The part and the whole: voids, $super$voids, and their ISW imprint

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by  András Kovács

MNRAS000,1–??(2017) Preprint31January2017 CompiledusingMNRASLATEXstylefilev3.0
The part and the whole: voids, supervoids, and their ISW
imprint
Andr´as Kov´acs(cid:63)
Institut de F´ısica d’Altes Energies, The Barcelona Institute of Science and Technology, E-08193 Bellaterra (Barcelona), Spain
Submitted2017
7
ABSTRACT
1
TheintegratedSachs-Wolfeimprintofextremestructuresinthecosmicwebprobesthe
0
dynamicalnatureofdarkenergy.Lookingthroughtypicalcosmicvoids,noanomalous
2
signal has been reported. On the contrary, supervoids, associated with large-scale

n fluctuations in the gravitational potential, have shown potentially disturbing excess
a signals. In this study, we used the Jubilee ISW simulation to demonstrate how the
J
stacked signal depends on the void definition. We found that large underdensities,

0 with at least ∼ 5 merged sub-voids, show a peculiar ISW imprint shape with central
3
coldspotsandsurroundinghotrings,offeringanaturalwaytodefinesupervoidsinthe

cosmic web. We then inspected the real-world BOSS DR12 data using the simulated
]
O imprints as templates. The imprinted profile of BOSS supervoids appears to be more
compact than in simulations, requiring an extra α ≈ 0.7 re-scaling of filter sizes.
C
The data reveals an excess ISW-like signal with A ≈ 9 amplitude at the ∼ 2.5σ
ISW
.
h significance level, unlike previous studies that used isolated voids and reported good
p consistency with A =1. The tension with the Jubilee-based ΛCDM predictions is
ISW
- ∼> 2σ, in consistency with independent analyses of supervoids in Dark Energy Survey
o
data. We show that such a very large enhancement of the A parameter hints at
r ISW
t a possible causal relation between the CMB Cold Spot and the Eridanus supervoid.
s
a The origin of these findings remains unclear.
[
Key words: large-scale structure of Universe – cosmic background radiation

1
v
3
8
5 1 INTRODUCTION the individual attempts and found AISW ≈ 1.00±0.25 in
8 cross-correlationfunctions(Planck2015results.XXI.2016).
A dynamical property of dark energy is the decay of large-
0 Alternatively, the ISW signal may also be detected lo-
scale gravitational potentials which imprint tiny secondary
.
1 anisotropies to the primary fluctuations of the Cosmic Mi- cally using catalogues of voids and superclusters. The mea-
0 crowave Background (CMB) radiation. This late-time re- surement involves the identification of individual voids in
7 thecosmicwebassumingavoiddefinitionandthenastack-
processionofCMBpatternsbythecosmicwebisstudiedin
1 ing of CMB temperatures on their locations as a measure
the framework of the Integrated Sachs-Wolfe effect (Sachs
: of their average imprint. Typically, no high-significance de-
v & Wolfe 1967, ISW) in the linear regime, and via the sub-
i dominant Rees-Sciama effect (Rees & Sciama 1968, RS) on tection has been reported (Ili´c et al. 2013; Planck 2013 re-
X
sults. XIX. 2014; Cai et al. 2014; Hotchkiss et al. 2015;
smaller scales. The weak ISW imprints on the primordial
r CMB temperature fluctuations can be measured in cross- Kov´acs & Granett 2015) with differently constructed void
a
cataloguesintheSloanDigitalSkySurvey(SDSS)dataus-
correlations with tracers of the matter distribution (Crit-
ing the ZOBOV algorithm (Neyrinck 2008). These studies all
tenden & Turok 1996).
allowedsomelevelofvoidmergingusing ZOBOV’swatershed
Summarizing the individual measurement efforts, Gi-
method, but specific analyses of potentially encompassing
annantonio et al. (2012) (see also references therein) com-
supervoids have not been attempted directly.
bined several tracer catalogues and reported an A =
ISW
∆T /∆T ≈ 1.38±0.32“amplitude”using angular Recently, Nadathur & Crittenden (2016) reported a
data ΛCDM
cross-correlationtechniques,whereA =1correspondsto 3.1σ detection of the ISW signal from“isolated”voids and
ISW
the concordance Λ-Cold Dark Matter (ΛCDM) prediction. superclusters in the Baryon Oscillations Spectroscopic Sur-
Withmoretracercatalogues,thePlanckteamalsocombined vey (BOSS) data release 12 (DR12). Their implementa-
tionofthewatershedalgorithmpreventedneighboringvoids
frommerging(seeNadathuretal.2016).Theyusedoptimal
(cid:63) [email protected] matched filters and found AISW ≈1.65±0.53.
(cid:13)c 2017TheAuthors
2 Andr´as Kov´acs
galaxies. Systems of voids lined up in our LOS, however,
Table1.Strategiesforcontrollingmerginginthevoidhierarchy.
SeeNadathur&Hotchkiss(2015)fordetails. are possible to detect with new algorithms and a good un-
derstanding of void properties and potential biases in void
identification (Sa´nchez et al. 2017).
Label Criteriaformerging:
If accounted for, this selection effect might actually be
Linkdensity Densityratio
anadvantagebecausesuper-structureselongatedinourLOS
VIDE nlink<0.2n unconstrained have a longer photon travel time compared to the spherical
Minimal nlink<n r<2 case,correspondingtolargerISWtemperatureshifts.How-
Isolated nomerging nomerging
ever,itisworthnotingthatFlenderetal.(2013)concluded
that the assumption of sphericity does not lead to a signifi-
cant underestimate of the ISW signal in a ΛCDM model.
BasedonthesameBOSStracerdatasetbutadifferent
Nevertheless,thehigher-than-expectedISW-likesignals
void catalogue, Cai et al. (2016) found A ≈ 6 with a
ISW seemtoemergewhenusingcataloguesofthiskindofmerged
marginal∼1.6σdetectionsignificance.However,usingthose
voids based on tracers affected by photo-z errors.
voidsseentobethemostprobablewith 3σ (i.e.,leastlikely
to occur in random catalogues), they found A ≈ 20 at
ISW
∼ 3.4σ significance. The imprint of these voids showed no
2.1 SDSS supervoids and their ISW-like effect
anomaly in the Planck CMB lensing convergence (κ) map.
Bothstudiesfocussedonefficientpruningstrategiesto, Foremost, Granett et al. (2008) (Gr08, hereafter) defined
above all, remove the so-called voids-in-clouds that are ex- a catalog of 50-50 significant supervoids and superclusters
pected to be aligned with hot spots on the CMB. Apart usingSDSSphoto-zdata.UsingaBOSSDR12spec-zgalaxy
from the different filtering methods applied, most impor- catalogue, Granett et al. (2015) reconstructed the average
tantly Cai et al. (2016) also considered merged voids. In shape of the Gr08 supervoids that were originally defined
part, this difference might explain the different outcomes byphoto-z tracers,findinganaxisratioR /R ≈2.6±0.4.
(cid:107) ⊥
because Hotchkiss et al. (2015) have pointed out in simula- For this sample, Gr08 found a higher-than-expected
tionsthattheshapeofthestackedISWimprintdoesdepend ISW-like signal that appears to be in ∼ 3σ tension with
on the void definition. ΛCDMpredictionswithA ∼10(Pa´pai&Szapudi2010;
ISW
Based on stacking probes with systems of merged sub- Pa´paietal.2011;Nadathuretal.2012;Flenderetal.2013;
voidsorsupervoids,however,thereisanotherbranchofob- Aiolaetal.2015).ThefreedomtovarytheΛCDMparame-
servationalresultsthatreportedA ∼10values(Granett ters, given other constraints, is not enough toovercome the
ISW
et al. 2008; Szapudi et al. 2015; Kova´cs et al. 2017, us- discrepancy with observation.
ingSDSS,Pan-STARRS11,andDarkEnergySurvey(DES) Besides,Herna´ndez-Monteagudo&Smith(2013)found
data,respectively).Inthispaper,wetesttheseclaimsusing thatvaryingthenumberoftheobjectsinthestackinglowers
yet another type of BOSS DR12 void catalogue. We focus the overall significance. The simulation analyses by Kova´cs
on systems of merged voids using so called“minimal”voids et al. (2017) have shown, however, that stacking all voids
(Nadathur & Hotchkiss 2015) that trace large-scale under- in a catalogue might not be the optimal strategy for the
densitiesinthecosmicweb.SeeTable1forexamplesofvoid highestsignal-to-noise(S/N,hereafter)detectionoftheISW
selection criteria. imprint. The largest voids have bigger impact but they are
WeusetheJubileeISWsimulation(Watsonetal.2014) less numerous therefore an optimum might exist halfway;
andamockluminousredgalaxy(LRG)cataloguetoapriori perhaps close to the serendipitous choice by Gr08.
define pruning strategies. We aim to understand the differ- Another problem with the original Gr08 is the a pos-
ences between ISW measurement techniques that consider teriori choice of filter size for their compensated hop-hats
isolatedvoidsandsupervoids.Finally,westudytheimplica- (CTH). Gr08 used a constant R = 4◦ filter size but the
tions of our findings to the problem of the CMB Cold Spot re-scaling of filters to the individual void size appears to
(Cruzetal.2005)andtheEridanussupervoid(Szapudietal. be important. For the Gr08 supervoids, a filter re-scaling
2015). of R/R ≈ 0.6 for R void radii maximized the signal (Ili´c
v v
The paper is organized as follows. In Section 2, we dis- et al. 2013). This is in line with the simulation analyses by
cuss the role of void definitions in the currently available Cai et al. (2014).
observationalISWlandscape.Datasetsanddetectionalgo- In summary, the original Gr08 signal has survived new
rithms are introduced in Section 3. Our simulated and ob- CMBdatareleasesandtestsagainstCMBandgalacticsys-
servationalresultsarepresentedinSection4andinSection tematics and remains a puzzle. It is important to look for
5, respectively, while the final section contains a summary, similarsignalselsewhereintheskytotestthehypothesisof
discussion and interpretation of our findings. a rare statistical fluctuation.
2.2 DES supervoids and their ISW-like effect
2 ISW IN PHOTO-Z CATALOGUES
Recently,Kova´cs et al. (2017)probed the Gr08claims with
In photometric data, finding typical voids surrounded by
photo-zdatainadifferentfootprint.Theyusedthefirstyear
overdensitites is challenging because of the smearing effect
data of the Dark Energy Survey (DES, The Dark Energy
of photo-z errors in the line-of-sight (LOS) distribution of
Survey Collaboration 2005). They identified 52 large voids
and 102 superclusters at redshifts 0.2<z <0.65 using the
1 http://pswww.ifa.hawaii.edu/pswww/ voidfindertooldescribedinSa´nchezetal.(2017).Theheart
MNRAS000,1–??(2017)
Cold imprint of voids and supervoids 3
RRAA [[°°]]
118800◦◦
222255◦◦
113355
◦◦
11000000
550000 77χχ55 [[00MMppcc//hh]]
Figure 1. The cross-section of voids in the LOWZ sample of the BOSS DR12 data with the cone Dec = 12◦, coloured according to
whether the average galaxy density within the void is δg <0 (red) or δg >0 (yellow). Galaxy positions in a slice of opening angle 2◦
centred at the angle are overlaid in blue, and buffer mocks around the survey edges in green. Voids with δg <0 tend to correspond to
under-compensatedunderdensities,formingsupervoidfeatures,whilethosewithδg >0areonaverageover-compensatedonlargescales,
i.e.voids-in-clouds.Minimalvoidscanbedefinedbymergingtheseisolatedvoidsunderspecificcriteria.(PlotfromNadathur(2016).)
of that method is a restriction to 2D slices of galaxy data, lousbutthecombinationofarathercoldareainthecentre
andmeasurementsoftheprojecteddensityfieldaroundcen- and a surrounding hot ring feature.
tersdefinedbyminimainthecorrespondingsmoothedden- Nevertheless there is growing observational evidence,
sity field. A larger smoothing automatically merges smaller again in photo-z data, for the presence of the low-z Eri-
sub-voids into larger voids, while too coarse smoothing can danussupervoidalmostperfectlyalignedwiththeColdSpot
increasetheuncertaintiesinthepositionandsizeestimates. (Rudnicketal.2007;Granettetal.2010;Bremeretal.2010;
They then tested the shapes and orientations of their Szapudietal.2015).SimilarlytoSDSSandDESsupervoids,
super-structures. Analyses of DES mock galaxy catalogues the Eridanus supervoid was found to be significantly elon-
revealedameanLOSelongationR /R ≈2.2forvoidsand gated in the LOS (Kova´cs & Garc´ıa-Bellido 2016) and it is
(cid:107) ⊥
R /R ≈2.6 for superclusters. In contrast, for voids in the a rare matter fluctuation. Its exact shape is not yet known
(cid:107) ⊥
BOSS spec-z data Nadathur (2016) found smaller average but it appears to be a complicated system of sub-voids.
ellipticities, and with a random orientation of void major Assumingviablevoidprofiles,analyticalmodelspredict
axes relative to the LOS. ISW imprint profiles for this supervoid that disagree with
In their analysis, Kova´cs et al. (2017) used the Jubilee theobservedprofileoftheColdSpot(Nadathuretal.2014;
simulation to a priori evaluate the configuration. Following Finelli et al. 2015; Marcos-Caballero et al. 2016; Kova´cs
Gr08 and others, they performed a stacking measurement & Garc´ıa-Bellido 2016; Naidoo et al. 2016). Relatedly, Na-
with the CTH filtering technique. For optimal configura- dathur & Crittenden (2016) concluded that the ISW expla-
tions,theyfoundacoldimprintofvoidswithA ≈8±6 nationisnotsupportedbytheirresultsbecauseaverylarge
ISW
that is ∼ 1.2σ higher than the imprint of such super- enhancement of the A parameter would be required.
ISW
structures in Jubilee’s ΛCDM universe. They also found The significance of these observational findings is un-
A ≈ 8±5 for their superclusters. If they instead used clear at the moment. Nevertheless a trend might be emerg-
ISW
an a posteriori selected filter size R/R = 0.6, they found ingintheshadowofa posterioribiasarguments,indicating
v
A ≈15 which exceeds ΛCDM expectations at the ∼2σ thatthegloballyestimatedA ≈1amplitudemighthave
ISW ISW
level. Note that Gr08 and DES supervoid catalogues both a larger value for the largest super-structures. We test this
showelongationalongtheline-of-sightandforbothsamples hypothesis with special samples of merged voids in BOSS
theR/R ≈0.6re-scalingmaximizestheirISW-likeimprint DR12 data and in the Jubilee simulation.
v
with a similarly high A amplitude.
ISW
2.3 The Eridanus supervoid: ISW-like effect?
3 DATA SETS FOR THE ISW ANALYSIS
The CMB Cold Spot (Cruz et al. 2005) is one of the large-
3.1 Isolated voids
scaleanomaliesintheCMB.Itssignificanceis∼2−3σ de-
pending on the statistical method applied. Nadathur et al. The concept of isolated voids does not include merging of
(2014)arguedthatitisnotitscoldnessthatmakesitanoma- voidsintosupervoids(seeFigure1).Theproblemwithmerg-
MNRAS000,1–??(2017)
4 Andr´as Kov´acs
200
N 5
BOSS DR12 merged≥
60
Gr08 p >3σ
void
N40 ∆T 0.6
∼ ISW
20 No merging
Granett et al. 150
0.5
h] 2 4 6 8
c/ θ [◦]
p
M 0.4z
[v100
R
0.3
0.2
50
0.65 0.70 0.75 0.80 0.85 0.90
δ
c
Figure 2. Summary plot of minimal void parameters Rv radius, δc central density, and z redshift in the BOSS DR12 CMASS and
LOWZjointcatalogue.CirclesizesindicaterelativecentralISWexpectations.OrangecirclesmarkGr08supervoids.Theinsetshowsthe
angular size distributions. Pentagon symbols show supervoids with at least 5 merged sub-voids (used later for final conclusions), while
red-edgedcirclesmarkobjectswithoutmerging.Blackpointsinthecentersofcirclesorpentagonsindicatep >3σ voidprobability.
void
ing, as Nadathur (2016) discussed, is the ambiguity in the et al. (2016) who considered an observable quantity λ that
void definition. Also, Nadathur & Hotchkiss (2015) argued is tightly correlated with Φ, namely
that the properties of the very largest and deepest voids,
(cid:18) R (cid:19)1.2
i.e. the ones of greatest interest and also the most likely λ≡δ eff (3)
to undergo merging, are very sensitive to the details of the g 1h−1Mpc
merging criteria chosen. Nevertheless, the environment of where R is the effective radius of voids. The majority of
eff
voidsisarelevantpropertythatinfluencesthegravitational voids identified by ZOBOV correspond to local underdensi-
potential (Φ) and therefore the ISW signal. Along these ties within globally overdense regions and thus do not give
lines,Nadathur&Hotchkiss(2015)foundahintthatunder- ∆T < 0. Applying a selection cut λ < 0 selects those
ISW
compensated voids with volume-weighted average density globally undercompensated voids which correspond to re-
δ¯g <0 might tend to cluster together in space, with gions with Φ>0 and thus a negative ISW shift.
(cid:80)
δ¯g = ρ1¯ (cid:80)iρViVi −1 (1)
i i 3.2 Minimal voids ∼ supervoids
where ρ¯is the mean tracer density in the galaxy catalogue
The analysis of isolated voids offers a great way to probe
andthesumrunsoverallVoronoicellsthatmakeupthevoid
theISWeffect.However,thecombinationoftheirdefinition
volume (see Figure 1). Further, they found a simple linear and the observed clustering of δ¯ < 0 voids suggests that
relation between δ¯ and the local density environment, g
g in fact many of them are imbedded in more extended back-
3 (cid:90) R ground underdensities, or supervoids. The largest minimal
∆(R)= δ(r)r2dr, (2) voids offer an interesting possibility to probe the ISW im-
R3
0 printofthesesuper-structures,i.e.thelargestfluctuationsin
thateffectivelydeterminesthevalueofΦ.Inthisframework, Φ.Wealsoexpectthatvoiddepthisimportant,asexpressed
∆(R=3R )<0suggeststhattheisolatedvoidisnotcom- in Eq. (3), and centres of isolated voids with the lowest λ
v
pensated by surrounding high density regions. Such voids valuesarethecentresofthelargestsurroundingsupervoids.
will correspond to regions of Φ > 0, i.e. ∆T < 0. With We start with a catalog of 6565 minimal ZOBOV voids
ISW
this cut, voids-in-clouds can effectively be removed. using both CMASS and LOWZ spec-z data from BOSS
This proxy for the Φ potential offers a good chance to DR12, spanning 0.15 < z < 0.7 in redshift. The λ ∼ Φ
refine the selection of under-compensated voids, potentially relation has not been tested on minimal voids, therefore we
better than void size alone. However, accurate relations are cannot use it blindly to bin our data. We instead follow
needed for a detailed study of the underlying gravitational thesimpleandmoreapproximateprescriptionbyNadathur
potentialthatmightdependontheshapeofthedensitypro- & Hotchkiss (2015) and select voids with weighted average
fileandthesizeofvoids,asnotedbyNadathur&Hotchkiss densities δ¯ < 0 or equivalently n /n¯ < 1 (the average
g avg
(2015).SucharelationhasactuallybeenfoundbyNadathur tracer number density within voids compared to the mean
MNRAS000,1–??(2017)
Cold imprint of voids and supervoids 5
tracer density). This cut guarantees a void population of correspond to larger ISW temperature shifts. This conclu-
Φ>0with∆T <0.Wefurtherprunethevoidcatalogue sion is validated by the results of Hotchkiss et al. (2015).
ISW
by removing objects located close to the survey boundary They estimated the ISW imprint for voids (and also super-
mask(EdgeFlag<2),leaving1446voidsoutof6565.InFig- clusters) in mock LRG catalogues with differing brightness
ure 2, we show a summary of selected void parameters for and sparsity in the Jubilee simulation, and found that the
ourprunedcatalogueincludingradius,centralunderdensity, sparser sample gave consistently larger |∆T|.
redshift,andangularsize.AcomparisontoGr08supervoids We therefore conclude that the expected stacked ISW
indicates that we are in good position to probe the claims signal we determine from Jubilee will be an overestimate
by Gr08 using more large voids to potentially illuminate a of that observable from superstructures in the BOSS data.
true signal, and with a large amount of small voids to see ForthegivengalaxynumberdensitiesthedifferenceinISW
how such signals might disappear. signalsisexpectedtoberelativelysmallandcertainlybelow
We thus apply an aggressive cut that removes ∼ 78% the level of noise in the measurement.
of the total catalogue. The full BOSS DR12 isolated void We make use of two catalogues of voids in the Jubilee
catalogue2, used as a base data set for the pruned analysis LRG mock using the ZOBOV algorithm. We considered the
presentedinNadathur&Crittenden(2016),contains10492 full-sky LRG mock data set with the LOWZ and CMASS
voids. For our main conclusions, we will apply additional redshift windows. The mock catalogue of isolated Jubilee
motivated pruning to the minimal sample, leaving only the voidsconsistsof19528voids.Asexpected,theminimalver-
96 largest minimal voids for the fiducial stacking analysis. sionislessnumerouswith11043objectsaftersub-voidmerg-
Forcomparison,1392isolatedvoidsareimbeddedinthese96 ing.TheadditionalpruningcutswedescribedinSection3.2
supervoids while Nadathur & Crittenden (2016) used 2446 result in 2446 minimal voids and 7446 isolated voids with
isolated voids. properties δ¯ <0 and EdgeFlag<2.
g
We note that not all the minimal voids in the cata-
loguehaveactuallybeenmerged,asdemonstratedinFigure
2. A parameter N indicates the number of isolated
merged
4 JUBILEE ISW ANALYSIS
sub-voids, reaching N ∼ 40 values for the largest su-
merged
pervoids. We mark objects with Nmerged (cid:62)5 values and see Following Hotchkiss et al. (2015) and Kova´cs et al. (2017),
agoodcorrelationwithasubsetdefinedbytheoftenconsid- westacktheISW-onlyJubileetemperaturemaponvoidlo-
ered pvoid > 3σ probability cut that selects the largest and cations. We re-scale the images knowing the angular size of
deepest objects in the sample. voids.Onthestackedimages,wethenmeasureazimuthally
Nevertheless,weareguidedtousesimulationstoa pri- averaged radial ISW profiles inR/R fractional voidradius
v
oridecideexactlywhichminimalvoidstostackfordetecting units.Whileenvironment,densityprofiles,redshifts,andex-
a specific ISW signal of supervoids. actshapescanbeimportantfortheaccurateestimates,the
ISW signal is expected to correlate with void size. In our
fiducial sample, therefore, we order the voids by their R
v
3.3 The Jubilee simulation
radius. We also split and explore our data in the following
We first analyzed simulated data from the Jubilee ISW ways:
project (Watson et al. 2014) to estimate the ΛCDM ex-
• most importantly, we compare the imprints of isolated
pectation for the stacked ISW imprint of voids, following
and minimal voids in all possible aspects.
Hotchkiss et al. (2015). The Jubilee ISW project is built
• secondly,wemeasurenon-filteredandCTH-filteredpro-
upon the Jubilee simulation, a ΛCDM N-body simulation
files for the objects and make a comparison.
with 60003 particles in a volume of (6h−1 Gpc)3, assuming
• basedontheR effectiveradiusparameterofvoids,we
v
WMAP-5cosmology.AcorrespondingmockLRGcatalogue
create 10 bins for 10% percentiles.
wasinitiallydesignedtomodelthepropertiesofSDSSLRGs
• usingthebinneddata,westacktheimagesbothcumu-
studied in Eisenstein et al. (2005). This mock provides a
latively and differentially.
sample with n¯ ≈ 8×10−5h3 Mpc−3 that is slightly lower
• we test the importance of the void center definition;
than the corresponding BOSS values. For CMASS the co-
barycenter vs. minimum density center.
movingnumberdensitypeaksatz≈0.5withn¯ ≈4×10−4h3 • we probe the effects of removing the 2 (cid:54)(cid:96)(cid:54)10 large-
Mpc−3, while it is n¯ ≈ 3×10−4h3 Mpc−3 for LOWZ that
scale modes from the ISW map.
slightly depends on redshift.
• beyondthefiducialascendingorderingbasedonR ,we
v
This difference could affect our conclusions about the
try alternative orderings based on λ, N , and p .
merged void
optimal stacking strategy. In sparser galaxy tracers, the
• weshowhowcombinedmodificationsaffecttheresults.
number of voids identified decreases, but the average void
size is larger (Sutter et al. 2014; Nadathur & Hotchkiss
2015). More importantly, voids resolved by sparse galaxy
samples also on average trace shallower but more extended 4.1 CTH filters
dark matter underdensities (Nadathur & Hotchkiss 2015),
In Figure 3, we start our analysis by showing how isolated
whichshouldhavealongerphotontraveltimeandtherefore
and minimal voids compare in the most traditional CTH-
filtering scheme with filtered CMB temperatures
2 The DR12 minimal catalogue we use is non-public but a pub- (cid:82)R∆T(r)dr (cid:82)√2R∆T(r)dr
lhitctcpa:t/a/lwowgwu.eicogf.mpoirntim.aacl.vuoki/dsstaisblaev/anialadbaltehuforr/vBoOidSsS/ DR11 at ∆Tf = 0 (cid:82)Rdr − R (cid:82)√2Rdr (4)
0 R
MNRAS000,1–??(2017)
6 Andr´as Kov´acs
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
Cai et al. Cai et al. Cai et al. Cai et al.
0.0
d)
e
er 0.2
TH-filt 0.4
C
(K] 0.6 10% 60%
∆T[µf 0.8 2300%% 7800%%
40% 90%
50% 100% MinDensCenter definition MinDensCenter definition MinDensCenter definition
1.0
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
Cai et al. Cai et al. Cai et al. Cai et al.
0.0
d)
e
er 0.2
TH-filt 0.4
C
(K] 0.6
µ
T[f
∆ 0.8
BaryCenter definition BaryCenter definition BaryCenter definition BaryCenter definition
1.0
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Figure 3. A color-coded set of curves shows the cumulatively or differentially binned CTH-filtered ISW profiles. We compare isolated
and minimal voids with both stacking protocols. Subfigures in the top row show our results using MinDensCenter definition while the
bottompanelcorrespondstoBaryCentervoidcentering.Theverticallineindicatesthebestre-scalingvalueobtainedbyCaietal.(2016)
fortheirvoidsample.Forthistest,weremovedthe2(cid:54)(cid:96)(cid:54)10modesfromtheISWmap.
where R is the filter radius. Centered on the voids, CMB On the other hand, minimal voids show different ISW
temperaturesareaveragedwithinacircularaperturer<R, imprints in Jubilee. The rightmost panel in figure 3 shows
andthenthebackgroundtemperatureaveragedinanequal- that the largest ∼ 20% of the sample produces a peak in
√
area concentric annulus with R < r < 2R is subtracted the CTH-filtered signal at R/R ≈ 0.7. In fact this largest
v
inordertomeasurethepossibleISWimprints.Forminimal ∼ 20% part of the minimal data appears to dominate the
voids,wecanimmediatelyvalidatetheapproximatefindings cumulative stacking results while the rest of the sample be-
by Cai et al. (2016) who reported in their simulations that havessimilarlytotheisolatedcase.Thisfeaturereflectsthe
a re-scaling of CTH filters with a R/R ≈ 0.7 factor guar- importanceofvoidmergingbecausethesearetypicallynon-
v
antees the highest filtered signal (second panels from the merged voids in the minimal catalogue.
left). On the other hand, figure 3 is also helpful to validate Aninterestingfeatureinthedataisthestrongerimprint
the findings by Hotchkiss et al. (2015) who found that this forthistop∼20%populationwhenconsideringBaryCenter
propertydoesdependonthevoiddefinition;thecumulative definition,becauseavoid’sdeepestregion(MinDensCenter)
stacking signal of isolated voids peaks closer to R/R ≈ 1. is expected to correspond best to the peak ISW signal. We
v
Apart from the different peak location for the CTH-filtered note that for isolated voids this expectation appears to be
signals,theshapeofthesignalappearstochangemuchless true. Among other properties, we investigate this difference
for isolated voids as, cumulatively, smaller voids are added in greater details in our additional tests below.
to the stacking.
Thedifferentialbinningofvoidsishelpfultounderstand
4.2 Non-filtered profiles and large-scale modes
this property (see the right panels of figure 3). For isolated
voids, the filtered signals tend to show a peak at R/R ≈1 We then consider azimuthally averaged radial ∆T(R/R )
v v
asinthecumulativecasebutthenthelocationofthispeak profiles without CTH filtering. We later use these profiles
shifts to larger R/R values with smaller and smaller voids as templates for the expected ISW profile of BOSS voids,
v
inthestack.Thesmallerhalfoftheisolatedsample((cid:62)50%) effectively defining a hybrid approach; in between the CTH
appears to show a peak at R/R (cid:62) 2 indicating that these measurement by Cai et al. (2016) and the optimal matched
v
voidsareindeedtypicallyimbeddedinlargercoldISWspots filtering technique by Nadathur & Crittenden (2016).
that are not unique to them. These findings hold for both InFigure4,weshowhowtheseprofilescompareforsize-
BaryCenter and MinDensCenter (the center of the largest ranked and binned isolated and minimal voids. We observe
empty sphere that can be inscribed within the void) void thatthemagnitudeofthecentralISWsignaliscomparable
center definitions. buttheshapeoftheimprintinR/R unitsisdifferent.Note
v
MNRAS000,1–??(2017)
Cold imprint of voids and supervoids 7
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
1
‘>10 ‘>10 ‘>10 ‘>10
Cai et al. Cai et al. Cai et al. Cai et al.
0
K]
µ 1
T[
∆
10% 60%
2 20% 70%
30% 80%
40% 90%
50% 100% BaryCenter definition BaryCenter definition BaryCenter definition
3
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
1
‘ 2 ‘ 2 ‘ 2 ‘ 2
Cai et al. ≥ Cai et al. ≥ Cai et al. ≥ Cai et al. ≥
0
K]
µ 1
T[
∆
2
BaryCenter definition BaryCenter definition BaryCenter definition BaryCenter definition
3
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
1
‘>10 ‘>10 ‘>10 ‘>10
Cai et al. Cai et al. Cai et al. Cai et al.
0
K]
µ 1
T[
∆
10% 60%
2 20% 70%
30% 80%
40% 90%
50% 100% MinDensCenter definition MinDensCenter definition MinDensCenter definition
3
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Isolated (cumulative) Minimal (cumulative) Isolated (differential) Minimal (differential)
1
‘ 2 ‘ 2 ‘ 2 ‘ 2
Cai et al. ≥ Cai et al. ≥ Cai et al. ≥ Cai et al. ≥
0
K]
µ 1
T[
∆
2
MinDensCenter definition MinDensCenter definition MinDensCenter definition MinDensCenter definition
3
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Figure 4. Azimuthally averaged ISW imprint profiles of different voids are compared as a function of R/Rv. Subfigure labels indicate
thestackingprotocol,voidtype,andvoidcenterdefinition.Theroleofthelarge-scale2(cid:54)(cid:96)(cid:54)10modesinreducingthefluctuationsand
biasesmaybeinvestigatedbycomparingthefirstandsecondrowsofsubfiguresforBaryCenterdefinition,andbycomparingthethird
andfourthrowsofsubfiguresforMinDensCenterdefinition.
MNRAS000,1–??(2017)
8 Andr´as Kov´acs
thatthisisacomparisonoftheISW-onlysignalsnotaS/N the most ISW-sensitive voids produce the coldest imprints
analysis.Themorenumerousisolatedvoidsareexpectedto inthevoidcentre.However,voidswithλvaluesapproaching
have higher S/N, with presumably higher covariance, even zeroappeartoleavea∆T >0imprintthatpointstothe
ISW
if the minimal voids have larger typical angular size that need of proper calibration of this technique.
means smaller CMB fluctuations. Finally, we again observe differences between stackings
We also compare the signals with and without the using center definitions, with one outstanding feature. The
2 (cid:54) (cid:96) (cid:54) 10 modes in the ISW-only map. Without these signal is typically suppressed for BaryCenter definition, as
modes,weexpectareducednoiseandnosignificantbiasin expected, but for the top ∼ 20% the signal is slightly in-
themeasuredprofilesattheexpenseofremovingsomeofthe creased.Sincethesevoidcenterdefinitionsarenotexpected
ISW signal. Relevantly, the use of these large-scale fluctua- to differ significantly, the importance and origin of this fea-
tionsisyetanotherdifferencebetweenthetworecentBOSS tureisunclearatthemoment,butapossiblecauseissimply
DR12 analyses; Cai et al. (2016) removed the 2 (cid:54) (cid:96) (cid:54) 10 cosmic variance.
modes while Nadathur & Crittenden (2016) used all avail-
ablemodes.Withoursimulationtests,wecanvalidateboth
choices to some extent. 4.4 ISW template for supervoids
Firstly, the cumulative stacking of isolated voids with
all (cid:96)(cid:62)2 modes included shows a factor of ∼2 stronger im- Thehotringfeaturearoundthecentersofthelargest∼20%
printsinthecentralregioncomparedtothe2(cid:54)(cid:96)(cid:54)10case of minimal voids suggests that these objects are good can-
(leftmostpanelsinFigure4).Inbothcases,theimprintsare didatestobecalledsupervoidsbecausethisadditionalISW
significantly more extended than the void radius, reaching feature is expected to be caused by the neighboring super-
R/Rv ∼> 3. However, the differential binning scheme shows clusters,i.e.neighborsinthesupercluster-supervoidnetwork
largefluctuationsandnocleartrendinthestackedISWpro- in the cosmic web (see e.g. Einasto et al. 1997). Most im-
files.Thesefeaturesareintroducedbythelarge-scalemodes portantly,thispropertymakestheseBOSSsupervoidsmore
intheJubileeISWmap,highlightingtheimportanceofcos- similar to the super-structures seen in SDSS and DES data
micvariance.Seesecondsub-plotsfromtherightinthetop that have shown anomalously high ISW-like signals.
rows of Figure 4. A natural argument against this conclusion is that the
The behavior of the largest ∼ 20% of minimal voids is stackedsignalofisolatedvoidswith(cid:96)(cid:62)2modesishigherin
different, as shown in the rightmost sub-figures in Figure magnitude. The S/N is also expected to be higher because
4. The differential binning technique proves that the shape therearemoreisolatedvoidsforagivenphysicalvolumeand
oftheirimprintprofileinR/Rv unitsismorecompactthan tracer catalogue. However, the R/Rv ∼> 3 extent of the im-
thatoftherestofthesample.With(cid:96)(cid:62)10modes,thisquali- printsofisolatedvoidssuggeststhattheseoftensmallvoids
tativedifferencebecomesclearwithcoldregionsclosetothe are imbedded in more extended background underdensities
re-scaledvoidcentersandhotimprintsinthesurroundings. orsupervoids.TheJubileesimulationshowedthatcoldspots
However, zero crossings are seen at slightly different loca- associatedwithdeepisolatedvoidsareinfactnotuniqueto
tions for BaryCenter and MinDensCenter definitions and them but produced due to the evolution of larger fluctu-
also the shape of the inner profiles seems to be different. ations in the gravitational potential. This might lead to a
With (cid:96)(cid:62)2 modes, however, the ISW imprints significantly significant covariance between imprints of isolated voids; a
fluctuateandshowbiasesevenforthecumulativelystacked feature that has in fact been reported by Nadathur & Crit-
sample but importantly for the differential binning scheme. tenden (2016). Naturally, we also expect a non-negligible
We thus conclude that the removal of the 2 (cid:54) (cid:96) (cid:54) 10 covariance for the supervoid sample due to overlap effects
modes helps to remove potential biases from the measured that we will take into account in the analysis.
profiles,resultinginaconvergencetozerosignalatR/R ∼
v
2 for these largest voids (see the first two rows of Figure
4). The rather special ISW imprint of the largest ∼20% of
5 BOSS ISW ANALYSIS
minimal voids becomes more easily testable.
Wehavecharacterizedtheresultingshapeandamplitudeof
theISWimprintsfordifferentvoiddefinitionsintheJubilee
4.3 The role of void ordering
simulation.WenowperformmeasurementswithBOSSmin-
As a final part in the Jubilee stacking analysis, we aim to imalvoidsusingthea prioriselectedmeasurementparame-
test the importance of the ordering scheme applied to the ters.NotethatwehaveadvancedtheCTHmethodologyby
data.Weconsideredthe(cid:96)(cid:62)10ISWmapforthesetests.In producingtemplateprofilesbasedontheJubileestackingof
Figure 5, we demonstrate, for both CTH-filtered and non- differentvoidtypes.However,wealsoshowresultsusingthe
filteredprofiles,thatthespecialnatureofthelargest∼20% traditional CTH filters for completeness.
of minimal voids is observable not just when the fiducial We define our data set as follows. In our Jubilee mock
R based ordering is applied, but also for λ, N , and minimalvoidcatalogue,thelargest∼20%withthefiducial
v merged
pvoid orderings. This is not surprising because these void Rv ordering defines a set of voids with Rv ∼> 110 Mpc/h.
parametersareexpectedtocorrelate,asseeninFigure2for Therefore, we are led to select the same minimal voids in
theBOSSDR12dataset.Asaconsequence,thetop∼20% our BOSS analysis with Rv ∼> 110 Mpc/h. We note that
cut applying ordering based on the number of merged sub- these voids might be imbedded in even slightly larger but
voids corresponds to Nmerged ∼> 5. shallower dark matter underdensities, considering the dis-
Wealsonotethattheλrelationhasnotbeencalibrated cussion in Section 3.3, because the galaxy sampling rates
forminimalvoidsbuttheλorderingappearstoperformwell; are different in Jubilee and BOSS.
MNRAS000,1–??(2017)
Cold imprint of voids and supervoids 9
R ordering λ ordering N ordering p ordering
v merged void
1
‘>10 ‘>10 ‘>10 ‘>10
Cai et al. Cai et al. Cai et al. Cai et al.
0
K]
µ 1
T[
∆
10% 60%
2 20% 70%
30% 80%
40% 90%
50% 100% BaryCenter definition BaryCenter definition BaryCenter definition
3
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
R ordering λ ordering N ordering p ordering
v merged void
0.2 ‘>10 ‘>10 ‘>10 ‘>10
d) 0.0
e
er
H-filt 0.2
CT 0.4
(K]
µ 0.6
T[f
∆
0.8
BaryCenter definition BaryCenter definition BaryCenter definition BaryCenter definition
1.0
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
R ordering λ ordering N ordering p ordering
v merged void
1
‘>10 ‘>10 ‘>10 ‘>10
Cai et al. Cai et al. Cai et al. Cai et al.
0
K]
µ 1
T[
∆
10% 60%
2 20% 70%
30% 80%
40% 90%
3 50% 100% MinDensCenter definition MinDensCenter definition MinDensCenter definition
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
R ordering λ ordering N ordering p ordering
v merged void
0.2 ‘>10 ‘>10 ‘>10 ‘>10
d) 0.0
e
H-filter 0.2
CT 0.4
(K]
µ 0.6
T[f
∆
0.8
MinDensCenter definition MinDensCenter definition MinDensCenter definition MinDensCenter definition
1.0
0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.5 2.0 2.5
R/R R/R R/R R/R
v v v v
Figure 5. Ordering strategies are compared for BaryCenter (top two rows) and MinDensCenter definitions (lower two rows). Beyond
thefiducialRv ordering,weconsideredotherschemesbasedonparametersλ,Nmerged,andpvoid.Color-codedcurvesshowdifferentially
stackedresultsintheusual10%bins.FirstandthirdrowsshowtheresultswithoutfilteringasafunctionofR/Rv,whilesub-figuresin
thesecondandfourthrowscorrespondtoCTH-filteredprofiles.Thetop∼20%ofthedataisqualitativelydifferentineachcaseanda
goodoverallconsistencyisseeninthistest.
MNRAS000,1–??(2017)
10 Andr´as Kov´acs
This final data set contains 96 supervoids that are ex-
pectedtorepresentthelargesthalfofthep >3σ subset
void
BOSS supervoids - MinDensCenter
shown in Figure 2. In total, these supervoids contain 1392 1.5
isolated sub-voids with 5(cid:54)N (cid:54)47.
merged
1.0 10
8
5.1 CMB temperature data 6
0.5
4
For our cross-correlations, we use the Planck Spectral
MatchingIndependentComponentAnalysis(SMICA)CMB Rv 0 02 µK]
temperature map (Planck 2015 results. XI. 2016) down- R/ 2 ∆T[
graded to Nside =512 resolution with HEALPix pixelization 0.5 4
(Gorskietal.2005).Wemaskcontaminatedpixelswiththe 6
Nside = 512 WMAP 9-year extended temperature analysis 8
mask(Hinshawetal.2013)toavoidre-pixelizationeffectsof 1.0 10
the N = 2048 CMB masks provided by Planck. Several
side
studies confirmed (see e.g. Planck 2013 results. XIX. 2014) 1.5
1.5 1.0 0.5 0 0.5 1.0 1.5
thatthecross-correlationsignaldetectedatvoidlocationsis
R/R
independent of the CMB data set when looking at WMAP v
Q, V, W, or Planck temperature maps. We thus limit our
Jubilee supervoids
analysis to the Planck SMICA temperature map. 1.5
1.0 2.0
5.2 Stacked images of BOSS supervoids 1.6
1.2
We then create a stacked image of the 96 BOSS supervoids 0.5 0.8
usisminuglatthioenPalannaclyksSesM,IwCeAreC-sMcaBleteeamchpeimraatugereamroaupn.dAtsheinvtohide Rv 0 00..04 µK]
center. The stacked signal in R/Rv units is shown in Fig- R/ 0.4∆T[
ure 6. We perform the stacking using both BaryCenter and 0.8
0.5
MinDensCenter definitions and compare the results to the 1.2
corresponding Jubilee image. 1.6
For the MinDensCenter case, the BOSS data shows a 1.0 2.0
visually compelling ∆T ≈−10 µK cold imprint in the cen-
tral region of the image at R/Rv ∼< 0.7 and a ∆T >0 area 1.51.5 1.0 0.5 0 0.5 1.0 1.5
in the surroundings. In its nature, this imprint appears to
R/R
beverysimilartotheJubileeresult,withtheBOSSimprint v
being more compact and having higher amplitude.
BOSS supervoids - BaryCenter
Theamplitudeoftheimprintappearstobemoremod- 1.5
estfortheBaryCenterdefinitionbuttheshapeisagainsim-
ilar.Thisreducedimprintisnotunexpectedsincethedeep- 1.0 10
estregionsofvoidsareexpectedtocorrespondtothecoldest 8
ISWimprints,evenifinoursimulationwefoundadifferent 6
0.5
trend for some voids, possibly due to cosmic variance. 4
Rv 0 02 µK]
R/ 2 ∆T[
5.3 CTH filter analysis
4
0.5
WethenmeasurethetraditionalCTH-filteredCMBtemper- 6
aturesasafunctionofR/R filterre-scalingtoquantifythe 8
results. We estimated statisvtical errors by performing 1000 1.0 10
random stacking measurements using Gaussian CMB simu-
lations.TherandomshavebeengeneratedwiththeHEALPix 1.5
1.5 1.0 0.5 0 0.5 1.0 1.5
(Gorski et al. 2005) synfast routine using the Planck 2015
R/R
v
datareleasebestfitCMBpowerspectrum(Planck2015re-
sults.XI.2016).GaussianCMBsimulationswithoutinstru- Figure6.ImprintofsupervoidsinBOSSdataandintheJubilee
mental noise suffice because the CMB error is dominated simulation.ForBOSSdata,weappliedasmoothingtotheindi-
by cosmic variance on the scales we consider (see Hotchkiss vidual raw CMB images only for this illustration using σ = 3◦
et al. 2015). We decided to keep the void positions fixed symmetricalGaussianbeaminHEALPix.Thedatashowshigher-
andvarytheCMBrealization,becauseinthiscaseoverlap- than-expectedimprintsforMinDensCenterdefinitionbutappears
effects for voids are accounted for more efficiently. to be rather normal for BaryCenter defined voids. Mind the 5×
smallertemperatureforthesimulatedimprint.Thedashedcircle
The results, shown in Figure 7, reflect the visual im-
pression.Whilethesignalismostlyconsistentwithzerofor marksthevoidradiusatR/Rv =1.
MNRAS000,1–??(2017)