustermembers (hereafter sample B).The
0300, MACSJ0647.7+7015 and MACSJ0717.5+3745) con-
numbers of cluster members in each sample and for each
tain multiple cD-type galaxies and show clear signs of
cluster are listed in Table 1.
substructure.ForMACSJ0018.5+1626,MACSJ0454.1–0300
and MACSJ0647.7+7015, we choose the BCG to be the
brightest galaxy within 200 kpc of the X-ray peak. For
3.2 Galaxy Orientation Measurement
MACSJ0025.4–1222 and MACSJ0717.5+3745, we choose
GalaxyorientationsaremeasuredwithSExtractorfromthe the brightest galaxy in the most massive substructure as
F814Wimages.Weusethewindowedpositionalparameters identifiedbyBradaˇc et al.(2008)andMa et al.(2009).The
from SExtractor with all derived quantities based on the choice of BCGs are indicated in Figure 1.
weighted second-order brightness moments,
2
Qij =Z d θWrg(|θ|)θiθjI(θ), (1) 4 RESULTS
4.1 Galaxy Orientation Distribution
whereWrg(|θ|)indicatesa2-dimensionalGaussianwith
a dispersion of rg, and I(θ) represents the brightness dis- PK05 and F07 findthat themajor axis of membergalaxies
tribution. The windowed positional parameters are derived innearbyclusterstendtoalign with theirradiusvector.To
adopting rg = FWHM/√8ln2. The impact of the precise examine whether such a radial alignment exists in our 12
choice of rg is discussed in 4.3.2. We apply a Gaussian clusters at z > 0.5, we study the distribution of the values
§
weighting function rather than constant weighting to avoid of φ, defined as the angle between the galaxy major axis
bias resulting from flux close to the noise level. Our analy- andthedirection toward thecluster centre(seeFig. 3). We
sis of galaxy orientations then uses the complex ellipticity stackthedistributionsinφobtainedforall12clusterfields,
e=e2+ie2andtheobjectpositionangle,θ,asderivedfrom using a metric scale to allow us to investigate the depen-
thesecond-order brightness moments: denceofanyalignmentsignalwithdistancefromthecluster
core. Notethat BCGs are excluded from this analysis since
e1 = Qxx−Qyy, (2) their alignments reflect the surrounding large-scale struc-
Qxx+Qyy
ture,asdiscussedin 1.Weusespectroscopically confirmed
§
e2 = 2Qxy , (3) foreground galaxies as ourcontrolsample (hereaftersample
Qxx+Qyy C) since, unlike background galaxies that may be gravita-
tionallylensed,theyshouldnotexhibitanypreferredorien-
θ= 1arctan( 2Qxy ), (4) tation.
2 Qxx−Qyy The distribution of galaxy orientations within the cen-
where θ can be uniquely determined from the sign of tral 500 kpc (corresponding to the largest circle enclosed
Qxy (Fig. 3). within the ACS images of all 12 target clusters) is shown
Galaxy Alignments in Clusters at z > 0.5 5
120 A 50 A (r<200kpc)
40
100
30
80 20
10
280 B 100 B (r<200 kpc)
er 260
b
um 240 80
n
220 er
b 60
40 C um 70 A (200<r <400kpc)
n 60
30
50
20
40
10 30
0 20 40 60 80 140 B (200<r <400kpc)
ϕ (degree)
120
Figure 4.Thedistributionofgalaxyorientationangleswithre-
spect to the radius vector; φ = 0 defines perfect radial align- 100
ment. The black and red solid lines represent the distributions
obtainedwhenadoptingtheX-raybrightnesspeakortheposition 0 20 40 60 80
ofBCGastheclustercentre,respectively.ErrorbarsassumePois- ϕ (degree)
sonstatistics,andthedottedlinesrepresenttheaveragenumber
ofgalaxiesperbin.Inthetop-leftcornerofeachpanelwedenote Figure 5. Same as Figure 4 but with the galaxy sample split
the respective subsample (A: spectroscopically confirmed mem-
according to distance fromthe cluster centre as indicated inthe
bers;B:colourselectedmembers;C:spectroscopicallyconfirmed
topleftcornerofeachpanel.
foregroundgalaxies).
the X-ray surface-brightness peak is adopted as the cluster
in Figure 4 for samples A and B. We find no tendency for
centre (Figure 5), yet a KS test still yields low probabili-
radial alignment for either sample; a Kolmogorov-Smirnov
ties of 77 and78 % for theobserved distributions deviating
test (KS test) finds the observed distributions to be con-
from uniformity. Similarly, the average alignment angle is
sistent with a uniform parent distribution at a probabil- measured to be φ = 43◦.43 2◦.26 and 43◦.47 1◦.24 for
ity of 31 (98)% and 62 (97)%, respectively, when the po- h i ± ±
sample A and B. No trends at all are observed when the
sitionoftheX-raybrightnesspeak(theBCG)isadoptedas
positionoftheBCGisadoptedastheclustercentre.Node-
the cluster centre. As expected, the distribution of galaxy
viation from uniformity is detected in the annulus between
orientations for our control sample (C) is also consistent
200and400kpc,regardlessofhowclustermembershipisde-
with random at a probability of 99 (99)%. Computing the
fined. The slight discrepancy between the results obtained
average alignment angle φ (where φ < 45◦ indicates
h i h i in these two radial bins may be the result of a mild depen-
a preferential radial alignment), we find values of φ of
45◦.45 1◦.13(44◦.69 1◦.15),45◦.21 0◦.68(44◦.55 0h◦.i69), denceof the strength of radial alignments on distance from
and44±◦.80 2◦.26(4±5◦.64 2◦.29)f±orsampleA,B±,andC. thecluster centre.
± ± Using again the average alignment angle φ as a mea-
h i
sure of deviations from a random distribution, we test for
any dependence on galaxy colour by splitting our spectro-
4.1.1 Dependence on Cluster Member Properties
scopically confirmed sample of cluster members into two
Althoughnoalignmentsignalisdetectedforthelargeststa- subsamples of red and bluegalaxies, where“red” is defined
tistical setsofclustermemberscompiled foroursample,we as lying within 2σ of the colour of the cluster red sequence
need to bear in mind the possibility that radial alignments (see 3.1). The results are shown in Fig. 6 (top panel) as a
§
could bepresent for a subset of thecluster galaxies but are function of distance from the cluster centre. As noted be-
diluted to the level of insignificance when the entire galaxy fore, a mild trend of increasing radial alignments with de-
sampleisconsidered.MotivedbythefindingsofF07,wethus creasing cluster-centric distances is observed, as evidenced
examine if any radial alignment can be found as a function bythefact that φ <45◦ in thefirst threeradial bins(bin
h i
of galaxy colour or distance from thecluster centre. size 100kpc); however, only red galaxies contribute to the
We first divide the samples A and B into two subsets, signal. Although statistically insignificant, these trends are
oneincludingall galaxies within 200 kpcof thecluster cen- qualitatively consistent with the findingsof F07.
tre,theothercomprisingallgalaxieswithinanannulusfrom In addition, we test for any dependence on galaxy lu-
200 to 400 kpc. A mild trend in favour of radial alignment minosity.Asimilarly mild,butstatistically moresignificant
isfoundinthecentral200kpcregionforbothspectroscopic trend is found for the dependence of φ on galaxy lumi-
h i
and colour-selected cluster members when the position of nosity (Figure 6; middle panel) in the sense that only the
6 Chao-Ling Hung & Harald Ebeling
55
20
50
10
>
ϕ 45
< er
b 0
m 30
40 u
n
20
35
0 100 200 300 400 500 10
radius (kpc)
0
0 20 40 60 80
55 ϕ (degree)
50
Figure7.AsFigure4butshowingthedistributionoforientation
> anglesfortwosubsetsofsampleA:thesixclustersclassifiedwith
ϕ 45
< Morphologycode=1&2(toppanel)andthesixclustersclassified
withMorphologycode=3&4(bottompanel).Bothplotsonlyuse
40 datafromthecentral200kpc.
35
−23.0 −22.5 −22.0 −21.5 −21.0 −20.5 usethevisualmorphological classifications of Ebeling et al.
absolute magnitude (2007)whicharebasedonX-raymorphologyandthegood-
ness of the optical/X-ray alignment and result in a mor-
phology codewhosevaluesrangefrom 1forfully relaxed to
−20.8
de −20.9 4 for extremely disturbed clusters. We here limit the anal-
u ysis to spectroscopically confirmed cluster members within
nit −21.0 thecentral 200 kpc,i.e. thedataset for which a mild trend
g
a −21.1 forradialalignmentsisfoundforthefullclustersample(but
m
e −21.2 onlywhentheX-raypeakisusedtodefinetheclustercentre;
olut −21.3 seeFig.5,toppanel).Theresultsforclusterswithmorphol-
s ogy codes of 1 or 2 and 3 or 4 are shown in Figure 7; no
b −21.4
a −21.5 significant difference between the two subsetsis observed.
0 100 200 300 400 500 Adopting an alternative, purely optical indicator of
radius (kpc) cluster relaxation state, we also examine the dependenceof
our findings on the presence of a single cD or multiple cD-
typegalaxies(see 3.3).AsshowninFig.8(blacklines),this
Figure6.Upperpanel:hφiasafunctionofradius.Middlepanel: §
trendoriginates primarily inthesubsampleofseven cluster
hφi as a function of absolute magnitude. Lower panel: absolute
magnitude as a function ofradius. TheX-raybrightness peak is featuringasingleBCG,butagainwithverylowsignificance
assumedastheclustercentreinthisplot.Ineachpanel,thewhole (KSprobabilityof84%).Thepresenceofjustoneorseveral
specsampleofclustermembersisinblack,redandblueindicate BCG candidates makes no difference for the distribution of
redandbluegalaxymembers,respectively. orientation angle when the position of the adopted BCG is
taken to definethecluster centre(Fig. 8; red lines).
most luminousred galaxies showatendencyforbeingradi-
allyaligned.Thistrendislikelytobeindependentfromthe 4.2 Complex Ellipticity as a Measure of Galaxy
slightincreaseof φ towardtheclustercoreregion,sinceno Alignments
h i
obvious correlation is found between a galaxy’s luminosity
Complementingouranalysisbasedonorientationangles,we
and its distance from thecluster centre.
also search for galaxy alignments using the two-component
complex ellipticity. Although the orientation angle and the
two-component ellipticity convey similar information since
4.1.2 Dependence on Cluster Relaxation State
they are mathematically dependent quantities, the two-
As a further test of whether subsets of our sample exhibit componentcomplexellipticityhastheadvantageofallowing
alignmentsthataredilutedwhenthefulldataset (Fig.4)is ustoisolateapossiblealignmentsignalwhilesimultaneously
considered,weexaminethedependenceofanysignalonthe testingforthepresenceofsystematiceffectsinourmeasure-
relaxation status of the host cluster. Ideally, we would like ment.Furthermore,thenetalignmentsignalgeneratedbya
to compare the alignment signal in virialized clusters with scalargravitationalclusterpotentialshouldbecurl-free.Un-
that found for morphologically disturbed, i.e., dynamically der the simplifying assumption that the cluster potential is
younger systems, and explore whether the strength of any isotropic,thecurl-freeandcurlalignmentscanbedecoupled
alignmentsevolvesasthehostclusterapproachesfullrelax- bysplittingthecomplexellipticityeintoatangential/radial
ationafteramerger.Tocrudelyquantifyrelaxationstatewe component and a cross-term component, i.e.,
Galaxy Alignments in Clusters at z > 0.5 7
40
3 arcsec 0.3 arcsec
30
20
er 10
b
m 30
u
n
20
10
0
0 20 40 60 80
ϕ (degree)
Figure 10. A comparison between the angular resolution and
pixel sampling typical of SDSS (r′ = 18.5 mag, left) and HST
Figure8.AsFigure4butshowingthedistributionoforientation
(F814W=23 mag, right) images of galaxies. Note the difference
angles for two subsets of sample A: the seven clusters featuring
inangularscalecoveredbyeitherimage.
a single dominant BCG (top panel) and the five clusters with
multiple BCG candidates (bottom panel). Both plots only use
datafromthecentral200kpc.
4.3 Possible Systematic Biases and Uncertainties
4.3.1 Shape Measurements
The high quality in terms of both angular resolution and
0.3 depth of the HST/ACS images available for our sample
yieldsexcellentpixelsamplingandthusallowsamuchmore
x 0.2 robustshapedeterminationthanthegroundbaseddataused
e
d in previous studies (see Fig. 10 for an illustration). Es-
n 0.1
a pecially the spectroscopically confirmed cluster members
et (which tend to be brighter) are exquisitely resolved. In this
d -0.0
e section,weexaminetherobustnessofourgalaxyshapemea-
z
mali -0.1 surementsunderdifferentweightingschemes(rgin§3.2)and
or detection thresholds.
n -0.2 Throughout our analysis we use weights parametrized
-0.3 by rg =FWHM/√8ln2 as provided by SExtractor. An al-
0 100 200 300 400 500 ternativeweightingscheme,givenbyrg =FWHM,hasbeen
radius (kpc) proposed by Schrabback et al. (2007). In order to quantify
theimpact oftheexactchoiceof rg onourresults,wemea-
surethepositionangleof 1000galaxiesinoneofourcluster
Figure9.Variationofthetwo-componentellipticitywithcluster- ∼
centric distance forSampleA.The solidand dashed linesrepre- fields (MACSJ2129.3–0741) for either value of rg. We find
sentet andex,respectively.Resultsbasedontheadoptionofthe theaveragedifferenceofh∆θi=−0◦.13±1◦.88betweenthe
locationoftheX-raysurfacebrightnesspeak(BCG)astheclus- derived position angles to be negligibly small compared to
tercentreareshowninblack(red).Toavoidcluttering,errorbars thebinsizeusedbyusfortheorientation-angledistribution
areshownonlyforonesetofresults. (Figs.4,5,7,8)andconcludethatouranalysisisnotsensitive
to thedetails of theadopted weighting scheme.
The impact of the chosen detection threshold can, in
principle,besubstantialbutdependsgreatlyontheweight-
et = [e exp( 2iξ)], (5) ingfunction.FortheGaussianweightingfunctionappliedby
−ℜ| | − usintheshapemeasurementprocess,theresultingposition
ex = [e exp( 2iξ)], (6) angle varies by only about 1◦ when the detection threshold
−ℑ| | − is raised from 5σ to 20σ. This effect too is thus negligible
for thepurposes of this study.
where ξ is the angle between the galaxy radius vector
and the image x axis (φ= θ ξ, see Fig. 3).
| − |
The variation of et and ex with cluster-centric radius 4.3.2 PSF Anisotropies across the Field of View
is shown in Fig. 9 for the sample of spectroscopically con-
firmed cluster members. We find a marginally significant The anisotropy of the HST Point Spread Function (PSF)
trend toward negative et in the central 200 kpc region, is known to be a potentially significant source of system-
∼
consistent with the faint radial alignment signal detected aticerrorsforstudiesinvolvinggalaxy shapemeasurements
in the orientation-angle distribution within the same radial (e.g.,weak-lensinganalyses).ThePSFvariesacrosstheACS
range (Fig. 6, top panel). No obvious trend is observed for field of view and is also a function of time due to focus
the cross term ex, suggesting that systematic errors (other changes caused by “thermal breathing” of HST in orbit
than thechoice of cluster centre) are negligible. (Rhodeset al. 2007). Since the cluster galaxies in our sam-
8 Chao-Ling Hung & Harald Ebeling
plearewellresolvedweexpectthesePSFvariationstohave We first note that the mass range probed by our clus-
little effect on our study. We nonetheless test this expecta- ter sample is considerably different from that used by F07.
tion by obtaining a quantitative estimate of the variations MACS,bydesign,selectsthemostX-rayluminousclusters,
in position angle introduced by PSFanisotropies. and the ones selected for this work feature total masses in
WeuseMACSJ2129.3–0741 as atestfield sinceit con- excessof5 1014M⊙ (Bradaˇc et al.2008;Smith et al.2009;
×
tains 80 stellar detections which allow us to sample the Mantz et al. 2010; Limousin et al. 2011); by contrast, the
∼
PSF across the field and fit position-dependent PSF mod- samplecompiledbyF07usingagroupfinderalgorithmcov-
els. As the ACS/WFC images of MACSJ2129.3–0741 were ers a much wider mass range of 5 1012M⊙ < Mvirial <
taken at six dithered positions with an integration time of 5 1014M⊙. The clusters in the sam×ple of PK05, however,
×
750secondseach,thePSFmodelforthisfieldwillhaveto areX-rayselectedjustlikeoursandtendtobemoremassive
∼
takeintoaccountbothspatialandtemporalPSFvariations. than those studied by F07, and yet these two studies find
We obtain a series of models for focus values ranging from consistentradialalignmentatlowredshift.Weconcludethat
10to5µmusingtheIDLTinyTimpackage(Rhodes et al. the lack of alignments observed by us at z >0.5 is unlikely
2−007) based on the Tiny Tim HST PSF modeling software to becaused by a differencein cluster masses.
(Krist 1995). For each individual exposure we find the best Another possible systematic difference between ours
telescopefocusbycomparingthemodelpredictionswiththe and previous work is the completeness of the spectroscopic
shape of the stellar detections in the field, and then create follow-upobservationsofclustergalaxies.Spectroscopiccov-
andstack thePSFmodels forthesesix best-fitfocusvalues eragetendstobeinhomogeneousacrossclustersduetocon-
according to theditherpattern used in our observations. flicts between slits or fibers specifically in the dense cluster
HavingthusobtainedaPSFmodelforMACSJ2129.3– cores.Sincethestrengthofanynetradialalignmentofclus-
0741,weapplyPSFcorrectionsusingthemethoddeveloped ter galaxies may depend on their distance from the cluster
byKaiser(1995)andHoekstra et al.(1998)whichmeasures centre, spectroscopic completeness as a function of radius
the response in complex ellipticity to convolution with a needs to be taken into account when comparing results ob-
small anisotropic kernel. The correction term in the com- tainedfordifferentdatasets.Extensivespectroscopicfollow-
plexellipticityofindividualgalaxiesdependsontheirsmear upobservationsofour12MACSclustersresultinanoverall
polarizabilitytensor,asdefinedinKaiser(1995),andonthe completeness of about 80% down to F814W=21.5 mag. As
second-order moments of the PSF model at each position. shown in Fig. 11 the spectroscopic completeness above this
Theresultingcorrectionfactorforthegalaxyposition angle limiting magnitude varies by only 15% from the central
issmallthough( ∆θ =1◦.57)forthe,ingeneral,brightand 200kpctotheedgeoftheACSfield∼ofview.Correctingfor
h i
well resolvedgalaxies inoursample.WeconcludethatPSF relative incompleteness of the spectroscopic coverage does
corrections haveanegligible effect ontheshapeparameters not change our finding that no significant radial alignment
measured for the galaxies in ourcluster fields. is detected within thecentral 500 kpc.Although a compar-
ison with PK05 is not possible since no information of this
kindisprovidedfortheirsample,wecannotimagineaselec-
tion bias in the spectroscopic survey underlying the PK05
5 DISCUSSION
dataset that would explain the stark discrepancy between
Evidence of radial galaxy alignments is sparse at best for theirresults at z 0.1 and ours at z>0.5.
∼
the 12 very massive clusters at z > 0.5 investigated here. Differences between our results and those in the liter-
Amarginaltrendfavouringradialalignmentisfoundwithin ature could also be caused by biases affecting the measure-
thecentral200kpcregionaroundthepeakoftheX-raysur- ment of galaxy shapes and orientations. We examine pos-
face brightness, but becomes entirely insignificant once the sible systematics in our analysis of HST/ACS data in 4.3,
§
uncertainties in the determination of the cluster centre are and find that both instrumental and measurement system-
takenintoaccount.Withinalargerregionencompassingthe aticsarenegligible.Instrumentalsystematicsshouldalsobe
central500kpc,the545spectroscopically confirmedcluster negligible for the datasets used by PK05 and F07 since the
members in our sample feature an average alignment angle SDSS is conducted in drift scans, paying multiple visits to
of φ = 45◦.38 1◦.14, which is perfectly consistent with each location. Systematic errors, however, can be expected
h i ±
random.Ourfindingsforclustersatz>0.5arethusincon- to be relevant for shape measurements based on ground-
flict with the prominent radial galaxy alignments reported basedSDSSdata,owingtopoorseeingandinsufficientpixel
by PK05 and F07 for nearby clusters. Specifically, PK05 sampling.
find φ =42◦.79 0◦.55for2200spectroscopicallyconfirmed Other potential biases inherent to alignment studies
h i ±
cluster members within the central 2 Mpc of the centres of based on SDSS data are investigated by Hao et al. (2011).
clusters at z 0.1. We note that this discrepancy can not Using SDSS DR7 data, they find that the radial alignment
∼
beattributedtostatisticaluncertainties:thesignalreported signal correlates withtheapparent magnitudeofBCGs but
byPK05wouldstillbesignificantatthe2σ confidencelevel notwiththeirabsolutemagnitude,causingthemtoconclude
if theirsample size werereduced bya factor of4 to550 ob- thatsuchalignmentsarecreatedbysystematicerrorsinthe
jects. The complete lack of evidence of a net radial galaxy galaxy orientation measurements caused by contamination
alignment for our z > 0.5 sample within a much smaller from diffuselight ofBCGs.Whilesuchabiasappearsplau-
distance from the cluster centres is particularly puzzling if sible in principle, it remains unclear how diffuse light from
radialalignmentsareindeedstrongestneartheclustercores, theBCGcan affect themeasurement ofgalaxy orientations
assuggestedbybothourresultsandF07.Inthissectionwe out to the large radii over which highly significant radial
discuss differences between our work and previous studies alignmentisreportedbyPK05andF07(2Mpcandatleast
that might explain thediscrepant results. 0.5Rvirial,respectively).Furthermore,sincethecontrolsam-
Galaxy Alignments in Clusters at z > 0.5 9
location of theBCG ischosen astheclustercentre,thesig-
1.0 nificanceof any deviation from uniformity in thealignment
angles isevenlower. Wefindnodifferenceregarding galaxy
0.9 orientations between two subsets of our cluster sample de-
s signedtoseparatethemorerelaxedfromthemoredisturbed
s
ne 0.8 systems.
e Inordertotestforsystematicerrorsinouranalysis,we
et
pl 0.7 examine the distribution of both components of the com-
m plex ellipticity; as expected for curl-free alignment signals
o
c generated by a scalar gravitational cluster potential, the
0.6
crosstermvanishesatallclustercentricradii.Wealsoverify
thenegligible impact of systematic uncertaintiesand biases
0.5
caused by the variability of the HST point-spread function
0 100 200 300 400 500 600
(bothtemporalandacrosstheACSfieldofview),andbyour
radius (kpc)
choice of weighting function and detection threshold when
measuring galaxy ellipticities and orientations using SEx-
Figure 11.Spectroscopic completenessofclustermemberswith tractor.
mF814W < 21.5 as a function of clustercentric radius for our The absence of significant radial galaxy alignments in
sampleof12MACSclustersatz>0.5. our z > 0.5 clusters stands in stark contrast to the promi-
nent radial alignment reported for nearby clusters. Specifi-
cally,wefindnosignificantradialalignmentofclustergalax-
pleusedbyPK05consistsoffieldgalaxiesinclusterfields,at
ieswithinthecentral0.5Mpcforclustersatz>0.5,whereas
leastsomeradialalignmenttrendshouldbepresentintheir
astrong alignment signal is detectedout to 2Mpcfor clus-
control sample too, if the measurement is indeed biased by
ters at z 0.1. We examine several systematic effects that
diffuselight from BCGs. To summarize, thesystematics af- ∼
could cause this discrepancy and rule out differences in the
fecting the results obtained from groundbased observations
selection ofclustersorclustermembers.Themostplausible
are still controversial and need further investigation.
explanations are (1) that the radial alignment evolves dra-
Finally, a possible physical explanation for the differ-
matically with cluster redshift, in the sense that the signal
ences in alignment strength between our z > 0.5 sample
is weaker in dynamically younger systems, or (2) that the
andsamplescomprisingnearbyclustersisthatradial align-
signalobservedinnearbyclustersisatleast partlyspurious
mentevolvesdramatically withredshift.Ifradial alignment
and the result of measurement biases in the low-resolution
istheresultofinteractionsofclustergalaxieswithlocaltidal
SDSSdatausedbytherespectivestudies.Bothoftheseex-
fields, cluster members newly accreted from the field pop-
planations are testable and will be examined in a future,
ulation may not have been orbiting the cluster centre long
extendedstudy.
enough for tidal torquing to have a measurable effect. This
effect can be expected to be stronger in younger clusters,
i.e.,athigherredshift.Indeed,clustersathigherredshiftare
known to be less relaxed than local ones (Mann & Ebeling ACKNOWLEDGMENTS
2011).Althoughwefindnocorrelationbetweenclustermor-
HE gratefully acknowledges financial support from STScI
phology and radial galaxy alignments within our sample
grantGO-09722.WeareindebtedtoDavidDonovan,Wendy
(see 4.1.2),perturbationsfromminorormajormergersex-
§ Everett,andMariaPereiraforcontributionsduringtheearly
pected tobemore common and frequentat larger lookback
phaseof this project.
timesmaywellpreventaradialalignmentsignalfromreach-
ing a significant level in distant clusters.
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