MILCANN : A neural network assessed tSZ map for galaxy cluster detection

2.9 MB·

by  G. Hurier

Astronomy&Astrophysicsmanuscriptno.milcann (cid:13)c ESO2017
February2,2017
MILCANN :
A neural network assessed tSZ map for galaxy cluster detection
G.Hurier1,N.Aghanim2 &M.Douspis2
1 CentrodeEstudiosdeFísicadelCosmosdeAragón(CEFCA),PlazadeSanJuan,1,planta2,E-44001,Teruel,Spain
2 Institutd’AstrophysiqueSpatiale,CNRS(UMR8617)UniversitéParis-Sud11,Bâtiment121,Orsay,France
e-mail:[email protected]
Received/Accepted
7
1 Abstract
0
2 WepresentthefirstcombinationofthermalSunyaev-Zel’dovich(tSZ)mapwithamulti-frequencyqualityassessmentoftheskypixels
basedonArtificialNeuralNetworks(ANN)aimingatdetectingtSZsourcesfromsub-millimeterobservationsoftheskybyPlanck.
n Weconstructanadaptedfull-skyANNassessmentonthefullskyandwepresenttheconstructionoftheresultingfilteredandcleaned
a tSZmap,MILCANN.Weshowthatthiscombinationallowstosignificantlyreducethenoisefluctuationsandforegroundresiduals
J
comparedtostandardtSZmaps.FromtheMILCANNmap,weconstructedtheHADtSZsourcecatalogthatconsistsof3969sources

1 withapurityof90%.Finally,Wecomparethiscatalogwithancillarycatalogsandshowthatthegalaxy-clustercandidatesintheHAD
3 catalogareessentiallylow-mass(downtoM =1014M )high-redshift(uptoz≤1)galaxyclustercandidates.
500 (cid:12)

Keywords.Cosmology:Observations–Cosmicbackgroundradiation–Sunyaev-Zel’dovicheffect
]
O
C
. 1. Introduction Neglectingrelativisticcorrectionswehave
h
p Galaxy clusters are the largest virialized structures in the (cid:20) (cid:18)x(cid:19) (cid:21)
g(ν)= xcoth −4 , (3)
o- Universe. They are excellent tracers of the matter distribution, 2
and their abundance can be used to constrain the cosmological
tr modelinanindependentway.Galaxyclustersareobjectscom- with x = hν/(kBTCMB). At z = 0, where TCMB(z =
as posed of dark matter, stars, cold gas and dust in galaxies, and 0) = 2.726±0.001 K, the tSZeffect is negative below 217GHz
[ a hot ionized intra-cluster medium (ICM). Consequently, they andpositiveforhigherfrequencies.

can be identified in optical bands as concentrations of galax-
1 ies (see e.g. Abell et al. 1989; Gladders & Yee 2005; Koester tSZsurveysprovidesadifferentwindowontheclusterpop-
v
etal.2007;Rykoffetal.2013),theycanbeobservedinX-rays ulation compared to other large scale structure tracers, allow-
5
by the bremsstrahlung emission produced by the ionized intra- ingtodetecthigherredshiftobjects.Theyalsoprovideanearly
7
0 cluster medium (ICM) (see e.g. Bohringer et al. 2000; Ebeling mass-limited census of the cluster population at high redshift,
0 etal.2000,2001;Böhringeretal.2001).ThesamehotICMalso where abundance is strongly sensitive to cosmological param-
0 creates a distortion in the black-body spectrum of the cosmic eters (Carlstrom et al. 2002; Planck Collaboration results. XX
2. microwave background (CMB) through the thermal Sunyaev- 2014).ThetSZintegratedComptonisationparameter,Ysz,isre-
Zel’dovich (tSZ) effect (Sunyaev & Zeldovich 1969, 1972), an latedtotheintegratedelectronpressureandhencethetotalther-
0
7 inverse-Compton scattering between the CMB photons and the malenergyoftheclustergas.Itcorrelateswithmasswithalow
1 ionizedelectronsintheICM. intrinsic scatter and small dependence on the dynamical prop-
: ThroughthetSZeffect,CMBphotonsreceiveanaverageen- erties of the cluster (eg: da Silva et al. 2004; Kay et al. 2012;
v ergyboostbycollisionwithhot(afewkeV)ionizedelectronsof Hoekstra et al. 2012; Planck Collaboration et al. 2013; Sifón
i
X the intra-cluster medium (see e.g. Birkinshaw 1999; Carlstrom etal.2013).
r etal.2002,forreviews).ThethermalSZComptonparameterin Recent large catalogues based on measurements of the tSZ
a agivendirection,n,ontheskyisgivenby effect have been produced from Planck (Planck Collaboration
early results. VIII 2011; Planck Collaboration results XXXII
(cid:90)
k T 2015),ACT(Marriageetal.2011),andSPT(Bleemetal.2014)
y(n)= n B eσ ds (1)
em c2 T data.
e
Several tSZ sources detection algorithm (see e.g., Melin et al.
wheredsisthedistancealongtheline-of-sight,n,andn andT 2006; Carvalho et al. 2009) have been proposed and compared
e e
aretheelectronnumberdensityandtemperature,respectively.In (Melin et al. 2012), demonstrating that a multi-frequency
unitsofCMBtemperaturethecontributionofthetSZeffectfor approach for the tSZ detection is more robust than a tSZ
agivenobservationfrequencyνis map-based approach. Especially, tSZ map-based detection
methods present a significantly lower level of purity then
∆T multi-frequency-basedapproaches.
CMB =g(ν)y. (2)
T
CMB
1
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
The expected number of galaxy clusters is extremely • Ancillarydatausedtocharacterizegalaxyclustercandidates:
sensitivetocosmologicalparameters(TheDarkEnergySurvey – the reprocessed IRAS maps, IRIS (Improved
Collaboration2005;Vanderlindeetal.2010;Sehgaletal.2011; ReprocessingoftheIRASSurvey,Miville-Deschênes&
Böhringer et al. 2014; Planck Collaboration results. XX 2014). Lagache2005),
Animportantfactorthatlimitstheaccuracyinthedetermination – TheAllWISESourceCatalog1
of cosmological parameters is the contamination of the tSZ
signalbyotherastrophysicalemissions,mainlyradio,infra-red
3. Artificialneuralnetworkfiltering
pointsources,andcosmicinfra-redbackground(Dunkleyetal.
2011;Shirokoffetal.2011;Reichardtetal.2012;Sieversetal. In this section, we describe how we build an artificial neural
2013;PlanckCollaborationresults.XXI2014)thatcanproduce network (ANN) filtered tSZ map. ANN-based quality assess-
spurious galaxy cluster detections and/or a significant bias the ment enables to directly learn from the data the characteristic
measured tSZ fluxes. A tailored quality assessment of the tSZ signature of real tSZ sources and spurious signal using a
signal from galaxy clusters is thus required to produced high- reference sample of astrophysical sources. This approach has
purityrobustgalaxyclustersamplesdetectedwiththetSZeffect. been shown as an efficient method to identify spurious tSZ
detections(Aghanimetal.2015;vanderBurgetal.2016)from
An artificial neural network (ANN) based quality assess- Planck tSZ candidate catalogs (Planck Collaboration results
ment method has been proposed (Aghanim et al. 2015) and XXXII 2015; Planck Collaboration 2015 results XXVII 2016).
appliedtoPlanckgalaxyclustercatalogs(PlanckCollaboration In the following, we extend this approach to each pixel of the
2015 results XXVII 2016). This method uses the Planck sky-mapsratherthantoapre-selectedsampleoftSZcandidates.
multi-frequency data to assess the quality of the tSZ signal by
decomposing the measured signal into the different astrophysi-
calcomponentsinterveningatthePlanckfrequencies.Itshowed
that the first Planck tSZ-source catalog (Planck Collaboration 3.1. NeuralNetworkTraining
resultsXXXII2015)suffersfromcontaminationbygalacticCO
WesummarizeherethekeyelementsoftheANNtrainingpro-
sources and infra-red emission (Aghanim et al. 2015). Recent
cessandrefertoAghanimetal.(2015)foramoredetailedde-
follow-up (van der Burg et al. 2016) of Planck tSZ sources in
scription.
theopticalhaveshowntheefficiencyofthisANN-basedquality
assessment by confirming the spurious nature of tSZ sources
withbadqualitycriteria. 3.1.1. SEDfitting
In this work, we propose a new approach for galaxy clus-
ter detection, that uses aN ANN-based filtering of tSZ full-sky
maps.First,insection2,wepresentthedifferentdatasetusedin
this work. In section 3 we detail the construction of the ANN-
basedfilterthatenablestoperformtSZsourcesdetectioninthe
tSZ-map space competitively with multi-frequency approches.
Then,insection4,weconstructasampleagalaxyclustercan-
didates and we present a detailed characterization of this new
galaxyclusterdetectionmethod.Finally,insect.5weperforma
multi-wavelengthassessmentofthedetectedgalaxyclustercan-
didates.
2. Data
Figure1.Matchedfilterin(cid:96)spaceusedfortheANN-basedqual-
Forthepresentanalysisweusedseveraldataset:
ityassessment.
• Planck intensity maps from 70 to 857 GHz (Planck
Collaboration 2015 results I 2016), assuming spectral re-
FollowingAghanimetal.(2015),wefocusontheastrophys-
sponse from Planck Collaboration results IX (2014) and icalemissionsthataffectthemostthetSZdetectioninmultifre-
gaussianbeams(PlanckCollaborationresults.VII2014).
quency experiments. This issue was addressed in both Planck
• Planck full-sky lensing map (Planck Collaboration et al.
Collaboration et al. (2011) and Planck Collaboration results
2015),
XXXII(2015).Wemodelthespectralenergydistribution(SED)
• Catalogsusedtodescribeastrophysicalsourcesproperties: takingintoaccountfivecomponents:thethermalSZ(tSZ)effect
– ametacatalogofX-raydetectedgalaxycluster(MCXC,
neglectingrelativisticcorrections;theCMBsignal;andtheCO
Piffarettietal.2011,andreferencetherein), emission. We also add an effective IR component representing
– theWHL12catalogue(132,684objects,Wenetal.2012)
the contaminationby dustemission, coldGalactic sources, and
ofgalaxyclustersdetectedintheSDSSdataYorketal. CIB fluctuations; and an effective radio component accounting
2000, for diffuse radio and synchrotron emission and radio sources.
– a catalog of tSZ sources detected in Planck data (PSZ1
Thefluxineachchannel,i.e.frequency,isthenwrittenas
hereafter, see Planck Collaboration results XXXII
2015). F =A F (ν)+A F (ν)+A F (ν)
ν SZ SZ CMB CMB IR IR
– catalogues of sources detected at 30 GHz and 353 GHz +A F (ν)+A F (ν)+N(ν), (4)
RAD RAD CO CO
fromthePlanckCatalogueofCompactSources(PCCS)
(PlanckCollaborationresultsXXVIII2014) 1 http://wise2.ipac.caltech.edu/docs/release/allwise/expsup/
2
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
where F (ν), F (ν), F (ν), F (ν), and F (ν) are the ThuswederiveanSED, F ,foreachpixels.whichisfitted
SZ CMB IR RAD CO ν
spectraoftSZ,CMB,IR,radio,andCOemissions; A , A , assuming the model in Eq. 4, where we fit for A , A , A ,
SZ CMB SZ CMB IR
A ,A ,andA arethecorrespondingamplitudes;andN(ν) A ,andA throughalinearfitoftheform
IR RAD CO RAD CO
istheinstrumentalnoise.
A=(FTC−1F)−1FTC−1F , (6)
N N ν
For F (ν), we consider a modified black-body spectrum
withtempIeRratureT = 17Kandindexβ = 1.6.Thisassump- with the mixing matrix FT, the instrumental noise covariance
d d
tion is representative of the dust properties at high galactic lat- matrix CN, and A a vector containing the fitted parameters. In
itudes. The contribution from CIB fluctuations affects the flux thisapproach,CN onlyaccountsfortheinstrumentalnoise,and
measurement, but is not a major contamination from the point weimplicitlyassumethatthefivecomponentsconsideredinthe
ofviewofthedetection,i.e.spurioussources.For F (ν),we modelreproducetheastrophysicalsignalinthedata.
considerapowerlawemission,ναr,withindexαr =R−A0D.7inin- Theefficiencyofthedimensionalityreduction2 isillustrated
tensity units representative of the average property of the radio inFig.2(rightpanel),whereweshowthecorrelationmatrixof
emission.InordertocomputetheSEDoftheconsideredpixels, the fitted SED parameters, compared to the correlation matrix
we use the Planck frequency maps from 70 to 857 GHz. First, ofmeasuredfluxesfrom70to857GHz(leftpanel).Weobserve
eachmapissettoaresolutionof13arcmin,i.e.thelowestreso- that we have a high degree of correlation between frequencies,
lution(70GHzmap). especially at low frequency due to the CMB component (<
217 GHz), and at higher frequency (> 217 GHz) due to the
thermalcomponent.Incontrast,intheSEDparameterspace,we
observe that the correlation matrix is almost diagonal, except
foraspatialcorrelationbetweenthermaldustandCOemission.
Thiscorrelationistheconsequenceofthethermaldustemission
from molecular clouds, and is thus physically motivated. We
alsonoteasignificantcorrelationbetweenthetSZeffectandthe
radio emission. This correlation is produced by the similarities
of tSZ and radio SEDs in Planck low-frequency channels that
dominates the tSZ flux estimation. Indeed, the tSZ effect is
negativeatlow-frequencyandconsequentlyintermsofbest-fit
ahightSZfluxcanbecompensatedbyastrongradioemission,
Figure2. Left panel: correlation matrix of the measured fluxes which induces a high degree of correlation between tSZ and
from 30 to 857 GHz estimated on 2000 random positions over radioemissionfluxes.
thesky.Rightpanel:correlationmatrixoffittedSEDparameters We also observe that the match-filtering approach for the SED
fromthesamepositions. estimation enables to obtain a correlation matrix for SED
parameters which is more diagonal, especially for the tSZ
amplitude A , than an aperture photometry SED estimate (see
SZ
By contrast to Aghanim et al. (2015), we compute the flux Fig.2inAghanimetal.2015,forcomparison).
foreachpixelandeachfrequencyusingamatch-filterin(cid:96)space
presented in Fig. 1. We choose this approach, rather than the
aperturephotometrytoimprovethephotometryoftSZsources.
To build this filter, we assume the power spectrum, y , of a 3.1.2. Full-skyANN-basedqualityassessment
(cid:96)
tSZ signal from a cluster with R = 5(cid:48) (point-like with re-
500 We consider a standard three-layer back-propagation ANN to
spect to the Planck experiment), and a universal pressure pro-
separate pixels of the sky maps into three populations of reli-
file (Arnaud et al. 2010). We also consider the power spectrum able quality (the Good), unreliable quality/false (the Bad), and
of the CMB,CCMB, computed using Planck best-fit cosmology
(cid:96) noisysources(theUgly).Theinputsoftheneuralnetworkcon-
(Planck Collaboration 2015 results XIII 2015), and the power
sist of the five SED parameters and the outputs represent the
spectrumofthenoise,CNN,inthe100GHzchannel(estimated
(cid:96) threeclassesusedtoclassifyeachskypixel.
using half-ring map difference) which is the frequency channel
Webrieflypresentherethebasicsoftheartificialneuralnetwork
with the highest noise level. We note that to obtain model in-
method.Wedefine
dependent flux estimations, the match-filter has to be the same
at all frequency. Considering that for relevant frequency chan- Q=g(W g(W (W F +b)+b )+b ), (7)
o h r ν r h o
nelsforthetSZfluxestimation(100to217GHz),angularscales
((cid:96)∈[1000,2000]),andgalacticlatitudesthethermaldustampli- whereg(x) = 1/(1+exp(−x))istheactivationfunction,W =
r
tudefromtheMilkyWayissmallcomparedtotheCMBcontri- (FTC−1F)−1FTC−1 corresponds to a physically-based dimen-
N N
bution,wedonotincludeagalacticthermaldustcontributionin sionalreduction,W aretheweightsbetweeninputandhidden
h
thecomputationofthematchfilter.Thenthefilteriscomputed layers, W are the weights between hidden and output layers,
o
as b arethebiasesbetweeninputandhiddenlayers,andb arethe
h o
biasesbetweenhiddenandoutputlayers.
(cid:115)
F = y(cid:96) , (5) To train the neural network, we use the same sample for
(cid:96) CCMB+CNN Good, Bad, and Ugly classes as in Aghanim et al. (2015). We
(cid:96) (cid:96)
2 TheprojectionofthemeasuredSEDonabasisofphysicallymo-
andappliedontheharmonicspacecoefficients,a∗ = F a ,
(cid:96),m (cid:96) (cid:96),m tivatedSEDsallowstoreducethenumberofparametersthatdescribe
ofPlanckintensitymapsfrom70to857GHz.Weverifiedthat themeasuredSED.Thismethodcanbecomparedtoprincipalcompo-
ourresultsdonotsignificantlydependsonthechosenamplitude nentanalysis,usingamodel-basedbasisinsteadofeigenvectorofthe
ofCNNforthematch-filtercomputation. observations.
(cid:96)
3
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
Figure3. From top to bottom: Planck tSZ MILCA map, neural network filter, MILCANN map, for the full-sky in mollweide
projection.Greyregionsaremaskedduetogalacticforegroundsorpointsourcescontamination.
4
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
Figure4. From left to right: Planck tSZ MILCA map, neural network filter, MILCANN map, for a patch of 8.5 × 8.5 degrees in
gnomonicprojectioncenteredongalacticcoordinates(l,b)=(263o,-24o).Greyregionsaremaskedduetopointsourcescontamina-
tion.
adaptthetheANNtothematch-filterSEDestimation.Thus,we emission.Radiopointsourcesproduceanegativesignalinterms
usethevalueinthecentralpixeltowardeachsourceasaproxy of Compton parameter, thus they can be easily separated from
ofthefluxoftheconsideredsource.Wesplitthetrainingsample a real tSZ-structure (Hurier et al. 2013). Significant CO emis-
into two sub-samples, the first one used to train the ANN, and sion is essentially located at low galactic latitudes, and can be
thesecondoneusedtopreventover-trainingoftheANN. maskedforgalaxyclustersdetectionpurposes.CIBemissionis
Wedefinedtheerrorontheclassificationas more complex to deal with, as it is homogeneously distributed
overthesky.InSect.3.2.3,wewillpropagateCIB-inducedun-
1 (cid:88)
E = (Q(true)−Q )2, (8) certainties.
2 class class
class
3.2.2. MILCANNmap
where class stands for Good, Bad, or Ugly and Q(true) = 1 or
class
0 depending on whether the source belongs to the considered On Fig. 3, we observed that the tSZ map reconstructed from
class. Planckdatasuffersfrombiasduetoresidulasfromotherastro-
physical emission. Using the neural-network based quality as-
sessment presented in sect. 3.1.2, we can obtain an estimation
3.2. tSZqualityassessedmap
of the quality of the tSZ signal in each line-of-sight of the sky.
3.2.1. MILCAPlancktSZmap First,wedefineanANN-basedfilter,QN,as
We perform the construction of a tSZ map with the MILCA Q = Q (1−Q ), (9)
N GOOD BAD
method (Hurier et al. 2013), using Planck HFI from at 100 to
857 GHz. We verified that including frequencies from 30 to WhereQGOOD andQBAD aretheANNclassificationoutputval-
70 GHz does not change significantly the reconstructed map, ues for the Good and Bad classes. By construction this ANN-
especiallyatgalaxyclusterscales. filter ranges from 0 to 1, with values close to 1 for pixels that
WeperformedtheconstructionofthetSZmapusing8filtersin presentahigh-qualitytSZsignal.Wedidnotapplyanyweight-
spherical harmonic space. For the first three filters we used 2 ingovertheUglyANNoutputtoavoidacatastrophicreduction
constraints(tSZandCMB), andforthelastfivefilterswe only oflowsignaltonoiseratiogalaxyclusters.Thenoiseamplitude
used a constraint on the tSZ SED. The map reconstruction is reductionisalreadyperformedbytheweightingoverQGOOD.
performedwithaneffectiveFWHMof7arcmin.Forallfilters, In Fig. 3 and 4, we show the full-sky ANN filter described in
2 degrees of freedom have been used to minimize the variance Sect. 3.1.2 and the MILCANN map. We observe a clear spa-
ofthenoise(seeHurieretal.2013,foradetaileddescriptionof tial correlation between the ANN filter and the tSZ MILCA
theMILCAmethod). map. However, we observe that the ANN filter presents values
close to 1 even for some pixels where no clear tSZ excess can
In Fig. 3, we show the MILCA full-sky map at 7 arcmin beobserved.Thesemisclassifiedpixelsareproducedbychance
FWHM. Figure 4 shows a zoom on a small region of 8.5×8.5 alignement between noise structure and tSZ spectral signature.
degrees where bright galaxy clusterS can be observed. In the Asaconsequence,atSZsourcesdetectionperformeddirectlyon
full-sky map, we observe a significant amount of foreground theANNfiltermapwouldleadstolow-puritysamples.
residuals near the galactic plane, where synchrotron and free- Then,weconvolvetheMILCAtSZmap,noted(cid:98)y,bythematched
free residuals appear as negative biases in the tSZ y-map sig- filterusedfortheSEDfittinginsection3.1.1.Thus,thefiltered
nal. We also observe contamination by bright galactic cirrus MILCAmap,(cid:98)yf,hasatransfertfunctionconsistentwiththemap
correlated with the zodiacal light. As demonstrated in previous usedtoperformtheANNclassification.
works (Hurier et al. 2013; Planck Collaboration 2015 results Finally,wederivedtheMILCANNmapas
XXII2015),themainsourcesofcontaminationintSZmapsbuilt
fromPlanckintensitymapsareradiopointsources,CO,andCIB MMILCANN =(cid:98)yfQN. (10)
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G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
Figure5. From top to bottom: Planck tSZ MILCA noise map MILCANN noise map for the full-sky in orthographic projection.
Greyregionsaremaskedduetopoint-sourcecontamination.
On Fig. 3, the MILCANN map shows that the ANN-filter has galaxyclusterdetection.However,itcannotbeusedtoproduced
significantly removed the foreground contamination, especially accurateestimationofthefluxortheshapeoftSZsources.
near the galactic plane, where synchrotron and free-free con-
taminationhavebeencompletelysuppressed.Similarly,thecon-
tamination produced by high latitude galactic cirrus has been
filtered out by the ANN. On Fig. 4, we also observe that the 3.2.3. NoiseandCIB-residualssimulations
MILCANN map presents a significantly reduced background,
butalmostconservestheintensityofbrighttSZpixels.However,
WehaveshownqualitativelythatMILCANNtSZmappresents
westressthattheANNfilteringdoesnotconservetheshapeof
a significantly reduced background compared to MILCA tSZ
thetSZsources,asitwillmodifytheintensityoffainttSZpixels
map. In this section, we describe our modeling of the noise
intheoutskirtsofgalaxyclusters.
and CIB-residuals in the MILCA and MILCANN tSZ maps
to quantify the improvement obtained by applying an ANN
AsshownbyMelinetal.(2012),tSZ-mapbasedgalaxyclus- filtering.
terdetectionmethodssufferfromahighlevelofcontamination
byspuriousdetectionsinceitisapriorinotpossibletodisentan-
gle real tSZ emission from biases induced by other astrophysi- ThetSZmapsarederivedfromcomponentseparationmeth-
calemissionresiduals.Bycontrastandduetoitssignificantre- ods. They are constructed through the linear combination of
ducedresidualsignals,theMILCANNmapseenswellsuitedfor Planck frequency maps that depends on the angular scale and
6
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
thepixel, p,as
(cid:88)
(cid:98)y= wi,p,νTi,p(ν), (11)
i,j,ν
T (ν) is the Planck map at frequency ν for the angular filter i,
i,p
and w are the weights of the linear combination. Then, the
i,p,ν
CIBcontaminationinthey-mapreads,
(cid:88)
y = w (ν)TCIB(ν), (12)
CIB i,p i,p
i,j,ν
where TCIB(ν) is the CIB emission at frequency ν. Using the
weights w , and considering the CIB luminosity function, it
i,p,ν Figure6.IntensitydistributionofpixelsinthetSZmapsfor:the
ispossibletopredicttheexpectedCIBleakageasafunctionof
MILCAmap(lightblue),theMILCANNmap(darkblue),sim-
the redshift of the source by propagating the SED through the ulationofnoise+CIBintheMILCAmap(orange),simulation
weightsthatareusedtobuildthetSZmap.AshownbyPlanck ofnoise+CIBintheMILCANNmap(red).
Collaboration2015resultsXXIII(2015),theCIBatlow-zleaks
with a small amplitude in the tSZ map, whereas high-z CIB
producesahigher,dominant,levelofleakage.Indeed,internal-
not present symmetric distribution. So, we are dealing with a
linear-combination-based component separation methods focus
non-Gaussian, inhomogeneous, correlated noise with an asym-
on Galactic thermal dust removal, and thus are less efficient to
metric distribution. As observed on Fig.6, the noise is more
subtracthigh-zCIBsourcesthatpresentadifferentSED.
likely to produce positive value in MILCANN map than nega-
The CIB power spectra have been constrained by previous
tive value. It implies that the noise has a non-zero expectation
Planck analyses (see e.g., Planck Collaboration results XXX
value. Consequently, in the following we used and propagated
2014). They can be used to predict the expected CIB leakage,
thecompletenoisedistribution.
y ,inthetSZmap,y.
CIB
Weperformed200Monte-CarlosimulationsofCIBthatfollow
CIBpowerspectra.Then,weaddinstrumentalnoisetothesim- 3.2.4. Noiseinhomogeneities
ulatedCIBmaps.Finally,weapplytheweightsusedtobuildthe
tSZ map to these simulations. We obtained 200 realizations of
instrumentalnoiseandCIBatthePlanckfrequencymapslevel,
consistent with noise and CIB realizations at the MILCA tSZ
maplevel.
ItisimportanttostressthatthenoiseinMILCAtSZmapis
byconstructioncorrelatedtothenoiseinfrequencymaps.Thus,
the noise on the ANN classes is also correlated with the noise
inMILCAtSZmap.Consequently,ifwewanttoproduceafair
descriptionofthenoise,wehavetotrainanotherneuralnetwork
on the simulated maps to reproduce the correlation feature be-
tweenthenoiseinMILCAmapandthenoiseonANNclassifi-
cation.ConsideringthatthetrainingofanANNisanon-linear
process,wealsoaddedCMB,pointsources,andthermaldustto
thenoise+CIBsimulationsduringthetrainingprocess.
Finally, we build and applied the noise-based ANN to the
MILCAnoise+CIB-residualssimulation.OnFig.5,wepresent
anoise+CIB-residualssimulationbeforeandafterapplyingthe
noise-based ANN-filter, we observe that the ANN filtering al-
Figure7.Distributionofthenoisestandarddeviation,σ across
lows to significantly reduce the noise level in the MILCA sim- y
theMILCANNfull-skymap.
ulatedmap.FromtheMILCANNsimulatedmap,wederivethe
standarddeviationofthenoiseinMILCANNmapbycomputing
thelocalstandarddeviationofMILCANNsimulatednoisemap
insideatwo-degreegaussianbeam. Due to Planck scanning strategy, the noise level on the sky
InFig.6,wecomparetheintensitydistributionsinMILCA isinhomogeneous.Eclipticpolespresentabetterredundancyof
andMILCANNmap.FortheMILCAmap,weobserveasignif- observationsandthusasignificantlylowerlevelofnoise(Planck
icanttailofnegativeintensity(mainlyproducebyradio-sources Collaboration2015resultsI2016).
contamination). We do not observe this contamination in the By construction, the noise of the ANN-filter is related to the
MILCANN map, as the ANN filter significantly reduces radio noise in MILCA map. The MILCANN map is obtained by the
sources contamination. We also observe that the noise in the product of the filtered MILCA map and the ANN filter, thus
MILCANN map is lower than in the MILCA map by a factor thenoiseinhomogeneitiesareamplified.Thedistributionofthe
offive.However,wenotethattheintensityofthebrightestpix- pixel-dependentnoiselevelispresentedonFig.7,thatpresents
elsinthemapisnotaffectedbytheANNfilter. the noise standard deviation, σ , distribution. This quantity is
y
We note that the noise in MILCANN is not Gaussian. estimated locally in a 4 degrees gaussian beam. The low noise
Considering the correlation between the ANN filter and the regionscorrespondtoeclipticpolesandhighnoiseregionscor-
noise in MILCA map, the noise in the MILCANN map does respond to the ecliptic plane. To obtain a map of the signal-to-
7
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
noiseratio,weconstructedthenoisenormalizedquantity,(cid:98)yσ,as 3.2.5. ANNresponse
In this section, we quantify the transfert function of the ANN-
filteringprocedurebetweenthetSZintensityintheMILCAmap
(cid:98)yσ = (cid:98)σyf . (13) andthetSZintensityintheMILCANNmap.
y
Wenotethatusingahomogeneousthresholdon(cid:98)yσisequivalent
tousingapixel-dependentthresholdon(cid:98)yf.
Figure9. ANN-filter average value as a function of the match-
filteredintensity.
By applying the artificial neural network filter, we reduce
the noise level. To a lesser extent, we also reduce the intensity
oftSZeffectfromgalaxyclusters.Indeed,thevalueofQ isnot
N
exactly1forallgalaxyclusters.Additionally,thevalueofQ is
N
sensitivetothefluxofthecluster,ahighfluxgalaxyclusterwill
haveQ (cid:39)1,whereaslowfluxgalaxyclusterswillbeclassified
N
asnoiseandwillhaveQ <<1.
N
Thus,weselect10000randompixelswithinthe84%maskused
for the detection and we added a constant amount of an emis-
sionfollowingatSZSED.Thisapproachallowstoproperlyac-
count for real sky background and noise level. Then, we apply
theANNonthese10000modifiedpixels,andderivedtheaver-
agevalueforQ asafunctionoftheinputedtSZintensity,which
N
givesthetransfertfunctionoftheANNfilteringprocedure.
OnFig.9,weshowtheaveragevalueoftheANN-filterasafunc-
tionofthefilteredtSZsignalintensity,y .WeobservethatANN
f
response present a steep transition, all signal below y = 10−8
f
Figure8. Distribution of the MILCANN map (top panel) and is completely suppressed by the ANN, whereas signal above
MILCANN noise simulation (bottom panel) as function of Q y = 210−7 is almost not affected by the ANN filtering. We
N f
and normalized intensity, y . The colors show the number of stress that these intensities are obtained after filtering and are
σ
pixelsinlogarithmicscale. notconsequentlycomparablewithtotaltSZintensityinMILCA
map. We verified that we derive a consistent transfert function
forQ whencomputedfromnoisesimulationsfromSect.3.2.3.
N
Figure 8 presents the distributions of MILCANN map and 4. tSZcandidatedetection
MILCANN noise simulation respectively as a function of y
σ
and Q .WeobservethattheMILCANNnoisesimulationdoes Inthissection,weusedtheimprovedtSZmapobtainedafterap-
N
notshowhigh-Q andhigh-y pixels.Wealsoobservethatfor plyingtheANN-basedfiltertoperformgalaxyclusterdetection.
N σ
Q (cid:39) 0theMILCANNmappresentsasignificantlylargerdis- Wealsocharacterizethepurityandcompletenessofthederived
N
tribution of y than the noise simulation. This is produced by galaxyclustercandidatesampletoassesstheimprovementcom-
σ
foreground residuals that are present in the MILCA tSZ map. paredtopreviousgalaxyclustercatalogderivedfromthePlanck
Weverifiedthattheseresidualsarestronglycorrelatedwiththe data.
galactic latitude, which ensures that they are related to system-
atic effects. However, we do not observe a similar behavior at
4.1. Methodology
largervaluesofQ .Thisconfirmsthatforegroundresidualsare
N
stronglyreducedusingtheANN-filteringprocedure,asalready To detect sources in MILCANN full-sky map, we applied a
observedonFig.6. maskofthegalacticplaneandpointsourcesdetectedbyPlanck
8
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
keeping84%oftheskydefinedinPlanckCollaborationresults of extended galaxy clusters. However, this is not an important
XXXII (2015). Then, using the noise standard deviation map limitationsinceourmaingoalistodetectcompacttSZsources
computedinsection3.2.3,wehomogenizedtheMILCANNmap associatedwithnewgalaxyclustersthatareeitherlow-massor
noiseleveltoperformthedetectioninsignal-to-noiseunitonthe high-z.ConsideringtheresolutionofPlancktSZmaps(roughly
full-skywithahomogeneousthreshold.Weappliedathreshold, 7 arcmin) such galaxy clusters are point-like. Furthermore for
y >3,totheMILCANNmap,andconsiderasdetectedsources theseclustersorformoreextendedones,wecancomputetheir
σ
allsetSofadjacentpixelsthatareabovethethreshold.Wefinally tSZsignaldireclyfromtheMILCAmaporfromthefrequency
cleanmultipledetectionsofasameobjectbymergingdetected maps.
sourcesinaradiusof10arcmin(consistentwithPlanckangular
resolution)andremoveallsourcesdetectedonlessthan5pixels
4.2.2. Completness
of1.7x1.7arcmin2 (toavoiddetectionsproducedbyanomalous
pixels). We derive a sample 3969 galaxy cluster candidates. In Applying all the steps we detailed in this section, we can write
the following, we refer to this sample of galaxy cluster candi- thecompleteprocessingweapplytotheastrophysicalsignalas
datesastheHADcatalog.
y (T )Q (y )
y =Y f 500 N f +N , (14)
σ 500 σ σ
4.2. CharacterizationoftheMILCANNdetectionmethod y
whereY isthetSZfluxofthegalaxycluster,y isthegalaxy
Inthissectionwecharacterizethedetectionmethod.Wepresent 500 f
clustersmatch-filteredintensitypresentedonFig.10,thedepen-
in detail each step that allow us to compute the selection func-
dancy of Q with y is presented on Fig. 9, the distribution of
tionofthegalaxyclusterdetection.Thus,wepresentadetailed N f
thenoiseacrossthemap,σ ,isshownonFig.7,and N isthe
descriptionofthegalaxyclustersignaltransfertfunctionacross y σ
homogenizednoiseintheMILCANNmap.
ourprocessing.
Consequently,foragiventotalmass,M ,andagivenredshift,
500
4.2.1. Fourrierspacefilteringresponse
Figure11. Completness of the HAD catalog as a function of
M andz.Thecolorscaleislogarithmicandrangesfrom10−2.5
500
(darkblue)to1(red).
Figure10.CentralintensityoftheSZsignalforagalaxycluster
with Y = 1 arcmin2 as a function of galaxy cluster typical
500
radiusT .
500
z, the galaxy cluster signal distribution for y maps is obtained
σ
by the convolution of the M − Y relation scatter (assum-
500 500
ingscalingrelationfromPlanckCollaborationresults.XX2014,
BeforeapplyingtheANN-filtertobuildtheMILCANNmap, and (1-b) = 0.8), the distribution of σ , and the distribution of
y
wehavefilteredtheMILCAmapusingthematchfilterpresented thenoiseN .WeassumedthattherelationM −T doesnot
σ 500 500
onFig.1.Inthissection,wepresenttheestimationofthetrans- presentanyscatter.
fertfunctionofthisfilteringprocess.First,webuildamockmap Thecompleteness,C(y ),isthenobtainedastheratioofthein-
σ
ofaskyprojectedtSZsignalfromagalaxyclusterwithY =1 tegral of y distribution, P(y ), above the detection threshold
500 σ σ
arcmin2assumingaGNFWpressureprofile(Arnaudetal.2010) normalizedbytheintegralofthefulldistribution,
with1000pixelsperR .Then,weconvolvethetSZmockmap
b30y..11.tt1ho.e1Wi0ne0stpareurcrmfmoerinnmt.aFtlhibniseaa5pl0mlr0yo,cawenedduetrxheterfaomcrtavtthcahleutfieSslZtoeirfnRpter5en0s0seirtnaytneagdtintihngeSfcreoecnmt-. C(yσ)= (cid:82)0∞P(1yσ)dyσ (cid:90)t∞P(yσ)dyσ, (15)
terofthegalaxyclusterontheconvolvedmockmap. wheretisthedetectionthresholdappliedonthey map.
σ
OnFig.10,wepresentthetSZintensity,y ,tofluxratioafterap- Figure11showsthecompletenessasafunctionofthemass,
f
plyingthematch-filterforagalaxyclusterwithauniversalpres- M andredshift,z,ofagivencluster.Weobservethatwecan
500
sureprofile.Thematch-filterweuseselectscompactobjectand detect, with a very basic detection methods applied on an opti-
thus presents a response that will significantly reduce the flux mally filtered and cleaned tSZ map, galaxy clusters down to a
9
G.Hurier,N.Aghanim&M.Douspis:MILCANN:AneuralnetworkassessedtSZmapforgalaxyclusterdetection
typicalmassofM =11014 M .Wealsoobservethatforvery
500 (cid:12)
large mass (> 21015 M ) the completeness is slightly smaller
(cid:12)
than 1. This effect is produced by the match-filter that signif-
icantly reduces the tSZ effect produced by extended (massive)
sources.
4.2.3. Purity
Then, we estimate the purity of the catalog by performing
the detection of tSZ sources on the MILCANN map and the
MILCANN noise simulation from Sect. 3.2.3. This estimate
doesnotaccountforallforegroundresidualsintheMILCANN
map.Thusthisestimatemayslightlyover-estimatethepurityof
theHADcatalog.Wefound N(1) detectionsfortheMILCANN
det
mapandN(2)forthesimulatednoisemap.Weperformedthede-
det
tectionforseveraldetectionthresholds.Thepurityisobtainedas
Figure13.NearestneighbordistancedistributionbetweenHAD
P = Nd(1e)t−Nd(2e)t. On Fig. 12 we present the purity as a function of sourcesandPSZ2publiccatalogsources.
N(1)
det
Figure12.PurityoftheHADcatalogasafunctionofthedetec- Figure14.NearestneighbordistancedistributionbetweenHAD
tionthreshold. sourcesandMCXCsources.
the detection threshold. For the threshold used in the construc-
the PSZ2 that have no counterpart in the HAD catalog) among
tion of the HAD catalog we derived an estimated purity above
which997areconfirmedgalaxyclustersandhaveQ >0.63
90%. Neural
in the PSZ2 catalog. We also detect 496 known clusters that
are missing from PSZ2 (considering ACT, SPT, Redmapper,
4.3. Comparisonwithreferencegalaxyclustercatalogs Wen+12,andMCXCcatalogs).Figure13showsclearlythetwo
populations of sources common and not common with PSZ2.
In this section, we present a brief comparison of the HAD Forcommonsourcesweobtainatypicalpositionmismatchbe-
galaxy-cluster candidate catalog and other reference catalogs. low 4 arcmin compared to the position presented in the PSZ2.
Weusedtwoapprochesforthecomparison. Forveryextendedsourcesthepositionmismatchcanreachupto
First we compare the numbers of galaxy cluster candidates 10arcmin.ThispositionmismatchisconsistentwiththePlanck
in the HAD catalog, and the predicted number of detections experimentresolution.Thecaseofextendedobjectsstronglyde-
assuming Planck-SZ cosmology (Planck Collaboration results. pendsontheexactmethodologyusedtodefinethegalaxycluster
XX 2014) and considering the completeness and purity of the position.Nevertheless,consideringthenumberdensityinPlanck
HADcatalog.Thispredictednumberisfoundtobe4082±700. SZ catalog and HAD catalog, within a radius of 10 arcmin the
The 3969 detected candidates in the HAD catalog is thus very numberofchanceassociationis15((cid:39) 1%ofthePSZ2sample)
well consistent with 4082 predicted detections from galaxy andwithinaradiusof4arcminthisnumberis4.Itimpliesthat
clusterbasedcosmologicalparameters. a10arcminmatchingdistanceprovidesarobustassociationbe-
tweenobjets.
Second, we perform a cross-match with reference galaxy Figure14presentsthenearestneighborsdistancedistributionbe-
clustercatalogs.Wecompareourdetectedcatalogofcandidates tweenHADandMCXCobjects,thatpresentssimilarproperties
withthePSZ2catalog.Thedistributionofnearestneighborsdis-
tance is shown on Fig. 13 From our 3969 detections, we find 3 Thisquantityisderivedfromapreviousqualityassessmentusing
1243 in common with the PSZ2 (and there is 418 objects in theANNpresentedinAghanimetal.(2015).
10