Cold imprint of supervoids in the Cosmic Microwave Background re-considered with Planck and BOSS DR10

0.71 MB·English

by  András Kovács

Mon.Not.R.Astron.Soc.000,1–??(2014) Printed19June2015 (MNLATEXstylefilev2.2)
Cold imprint of supervoids in the Cosmic Microwave
Background re-considered with Planck and BOSS DR10
Andr´as Kova´cs1, Benjamin R. Granett2
1 Institut de F´ısica d’Altes Energies, Universitat Auto´noma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
2 INAF OA Brera, ViaE. Bianchi 46, Merate, Italy
5
1
Submitted2015
0
2

n ABSTRACT
u
J WeanalyzepubliclyavailablevoidcatalogsoftheBaryonOscillationSpectroscopic

8 Survey Data Release 10 at redshifts 0.4 < z < 0.7. The first goal of this paper is to
1 extendthe CosmicMicrowaveBackgroundstackinganalysisofpreviousspectroscopic
void samples at z <0.4. In addition, the DR10 void catalog provides the first chance

] to spectroscopically probe the volume of the Granett et al. (2008) supervoid catalog
O
that constitutes the only set of voids which has shown a significant detection of a
C
cross-correlationsignalbetween voidlocationsandaverageCMB chill.We foundthat
. the positions of voids identified in the spectroscopic DR10 galaxy catalog typically
h
do not coincide with the locations of the Granett et al. supervoids in the overlapping
p
- volume, in spite of the presence of large underdense regions of high void-density in
o DR10.Thisfailuretolocatethesamestructureswithspectroscopicredshiftsmayarise
r
due to systematic differences in the properties of voids detected in photometric and
t
s spectroscopic samples. In the stacking measurement, we first find a ∆T = −11.5±
a
3.7µKimprintfor35ofthe50Granettetal.supervoidsavailableintheDR10volume.
[
Forthe DR10 voidcatalog,lackinga prioronthe number ofvoidsto be consideredin

2 thestackinganalysis,wefindthatthecorrelationmeasurementisfullyconsistentwith
v nocorrelation.However,the measurementpeakswithamplitude ∆T =−9.8±4.8µK
6 fortheaposteriori-selected44largestvoidsofsizeR>65h−1Mpcthatdoesmatchin
7
terms ofamplitude andnumber ofstructuresthe Granettetal.observation,although
3
at different void positions.
3
0 Key words: surveys – cosmology:observations – large-scale structure of Universe –
.
1 cosmic backgroundradiation
0
5
1
:
v 1 INTRODUCTION relativestrengthmaybedifferentinalternativecosmologies
Xi (Cai et al. 2014).
Large-scale structures at low redshift leave their mark on
ThetypicalISWandRSimprintsarethussmallenough
r the Cosmic Microwave Background (CMB) radiation pro-
a tobeimmeasurableinpractice.Thetraditionalapproachfor
viding direct probes of the late time cosmic acceleration
detecting the weak signal is the angular cross-correlation
and the physics of Dark Energy (Aghanim et al. 2008).
measurement between galaxy density maps and the CMB.
In particular, large voids and clusters can imprint them-
This detection strategy has been followed by a series of
selves to the primary fluctuations of the CMB via phys-
studies findingboth marginally (see e.g. Francis & Peacock
ical mechanisms called the Integrated Sachs-Wolfe effect
(2010), Kova´cs et al. (2013)) and moderately significant
(Sachs& Wolfe 1967, ISW) in the linear regime, and the
(see e.g. Ho et al. (2008); Giannantonio et al. (2008, 2012);
Rees-Sciamaeffect(Rees & Sciama1968,RS)onnon-linear
Planck Collaboration et al. (2014a) and references therein)
scales. The expected ISW correlation in the ΛCDM model
ISW-likesignals.Anotherapproachisfocussedonthelargest
is on the order of 0.1 µK < ∆T < 1 µK for typical voids
| | structuresinthedensityfield,wheretheISW-RSeffectisex-
(Cai et al. 2010), extending up to ∆T 20 µK for the
| | ≈ pected to be the strongest. Foremost, Granett et al. (2008)
largest observable superstructureswhich are also the rarest created a catalog of supervoids and superclusters1 (Gr08,
(seee.g.Szapudiet al.(2014);Nadathuret al.(2014)).The
contribution of the non-linear RS effects remains typically
at the 10% level compared to the linear expectation
(Cai et a∼l.2010).However,theISWandRSeffectsandtheir 1 http://ifa.hawaii.edu/cosmowave/supervoids/
(cid:13)c 2014RAS
2 Andr´as Kov´acs and Benjamin R. Granett
hereafter) using the SDSS Data Release 4 (DR4) Mega-z of 0.4<z <0.7. Two distinct conclusions are possible: our
photometric LRG catalog (Collister et al. 2007) with some stackinganalysiscouldconfirmtheGranett et al.(2008)de-
additional area from DR6.They used theZOBOV algorithm2 tection for the first time with an independent void catalog,
(Neyrinck2008)toidentifythemostprominentextremesof or the ISW(-like) signal could disappear. In any case, some
the large-scale density field. The superstructures were then puzzle will certainly remain for future analyses with BOSS
used for stacking the CMB temperature centered on these DR12and Planck DR2.
locations, and to measure an average effect through a com- Thepaperisorganizedasfollows.Datasets,algorithms,
pensated top-hat filter. andourobservationalresultsarepresentedinSection2;the
This rather simple statistic averages theCMB temper- finalsectioncontainsasummary,discussion andinterpreta-
ature centered on voids within a circular aperture r < R, tion of our results.
and then subtracts the background temperature averaged
in an equal-area concentric annulus with R < r < √2R.
Granett et al. (2008) found a ∆T = 9.6 2.2 µK signal
2 DATA SETS AND MEASUREMENTS
| | ±
for their 100 most significant (> 3σ) superstructures us-
ing an aperture size of R = 4◦. This signal appears to be 2.1 CMB data
in > 2σ tension with ΛCDM predictions, as pointed out On the CMB side we use Planck’s SMICA3 map
in s∼everal follow-up studies using theory and simulations
(Planck Collaboration et al. 2014b) with resolution down-
(Pa´pai et al. 2011; Pa´pai & Szapudi 2010; Nadathuret al.
graded to N = 512 with the HEALPix(Gorski et al.
2012; Flender et al. 2013; Hern´andez-Monteagudo & Smith side
2005) pixelization. We mask out potentially contaminated
2013;Hotchkisset al.2015;Aiola et al.2015).Theexpecta-
CMB pixels using the WMAP 9-year extended tempera-
lteiovnelffoorrthe5s0tascukpeedrsItSrWuctsuigrensalsirmemilaarintsoaGtrt0h8eo|∆bjTec|t∼<s.2µK ture analysis mask4 (Hinshaw et al. 2013) at Nside = 512
∼ to avoid repixelization effects of the Nside = 2048 CMB
Also, numerous additional tests have been performed
masks provided by Planck. It has already been pointed out
to uncover possible systematic problems and statistical
by Granett et al. (2008), and later confirmed by Ili´c et al.
biases (Ili´c et al. 2013; Planck Collaboration et al. 2014a;
(2013), Planck Collaboration et al. (2014a), and Cai et al.
Cai et al. 2014). It was found that varying the number of
(2014)thattheISW-likecross-correlation signaldetectedat
theobjectsinthestacking,orusingdifferentfiltersizestyp-
void locations is independent of the CMB data set when
ically lowers the overall significance. Otherwise the original
looking at WMAP Q, V, W, or Planck SMICA tempera-
Gr08 signal has survived every revision and remains a puz-
ture maps. We thus limit our analysis to the latest Planck
zle.
SMICA sky map.
Additionally, Planck Collaboration et al. (2014a),
Cai et al. (2014), and Ili´c et al. (2013) repeated the CMB
stacking analysis of Granett et al. (2008) using com- 2.2 Catalogs of cosmic voids
plementary void catalogs (Sutteret al. 2012) based on
We use public void catalogs by Sutteret al. (2014) where
spectroscopic measurements at z < 0.4. These studies,
the authors identified voids in BOSS DR10 spectroscopic
however,didnotreportahighlysignificant detectionofthe
galaxy samples (Ahnet al. 2014). Thevoidswere identified
ISW-likeeffect foundinGr08, exceptthe 2σ evidencefor
∼ withtheZOBOVtool(Neyrinck2008)withintheVIDE5frame-
a correlation in Cai et al. (2014).
work(Sutteret al.2015).Thevoid-finderZOBOVisbasedon
Duetotheoverwhelmingcontributionfromcosmicvari-
thewatershed algorithm which buildsa hierarchy of under-
ance,ISWstackingmeasurementscanbepronetomisinter-
densities. We first remove voids with size R < 40 h−1Mpc
pretation due to the ‘look elsewhere’ effect (Peiris 2014).
to cut thehierarchy.
The measurement parameter space has a high dimension-
Supervoids encompassing smaller voids, walls, and fil-
ality when counting the choices made in the void catalogue
aments may be represented by multiple voids in a dense
selectionandmethodologydetailssuchasfiltersize,andthe
tracer catalog, or by one large void in sparsely sampled
inherentlyweaksignalcanleadtotheoverinterpretationof
data or in the presence of photometric redshift uncertain-
statistical flukes(Hern´andez-Monteagudo & Smith 2013).
ties(Sutteret al.2014).Thegalaxy numberdensityfor the
Inthisworkwedonotformallycarryoutablindanaly-
CMASScatalogpeaksatz=0.5withmeaninter-galaxysep-
sistomitigate theeffects;however,wefixthemeasurement
aration L 16 h−1Mpc which rises to 25 h−1Mpc at
methodology using parameters determined externally. We
≈ ∼
z = 0.65, thus a lower cut of roughly twice this character-
test the robustness of the signal by varying these parame-
istic scale is a safe and reasonable choice to prune spurious
ters,expectingthatatruesignalwillberobusttoperturba-
voiddetectionsthatwouldcontributeonlynoisetothemea-
tions in the catalogue properties or methodology. We com-
surement (Sutteret al. 2014, 2015).
pare the Gr08 void catalog to theBaryon Oscillation Spec-
Furthermore,thesesmallandpotentiallyspuriousvoids
troscopic Survey (BOSS) DR10 CMASS and LOW-Z void
mayoccupyoverdenseregions.Cai et al.(2014)testedthis
catalogs provided by Sutteret al. (2014). On one hand, we
effect in mock catalogs. They suggest a lower size cut of
are able to probe a significant fraction of the Gr08 volume
R > 65 h−1Mpc for a complete removal of potentially
(surveyedwithphoto-zdata)nowwithvoidsdetectedusing
spurious voids at z 0.43 in their lrgbright sample
spectroscopic redshifts. On the other hand, we extend pre- med
≈
vious low-z DR7 void stacking measurements to the range
3 http://www.cosmos.esa.int/web/planck
4 http://lambda.gsfc.nasa.gov/product/map/dr5/
2 http://skysrv.pha.jhu.edu/neyrinck/voboz/ 5 http://www.cosmicvoids.net
(cid:13)c 2014RAS,MNRAS000,1–??
Cold imprint of supervoids with Planck and BOSS DR10 3
Denisty of DR10 voids vs. Gr08 void positions
Figure 1.VoidpositionsoftheGr08sample(gold)vs.DR10voidcatalog(purple). RedpointsshowasubclassoflargeDR10voidsof
sizeRv>60h−1Mpc.TheunderlyingNside=32HEALPixmapistheDR10voiddensitysamplesmoothedwithaσ=4◦ Gaussian.Due
to the hierarchical organisation of the void catalogue, an underdense region may besplitinto a number of voids of various sizes inthe
catalogue. Darkbluecolorsindicatehighervoidabundance thus loweraverageprojecteddensity. Thefactthatthetwovoidcatalogues
tracedifferentstructurespointstosystematicdifferences inthegalaxycatalogues andvoidfindingalgorithms.
(L 38 h−1Mpc), i.e. the DR7 subsample that is possi- Weshowourvoidsampletogetherwiththe50Gr08su-
≈
bly the most similar to the better sampled DR10 data we pervoidsin Figure 1 (35 of the50 Gr08 voidsshould bede-
considerhere.Althoughitisnotpossibletoadoptsuchcuts tectableinDR10,i.e.notmaskedoutorresidingclosetothe
for DR10 voids without proper simulations of the source boundary). On average DR10 voids are smaller in angular
catalogs, aroughcomparison ofthesourcedensitiesofDR7 andphysicalsizethantheGr08 superstructures,duetothe
andDR10catalogs indicatesthatR>40h−1Mpcmightbe abilityofresolvingsmall-scalestructureswithspectroscopic
a reasonable cut. redshifts.However,wefoundlargeregionsofhighdensityof
Wealsorestrictouranalysistocentralvoidstominimise DR10 voids, which typically do not overlap with the larger
possiblecontaminationscausedbythesurveymask(seee.g. Gr08 supervoids. Thus the expected fragmentation of su-
Sutteret al. (2014) for details). perstructures into smaller voids is not observed, but addi-
These moderately conservative cuts remove 65% of tional large underdenseregions appear in the spectroscopic
∼
thevoidsfrom theDR10catalog. Ourapproach is toprobe data. This somewhat counter-intuitive finding means that
the 0.4 < z < 0.7 redshift range thus we consider CMASS a potential (and expected) ISW(-like) signal in the shared
data in our analysis, with 13 extra voids from the LOW-Z DR10-Gr08volumeisinthiscasecarriedbyvoidsatdistinct
4sampleat 0.4<z <0.45, i.e. aredshift rangeoftheGr08 locations in thesky.
catalog not covered by CMASS data. The numberdensities of the two catalogues are of sim-
Following Sutteret al. (2014), we divide the result- ilar order: while the CMASS tracer inter-galaxy separation
ing DR10 void catalog into three subsamples; a combined is n¯−1/3 14 22 h−1Mpc, the photometric LRG sample
CMASS 1 + LOW-Z 4 at 0.4 < z < 0.5 (56+13 voids), is 2.2 t≈imes−more dense with n¯−1/3 10 17 h−1Mpc.
∼ ≈ −
CMASS 2 at 0.5 < z < 0.6 (237 voids), and CMASS 3 at Thelargest DR10voids(minimumaslargeasthetypi-
0.6 < z < 0.7 (172 voids). We analyze these catalogs both calGr08supervoids),however,arelocatedclosertotheGr08
separately and jointly. We removed 6 voids from the anal- supervoids on average. DR10 voids of size R> 60 h−1Mpc
ysis, as their position was curiously outside of the rough are shown separately in Figure 1. Appropriate analysis of
◦
N =32 DR10 footprint by 2 , indicating an inconsis- the properties of this subclass of voids is one of the main
side
tency in the void catalog6. We∼checked the effects of these goals of thispaper.
objects on our main results and found no difference.
theseobjectswillberevisedinalaterversionoftheirDR10void
6 We consulted Sutter et al. about this issue, and learned that catalog,andshouldberemovedatthemoment.
(cid:13)c 2014RAS,MNRAS000,1–??
4 Andr´as Kov´acs and Benjamin R. Granett
CMASS 1 + LOW-Z 4 CMASS 2 CMASS 3
90 90 90 0.68
0.477 0.57 0.67
80 0.474 80 80
0.56 0.66
0.471
]pc70 0.468 ]pc70 0.55 ]pc70 0.65
M M M
1h−60 0.465 1h−60 0.54 1h−60 0.64
R [ 0.462 R [ 0.53 R [ 0.63
50 0.459 50 0.52 50 0.62
0.456
0.51 0.61
40 0.453 40 40
−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100
∆T [µK] ∆T [µK] ∆T [µK]
Figure 2. Filtered temperatures in re-scaled top-hats are shown as a function of their physical size. Crosses in the left panel mark
LOW-Z4voids.Colorbarsindicatetheredshiftsofthevoids,withoutanyapparenttrendorclusteringinthisparameterspace.Wenote,
however, that there is aslight extra average cooling for smallCMASS2 voids. Interestingly, CMASS3 voids behave inversely showing
hotter temperature differences on average for the smallest voids. Shaded regions mark out 2σ statistical uncertainties scaled with the
numberofobjects considered,whilesolidlinesindicatethestacked temperatureforagivensubsample.
2.3 Methods & Results
Foremost,werepeatedthestackinganalysisofGranett et al. 150
(2008) for the 35 supervoids available in the DR10 volume Gr08
◦ LOW-Z 4
with constant R = 4 filter radius. The original signal of
CMASS 1
∆T = 11.3 3.1 µK signal as measured by Granett et al. 100 CMASS 2
(2008)−now li±mited to the DR10 area is changed to ∆T = CMASS 3
11.5 3.7 µK. We then expected to detect a similar sig-
− ±
nal in the same physical volume with voids identified using
50
spectroscopic redshift from theDR10 CMASS catalog. ]K
In our methods, we closely follow Ili´c et al. (2013) and µ
Cai et al. (2014). Wefirst measure average temperaturesin [∆T
the SMICA map at void locations using the compensated 0
top-hat filter technique applied by Granett et al. (2008).
We further scale the filter by angular size as advanced
by Ili´c et al. (2013), Cai et al. (2014), and Hotchkiss et al. −50
(2015). The same authors empirically found in data and in
simulations that the optimal filter size to maximize S/N is
60%ofthere-scaledvoidradius.Thephysicalmotivation
∼ −100
behindsuchascalingisthecoincidencewiththezerocross- 0.40 0.45 0.50 0.55 0.60 0.65 0.70
ings of the void density profile and the cumulativeISW-RS z
signal found in N-body simulations (Cai et al. 2014). We
adopt this refinement in order to maximize the expected Figure3.Filteredtemperaturesinre-scaledtop-hatsareshown
as a function of their redshift, covering the full range of Gr08
signal-to-noise in our tests. The resulting typical re-scaled
◦ voids.Nomeaningfultrendisobservable,asallsub-samplesshow
filter radius is r 1.2 for all sub-samples.
mean ≈ similardistributions. The greyshaded region marks the 1σ fluc-
Ourfindingsare presented in Figures 2 and 3, showing
tuationσ∆T ≈32µKforasingleobject,asmeasuredusingCMB
the void temperature measured as a function of void ra- simulations.
dius and redshift. We compare the redshift distributions of
DR10andGr08voidsinFigure3.Theseplotsshowthetyp-
ical behavior of such top-hat filtered temperatures, as they generated with the HEALPix (Gorski et al. 2005) synfast
containlargefluctuationsforindividualobjectsofbothpos- routine using the Planck DR1 best fit CMB power spec-
itiveandnegativesigns.However,thereisnoobviousexcess trum(Planck Collaboration et al.2014b).Gaussian simula-
clustering or other oddity in these parameter spaces. Two tions without considering instrument noise suffice because
exceptions are the slight average shift to the negative side the CMB signal is dominated by cosmic variance on the
for R < 50 h−1Mpc CMASS 2 objects, and the counterac- scales we consider (See e.g. Hotchkisset al. (2015)).
tive change at R < 50 h−1Mpc for CMASS 3. Note that The ISW-RS signal expected in ΛCDM is so small
these voids should carry the lowest ISW-RS signal among that it is dominated by the uncertainty of the primary
thecatalog, and their robustness is questionable dueto the anisotropies even with stacking applied. More precisely,
occurrence of voidsin clouds (Cai et al. 2014). S/N < 0.4forfiltersR<2◦ wasestimatedbyFlender et al.
We then average the filtered temperatures for the 478 (2013∼). Nadathuret al. (2012) pointed out that N
stack
≈
DR10 voids, sorted by radius. We estimated statistical un- 3000supervoidscouldprovideS/N 2.5for∆T 2µK,
∼ ≈−
certainties by analyzing 1000 Gaussian CMB simulations i.e.asignalthatcanbeproducedbythemostextremesuper-
(cid:13)c 2014RAS,MNRAS000,1–??
Cold imprint of supervoids with Planck and BOSS DR10 5
0.25
15 N =478
stack
10 All voids with R/Rv=0.6
0.5
]K 5 0.20
[∆Tµ−−1005 R/Rv=0.4, Nstack=118 00..31
−15 0.15
0 100 200 300 400 2) 0 1 2 3
15 >
10 CMASS 1 + LOW-Z 4 N Max S/N
/
[]∆TµK −055 p(S 0.10
−10
−15 0.05
0 10 20 30 40 50 60
15
10 CMASS 2
]K 5
[∆Tµ −05 0.01000 101 102
N
−10 stack
−15
0 50 100 150 200
15
Figure5.Theprobabilityoffindingatleastonespurioussignal
10 CMASS 3
atthenegativeextremewithS/N >2isplottedasafunctionof
]K 5
[∆Tµ −05 Nabsitlaitcyk dinisttrhiebuGtiaounssoiafnmnaoxiismeummodSe/l.NThfoerinthseetcsahsoewosftahlel pvrooidbs-
consideredinthestacking.
−10
−15
0 20 40 60 80 100 120 140 160
N
stack withthetwomethodsshowinggoodagreement.Thisfinding
is in agreement with that of Granett et al. (2008) confirm-
ingthatthemeasurementswiththecompensatedfiltermay
Figure4.StackedCMBtemperaturesasafunctionofthenum-
be considered to be independent.Granett et al. (2008) also
beroftheobjectsconsidered.Aphysicallymotivatedorderingof
pointedout thaterrorsobtained bydrawingrandom points
the voids by radius is applied, as the largest voids should leave
to a given CMB map, and errors measured with fixed void
the coldest imprintson the CMB.Dotted linesrepresent our re-
sultswhenanadditionalweightingbyvoidprobabilityisapplied. positions varying the CMB realization agree at the 2%
∼
Orange dashes in panel 2 mark the errors obtained by measur- level.
ing standard deviations for all filter sizes in simulations inde- The mean error we obtained is higher than the
pendently. In the top panel, we compare our results to the best σ∆T 22 µK uncertainty for a single supervoid found by
signal-to-noiseachieved bynon-optimalrescalingstrategy. Grane≈tt et al. (2008), due to larger CMB fluctuations at
smallerscales.Notethatthishighernoiselevelpreventshigh
signal-to-noise measurements using relatively small voids.
structures in ΛCDM. Unfortunately, current observational Thisprocedureallowsustoestimatethesignificanceof
capabilitiescannotprovidesuchanumerouscatalogofvoids. a measurement given a fixed number of voids N . How-
stack
We adapt the error analysis for the stacking pre- ever, with uncertainties in the properties of the voids and
sented e.g. in Granett et al. (2008), Flender et al. (2013), theoriginofthesignalwedonothaveastrongprioronthe
and Cai et al. (2014), and compare two error estimators. number to average in the analysis. Using only the largest
First, we repeated the stacking analysis 1000 times varying voids we do not have the precision to measure a weak sig-
the CMB realization and fixing the position and scaling of nal,whileaddingthesmallervoidswecanwash-outasignal
the 56 top-hat filters from the CMASS 1 data. We com- if it exists.
pare this against a simpler approach in which the variance Toaddressthissituation,Granett et al.(2008)definea
is computed for a single filter (assumed to be independent) cutoffbaseduponvoidprobability,takingallvoidswithde-
and rescaled by the number of voids in the catalogue. The tection signficance > 3σ. Further, Cai et al. (2014) applied
mean variance is estimated from 1000 realizations but on aweighting asafunction of void probability;however,they
each realization the filter size is randomly drawn from the found no significant difference in the measured signal. We
size distribution. This gives a mean standard deviation of alsotestthisweightingschemehere,asshowninFig.4and
σ∆T 32 µK and we find that this error does not depend discussed below.
≈
ontheredshift bin.Wethenscalethevariancebythenum- Without using a prior as to which voids to consider
ber of objects in thestack: σ∆T(Nstack)=32 µK/√Nstack. in the measurement we are led to examine the signal as a
Thisapproachsimplifiesthecomputationandtestsrevealed function of N ordered by void size, as in Fig. 4. The
stack
thatthetwoestimators agreeatthepercentlevelbasedon temperaturemeasuredafteraveragingN structuresap-
stack
the standard deviation measurement. The CMASS 1 panel pearsasarandomwalkand,giventhenullhypothesisofno
ofFigure4containsacomparisonoftheerrorbarsobtained correlation, we may estimate the probability that the tra-
(cid:13)c 2014RAS,MNRAS000,1–??
6 Andr´as Kov´acs and Benjamin R. Granett
jectory crosses agiventhreshold fordetection.Wecompute
thisprobabilityinMonteCarlo fashion assumingtheGaus-
sian noise model. We generate a vector of Ntot Gaussian 15
distributedvalueswithσ=32µK.Wethencheckifthecu- R/Rv=0.6
mulative sum crosses a given significance threshold at any 10 weighted by pvoid
point. This is repeated and we keep count of the fraction 5 Rℓ<v±101 0r%emoved
of runs that give a significance above 2σ. The result after ] 0
K
100000 runs is shown as a function of Nstack in Fig. 5. We [µ −5
findthatgivenacatalogueof478voids,theoddsoffindinga T
∆ −10 N=70
2σsignalinthecumulativetemperaturemeasurementgiven ∆T= 5.8 2.8µK
thenull hypothesisis 24%. −15 N=50 − ±
∆T= 11.3 3.1µK
We now consider the stacked temperature measure- −20 − ±
mentsshown in Fig. 4. −25
10 20 30 40 50 60 70 80
the(i)sigCnoanlsiflduecritnugattehseacroomubnidnetdhesa1mσplleev(eFl.igA.4.c,otlodpipmapnreiln)t, 2 5 Mpc/h RRR///RRRvvv===000...246
p44ealkasrgwesitthvoaindsamwipthlitsuidzeesoRf −>96.85±h−41.M8 µpKc.Horow∼ev2eσr,fothritshies 1 R=6 RR//RRvv==01..80
unremarkable given that the probability of finding such an /N 0
extreme somewhere in the cumulative stacked temperature S
with a total of 478 structuresis 24%. −1
∼
(ii) However,theGr08 sample contains 50significant su-
pervoids, thus in terms of the largest 50 fluctuations the −2
∼
twocatalogsseemtoagreewitheachotherevenifthestruc-
10 20 30 40 50 60 70 80
tures differin size and are not at thesame positions.
N
(iii) Counting all 478 voids down to R=40 h−1Mpc the stack
signal sharply approaches to zero and becomes ∆T 1.2
≈ ±
1.5 µK. Note that the overall measurement, including the
peak, is unchanged when weighting by void probability. Figure 6. Stacked CMB temperatures for voids of size Rv >
60h−1Mpcorderedbyradius.Inthebottompanel,weshowthe
(iv) Applying a presumably non-optimal filter scaling of
signal-to-noise ratio of our measurement for different re-scaling
40% of the void radius, we found 5.8 3.0 µK or 1.9σ
for the 118 largest voids with size−s R >±55 h−1Mpc∼. This parameters. In the top panel, we compare various measurement
strategies for case R/Rv = 0.6, i.e. the best filter size obtained
signal,shownbytheerrorbarinthetoppanelofFigure4,is
inboth simulation and data. The maximal signal-to-noiseis ob-
thelargestmeasuredusingdifferentrescaledfiltersizes.Note servedatthelowersizelimitofRv>65h−1Mpc.Thesignalwe
thatthissignalisalsoobservedatrelativelylargevoidradii, detected iscomparabletotheGr08observation(showninblue),
and it is consistent with our measurement at N = 118 althoughlesssignificant.
stack
using R/R =0.6.
v
(v) The combined CMASS 1+LOW-Z 4 sample shows a
signalfluctuatinginsidethe1σlevel,resultinginafinalvalue 2.4 Imprint of DR10 supervoids
of ∆T 1.3 3.9 µK for the full sub-catalog with 69 void
≈ ± We have an indication that the largest structures in DR10
members.Notetheeffectoftheprobabilityweightingwhich
may produce an imprint on the CMB characterised by the
reduces theamplitude.
9.8 4.8 µKor 2σ signal that wemeasuredfor voidsof
(vi) The CMASS 2 sample with the largest number of −sizeR±>65h−1M∼pc.Althoughonitsowntheoccurrenceof
voids contributes most strongly to the combined sample, the signal is unremarkable in the light of our Monte Carlo
thusthesignalissimilartothatdescribedabove.Afterfluc- tests, it does match theGr08 measurement in terms of am-
tuating inside the 1σ expectation and reaching the 1.5σ plitudeandnumberofstructures.Thusthisresultwarrants
levelor∆T 10µKatR>65h−1Mpc,theoverall∼signal- further inspection. Our findings, based on additional sys-
≈−
to-noise with all voids included is ∆T 1.7 2.1 µK for tematictestsareshown inFigure6,andsummarized below
≈ − ±
the237CMASS2objects.Theweightingbyvoidprobability
results in a more effective convergenceto zero. (i) the lower panel of Figure 6 demonstrates that the
(vii) TheCMASS3temperaturesignalfluctuatesaround R/Rv =0.6 scaling gives thehighest S/N, as found in sim-
the 1σ level. Adding smaller scale voids the signal becomes ulations and DR7data.
positiveandresultsinacuriouspositive∆T 5.3 2.5µK. (ii) the shape of the dotted purple curve in the upper
However,thegalaxynumberdensityislowest≈inthe±CMASS panel indicates that this signal is robust against weighting
3bin,soalargerfractionofthesmallestvoidsmaybespuri- byvoid probability,in agreement with Cai et al. (2014).
ouscomparedwiththeothermoredenselysampledredshift (iii) we randomly changed the void radius by +10% or
bins. This intuition is verified by the probability weighting 10% for all voids, and the signal nearly disappeared, as
−
test,thatlowersthesignificanceofthespuriouspositivesig- shown in blue.
nal, resulting in ∆T 2.0 2.5 µK. (iv) we artificially removed large-scale fluctuations (i.e.
≈ ± muchlargerthanthevoidsize)fromtheSMICACMBmap
usingHEALPixroutines,andrepeatedthestacking.Without
(cid:13)c 2014RAS,MNRAS000,1–??
Cold imprint of supervoids with Planck and BOSS DR10 7
(SZ)effecthavealreadybeenexcludedbyGr08withconser-
vativemaskingandprobesofCMBcolordependencefurther
140 constrainedbyPlanckanalyses(Planck Collaboration et al.
DR10 stacked 2015).Anotheruncertaintyinthesuperstructurecatalog,in-
Gr08 stacked
troducedbyσ 0.05photometricredshifterrorsofMega-z
DR10 voids z ≈
LRGs, havenot been investigated.
120 Gr08 voids
Figure 7 shows a comparison of filtered temperatures
for Gr08 and DR10 voids as a function of their radius. In
summary,themain properties are as follows.
]c100 (i) larger fluctuations are observed in DR10 results due
p
M to smaller filtersize.
1− (ii) proportionally more R > 65 h−1Mpc (super)voids
h
R [ 80 werefoundinGr08thaninDR10,possiblyduetosystematic
differences in void detection and source catalogs.
(iii) inGr08,thelargestsupervoidsleaveaneverstronger
stacked imprint in theCMB.
60 Large underdense regions of diameter 130 h−1Mpc,
∼
perhaps better thought of as long wavelength fluctuations,
can contain smaller voids, walls, and filaments. Therefore,
toidentifythesesupervoidsingalaxysurveysitwillbenec-
40
−80 −60 −40 −20 0 20 40 60 80 essary to modify void detection algorithms. The voids ef-
∆T [µK] fectively resolved by spectroscopic redshift surveys may be
grouped together and unified to identify under-densities on
thelargestscales.Focusingontheclassofsupervoidswould
Figure7.AcomparisonoffilteredCMBtemperaturesasafunc- furthersimplify theinterpretation ofresultsbylimiting the
tion of the physical size of voids. Shaded regions mark 2σ fluc- selection effects arising from a posteriori choices and illu-
tuations,whilesolidlinesshowthemeasurementsbyGr08anda
minate the possible connection between the apparent ISW
resultobtained usingourfinalsub-catalog.
excess and thedensity field on thelargest scales.
ℓ<10modes,themaphaschanged,anderrorsdecreasedby
3%,butthefilteredtemperaturesremainalmostthesame 3 CONCLUSIONS
≈
(shown with green dashes). This finding is again consistent
We probed the volume of the Granett et al. (2008) super-
with theDR7analysis by Cai et al. (2014).
void catalog with the BOSS DR10 void catalog provided
(v) despitethedifferentstackingmethodsandvoidprop-
bySutteret al.(2014).Ourprincipalaim wastorevisit the
erties, the signal we found is in 1σ agreement with Gr08,
strong ISW(-like) signal found in Gr08 with a catalog that
although less significant due to larger CMB fluctuations at
smaller angular scales (Gr08: constant R=4◦ filter, DR10: probesthesamedensityfield.WeprunedtheDR10catalog
following the protocol of Cai et al. (2014) and the sugges-
R/R =0.6 re-scaling)
v
tion of Sutteret al. (2014) for removing the smallest and
Therefore, we see that the our measurement appears least reliable voids which are also expected to produce the
to be robust against physically motivated changes in the smallest ISW-RS signals in ΛCDM. The voids identified
analysis,whiletheweaksignaldisappearswhennon-optimal with spectroscopic redshifts in DR10 are smaller than the
techniquesareapplied.Theexceptioniswhenthevoidradii Gr08structurestracedwithphotometricredshifts.Evenso,
wereperturbedby10%andwefindareductioninthesignal. we find that the Gr08 supervoid positions do not coincide
Aninherentuncertaintyisexpectedinthevoidradiidueto with regions abundant in DR10 voids which indicates that
samplingerrorandvariationinvoidshape,sothismaypoint the void finders are sensitive to different structures. This
to a fragility of the signal. situationmeritsfurtherstudytounderstandthesystematic
Keeping in mind that the ISW-RS signal expected in differences between voids identified in spectroscopic versus
ΛCDM remains below ∆T 2.0 µK even for the 50 photometric samples.
≈ −
largest posteriori-selected supervoids we also lack the the- We measured the stacked CMB temperatures for the
oretical motivation for this signal. 35 Gr08 supervoids in the DR10 footprint using the orig-
Whilethe4.4σsignalfortheposteriori-selected,50most inal filter size. The ∆T = 11.5 3.7 µK signal that we
− ±
significantGr08superstructuresappearstobetoolargefora found is consistent with the Gr08 measurement. We then
plausibleprimordialfluctuation,Planck Collaboration et al. performed astacking analysis using478 DR10CMASS and
(2015)explicitlypointedoutthatthelackofastrongT E LOW-Zvoids.Ingeneral,nosignificantimprintwasdetected
∼
correlation in the CMB polarization data by Planck in the inthepresenceoflargecosmicvariance.However,wefound
location of the Gr08 structures provides evidence that the a∆T = 9.8 4.8µKor2σsignalforthelargest44voidsof
effect is not a primordial fluctuation. Also, systematic ef- size R>−65 h±−1Mpc in thecombined sample. Wenotethat
fectsareobvioussuspects,butexplanationssuchasspurious thisdetectioninitselfisunremarkablewithoutastrongprior
correlations caused by stellar contamination, extragalactic on the numberof sources or minimum void size used in the
radio sources, or contamination via the Sunyaev-Zeldovich analysis,aswefoundthattheprobabilityoffindinga2σsig-
(cid:13)c 2014RAS,MNRAS000,1–??
8 Andr´as Kov´acs and Benjamin R. Granett
nalsomewhereinthecumulativetemperaturemeasurement CaiY.-C.,ColeS.,JenkinsA.,FrenkC.S.,2010,MNRAS,
with 478 voids is p 24%. However, the measurement is of 407, 201
≈
interestconsideringthedetectionbasedontheGr08sample. Cai Y.-C., Li B., Cole S., Frenk C. S., Neyrinck M., 2014,
We examined how robust the measurement is to variations MNRAS,439, 2978
in the methodology. Varying the filter size, we found that CaiY.-C.,NeyrinckM.C.,SzapudiI.,ColeS.,FrenkC.S.,
the signal is maximised when using a filter radius found to 2014, ApJ, 786, 110
beoptimal in N-bodysimulations. Collister A., Lahav O., Blake C., Cannon R., Croom S.,
Our results highlight that ISW detections with the DrinkwaterM.,EdgeA.,EisensteinD.,LovedayJ.,Nichol
stacking protocol strongly depend on the properties of the R., Pimbblet K., de Propris R., Roseboom I., Ross N.,
tracer population and the void finder. While the effect of SchneiderD.P.,ShanksT.,WakeD.,2007,MNRAS,375,
photo-z errors on the performance of ZOBOV have not been 68
tested, it has been emphasized by Sutteret al. (2014) that Flender S., HotchkissS., NadathurS., 2013, 2, 13
masking and the density of the tracer population strongly Francis C. L., Peacock J. A., 2010, MNRAS,406, 2
affects the resulting void catalogs. Further systematic un- Giannantonio T., Crittenden R., Nichol R., Ross A. J.,
certainties remain in how the hierarchy of voids is cut and 2012, MNRAS,426, 2581
thelocation of void centers. Giannantonio T., Scranton R., Crittenden R. G., et al.
2008, Phys. Rev.D,77, 123520
Gorski K.M., Hivon E., et al. 2005, ApJ, 622, 759
GranettB.R.,NeyrinckM.C.,SzapudiI.,2008,ApJ,683,
ACKNOWLEDGMENTS
L99
WethankMarkNeyrinckandYanchuanCaiforgivingcom- Hern´andez-Monteagudo C., Smith R. E., 2013, MNRAS,
mentsthatimprovedthepaper.AKtakesimmensepleasure 435, 1094
in thanking the support provided by the Campus Hungary Hinshaw G., Larson D., Komatsu E., et al. 2013, ApJS,
fellowship program. Funding for this project was partially 208, 19
provided by the Spanish Ministerio de Economa y Com- HoS., HirataC., Padmanabhan N.,Seljak U.,Bahcall N.,
petitividad(MINECO)underprojectsFPA2012-39684, and 2008, Physical Review D, 78, 043519
Centro de Excelencia Severo Ochoa SEV-2012-0234. BRG HotchkissS.,NadathurS.,Gottl¨oberS.,Iliev I.T., Knebe
acknowledges support of the European Research Council A.,Watson W. A., YepesG., 2015, MNRAS,446, 1321
through the Darklight ERC Advanced Research Grant (# Ili´c S., Langer M., Douspis M., 2013, A&A,556, A51
291521). Kova´cs A., Szapudi I., Granett B. R., Frei Z., 2013, MN-
Funding for SDSS-III has been provided by the Al- RAS,431, L28
fred P. Sloan Foundation, the Participating Institutions, NadathurS., HotchkissS., Sarkar S., 2012, 6, 42
the National Science Foundation, and the U.S. Depart- Nadathur S., Lavinto M., Hotchkiss S., Ra¨s¨anen S., 2014,
ment of Energy Office of Science. The SDSS-III web site is Phys.Rev.D, 90, 103510
http://www.sdss3.org/. SDSS-IIIis managed by the Astro- Neyrinck M. C., 2008, MNRAS,386, 2101
physicalResearch Consortium fortheParticipatingInstitu- Pa´pai P., SzapudiI., 2010, ApJ, 725, 2078
tionsoftheSDSS-IIICollaborationincludingtheUniversity Pa´pai P., SzapudiI., Granett B. R., 2011, ApJ, 732, 27
of Arizona, the Brazilian Participation Group, Brookhaven Peiris H. V.,2014, ArXiv e-prints
National Laboratory, Carnegie Mellon University, Univer- PlanckCollaborationAdeP.A.R.,AghanimN.,Armitage-
sity of Florida, the French Participation Group, the Ger- CaplanC.,ArnaudM.,AshdownM.,Atrio-BarandelaF.,
man Participation Group, Harvard University, the Insti- Aumont J., Baccigalupi C., Banday A. J., et al. 2014a,
tuto de Astrofisica de Canarias, the Michigan State/Notre A&A,571, A19
Dame/JINA Participation Group, Johns Hopkins Univer- PlanckCollaborationAdeP.A.R.,AghanimN.,Armitage-
sity, Lawrence Berkeley National Laboratory, Max Planck CaplanC.,ArnaudM.,AshdownM.,Atrio-BarandelaF.,
Institute for Astrophysics, Max Planck Institute for Ex- Aumont J., Baccigalupi C., Banday A. J., et al. 2014b,
traterrestrial Physics, New Mexico State University, New A&A,571, A16
York University, Ohio State University, Pennsylvania State Planck Collaboration Ade P. A. R., Aghanim N., Arnaud
University,Universityof Portsmouth, Princeton University, M., Ashdown M., Aumont J., Baccigalupi C., Banday
theSpanishParticipation Group,Universityof Tokyo,Uni- A. J., Barreiro R. B., Bartolo N., et al. 2015, ArXiv e-
versity of Utah, Vanderbilt University, University of Vir- prints
ginia, University of Washington, and YaleUniversity. Rees M. J., Sciama D. W., 1968, Nature,217, 511
Sachs R.K., Wolfe A.M., 1967, ApJL, 147, 73
Sutter P. M., Lavaux G., Hamaus N., Pisani A., Wandelt
B.D.,WarrenM.,Villaescusa-NavarroF.,ZivickP.,Mao
REFERENCES
Q., Thompson B. B., 2015, Astronomy and Computing,
Aghanim N., Majumdar S., Silk J., 2008, Reports on 9, 1
Progress in Physics, 71, 066902 Sutter P. M., Lavaux G., Wandelt B. D., Weinberg D. H.,
Ahn C. P., Alexandroff R., Allende Prieto C., Anders F., 2012, ApJ, 761, 44
Anderson S. F., Anderton T., Andrews B. H., Aubourg Sutter P. M., Lavaux G., Wandelt B. D., Weinberg D. H.,
E´., Bailey S., Bastien F. A., et al. 2014, ApJS, 211, 17 Warren M. S., 2014, MNRAS,438, 3177
Aiola S., Kosowsky A., Wang B., 2015, Phys. Rev. D, 91, Sutter P. M., Lavaux G., Wandelt B. D., Weinberg D. H.,
043510 Warren M. S., Pisani A., 2014, MNRAS,442, 3127
(cid:13)c 2014RAS,MNRAS000,1–??
Cold imprint of supervoids with Planck and BOSS DR10 9
Sutter P. M., Pisani A., Wandelt B. D., Weinberg D. H.,
2014, MNRAS,443, 2983
SzapudiI.,Kova´csA.,GranettB.R.,FreiZ.,SilkJ.,Bur-
gett W., Cole S., Draper P. W., Farrow D. J., Kaiser N.,
MagnierE.A.,MetcalfeN.,MorganJ.S.,PriceP.,Tonry
J., Wainscoat R., 2014, ArXiv e-prints
(cid:13)c 2014RAS,MNRAS000,1–??