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Nature Astronomy
natureastronomy
https://doi.org/10.1038/s41550-023-02164-w
Article
Weak-lensingdetectionofintracluster
filamentsintheComacluster
Kim HyeongHan 1
, M. James Jee 1,2
, Sangjun Cha 1
& Hyejeon Cho 1,3
Theconcordancecosmologicalmodelpredictsthatgalaxyclustersgrow
attheintersectionoffilamentsthatstructurethecosmicwebandextend
tensofmegaparsecs.Althoughthishypothesishasbeensupportedbythe
baryoniccomponents,noobservationalstudyhasdetectedthedarkmatter
componentoftheintraclusterfilaments(ICFs),theterminalsegmentofthe
large-scalecosmicfilamentsattheirconjunctionwithindividualclusters.
Wereportweak-lensingdetectionofICFsintheComaclusterfieldfromthe
∼12-deg2
HyperSuprime-Camimagingdata.Thedetectionisbasedontwo
methods,thematched-filtertechniqueandtheshear-peakstatistic.The
matched-filtertechniqueyieldsdetectionsignificancesof6.6σand3.6σfor
thenorthernandwesternICFsat110°and340°,respectively.Theshear-peak
statisticyieldsdetectionsignificancesof3.1σand2.8σfortheseICFs.Both
ICFsarehighlycorrelatedwiththeoverdensitiesintheweak-lensingmass
reconstructionandarewellalignedwiththeknownlarge-scale(>10 Mpc)
cosmicfilamentsassociatedwiththeComasupercluster.
An intracluster filament (ICF) is a terminal segment of a cosmic-web
filament, which, as numerical simulations show1–3
, often penetrates
wellinsidethevirialradiusofthecluster.WedetectedICFsintheComa
cluster(z = 0.023; A1656)withthe12-deg2
high-qualitySubaruHyper
Suprime-Cam (HSC) wide-field imaging data based on the two
shear-based approaches (Methods): the matched-filter technique4
(Fig. 1) and the shear-peak statistic (Fig. 2). We were able to measure
theweak-lensing(WL)signalfromtheICFsbecause(1)thesurfacemass
density of the filament escalates toward the galaxy cluster1,5
, thus
increasingitsdensitycontrastagainstthebackground,and(2)alarge
number of source galaxies per physical area of the lens boost the WL
statistical power, due to the proximity of the Coma cluster (Methods
and Extended Data Fig. 1).
Results
Matched-filterstatistic
Figure 1 (see also Extended Data Fig. 2) shows the matched-filter sta-
tistic Γ+ in polar coordinates together with the reconstructed mass
distributionoftheComacluster.TherearethreeoutstandingΓ+ peaks
withsignificanceabove3σat∼110°(justcounterclockwisefromNorth
(N) in Fig. 1), ∼240° (at Southeast (SE)) and ∼340° (near West (W)).
WeestimatethesignificancesoftheN,SEandWfeaturestobe6.6σ,4.3σ
and3.6σ,respectively,consideringboththeshotnoiseandlarge-scale
structure (LSS) along the line-of-sight (LOS). As seen in the mock test
(MethodsandExtendedDataFig.3),thecrossmatched-filterstatistic
(Γ×)alsovanishesattheseangles.AmongthethreeICFcandidates,theN
andWfeaturesareincoincidencewiththeshear-peak-baseddetection.
We find that the matched-filter statistic result is consistent with
the features identified in the two-dimensional mass reconstruction
(Fig. 1). The correlation between the matched-filter statistic peaks
andmassoverdensitiescanbeclearlyseen.Thenorthernandwestern
regionsatr > 1 Mpcarecharacterizedbyoverdensitiesformingradially
alignedlinearstructureswhereastheSEregiondoesnotpossesssuch
acoherentstructure.Thelinearstructureat∼30°isalsoingoodagree-
ment with the location of the matched-filter peak. However, since its
matched-filtersignificanceisrelativelylow(∼2.5σ),weclassifyitasan
ICFcandidateinthispaper.
As there is a strong concentration of mass on the northern ICF
(∼2.3 Mpc away from the Coma cluster centre at ∼110°), we investi-
gated whether this mass clump is a main contributor to the detec-
tion.Whenwelimitouranalysistotheannulusatrbetween1 Mpcand
2 Mpc, excluding this overdense region, we still find the peak at the
Received: 7 June 2023
Accepted: 3 November 2023
Published online: xx xx xxxx
Check for updates
1
Department of Astronomy, Yonsei University, Seoul, Korea. 2
Department of Physics and Astronomy, University of California Davis, Davis, CA, USA. 3
Center
for Galaxy Evolution Research, Yonsei University, Seoul, Korea. e-mail: mkjee@yonsei.ac.kr
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
northern and western peaks possess significances of 3.1σ and 2.8σ,
respectively. The southeastern peak has a significance of 2.0σ, which
ismuchlowerthanthematched-filterresult(4.3σ).Thefeatureat∼30°
is consistent with the baseline and not significant in this shear-peak
statistic.
Discussion
WemeasuredthepropertiesoftheICFsfromourMarkovChainMonte
Carlo sampling using the parametric model (equation (1)), and the
result is presented in Extended Data Table 1. In Fig. 3, we display the
posterior distributions of the normalization κ0 and the characteristic
width hc. Although we do not consider the SE peak at θ = 240° a solid
detection, we include it in the analysis to illustrate that its properties
differfromthoseoftheothertwo.ThenorthernandwesternICFshave
acharacteristicwidthofhc = 0.29
+0.05
−0.05 Mpcand 0.10
+0.05
−0.04 Mpc,respec-
tively, and a normalization constant (that is, the peak density) of
κ0 = 0.0168
+0.0024
−0.0023 and 0.0188
+0.0055
−0.0044,respectively.Ontheotherhand,
inthecaseoftheSEfilamentcandidate,thenormalizationconstantis
afactoroftwolower(0.0080
+0.0018
−0.0015)thanthoseoftheothertwo.Also,
its characteristic width is much larger (hc = 1.07
+0.43
−0.30 Mpc) than the
other two. The properties of the SE feature suggest that perhaps the
signalmaycomefrommultipleoverlappingfilaments,ifitisafilament.
Assumingacylindricalsymmetrywithin4hc,themeandensitiesofthe
northern and western ICFs are 103 and 115 times the critical density
(343 and 383 times the background density) at the Coma redshift,
respectively.
To compare the ICFs with the larger filaments traced by galaxies
around the Coma cluster, we retrieved the galaxy catalogue within
the r = 10° (∼16.8 Mpc) radius of NGC 4874 from the Sloan Digital Sky
SurveyDataRelease16(SDSSDR16)13
.Figure4displaysthedistribution
ofgalaxiesaroundtheComacluster.Weshowthedirections(magenta
arrows)ofthefourlarge-scalefilamentsintheliterature6,7
detectedwith
galaxyoverdensities.TheorientationofthewesternICFiswellaligned
withthefilamentdirectionintheliteratureanditiswell-tracedbythe
galaxies at similar redshifts to the Coma cluster within this field. The
northernICForientationisalsoconsistentwiththefilamentdirection
in the literature. Its presence is not clear in galaxy overdensity within
theHSCfield(r < 2°).Interestingly,theSEpeakat∼240°,whichweclas-
sified as an ICF candidate, is also aligned with the filament suggested
bythegalaxyoverdensity.
ThedashedcircleinFig.4illustratestherelativelysmallfieldsize
of the HSC imaging data. If galaxies are assumed to Poisson-sample
thedarkmatterdistribution,itisdifficulttotracetheICFwithgalaxies
alonebecausetheregionisalreadycrowdedwiththeComaclustergal-
axies,aswellasthegalaxiesbelongingtothefilaments.Inthisregard,
the matched-filter WL analysis may serve as a useful (and perhaps
better) tool to identify the ICFs, because the filter is designed to be
sensitivetothinlinearmassdistributions.
A recent study based on the state-of-the-art cosmological
hydro-dynamicalsimulation14
findsthatthemeancharacteristicwidths
of the short (L < 9 Mpc) and long (L > 20 Mpc) cosmic filaments are
0.25 ± 0.03 Mpcand0.24 ± 0.03 Mpc,respectively,atz = 0.Thecharac-
teristicwidthofthenorthernICFinComaapproximatelycorresponds
tothesemeanvalues,whereasthatofthewesternICFisatthelowend
of the distribution. Also, from the result of this study14
, we estimate
the mean densities for the short and long filaments within the cylin-
drical volume at r < 4hc to be 67 and 33 times the background density,
respectively. Considering the large filament-to-filament variation14
and the three-fold filament density increase at the cluster junction1,5
,
we find that the properties of the ICFs in Coma are at the high end of
thedistributionbutnotexceptional.
The current study differs from the previous studies reporting
filamentdetectionsinA222/A223(ref.15)andMACSJ0717(refs.16,17),
whichwereprimarilybasedonweaklensing.TheA222/A223detection
was a mass bridge between the two massive clusters, which can be
same orientation with a similar significance (∼6σ). As demonstrated
in our mock test (Extended Data Fig. 3), isotropic mass distributions
are not likely to masquerade as significant filament detection in the
matched-filterstatistic.
One of the extensively studied filaments of the Coma cluster
in the literature is the western filament in the direction of the Leo
cluster (A1367), which, together with A1656, comprises the Coma
supercluster6–12
. The orientation of the western ICF is highly con-
sistent with this filament. It is also remarkable that the central mass
substructures within r < 1 Mpc form a short (∼1 Mpc) filament well
aligned with this ICF.
Shear-peakcountstatistic
Figure2showstheshear-peakmapandtheazimuthalshear-peakden-
sityvariation.Althoughitisdifficulttodetectshear-peakdensityexcess
from the two-dimensional map alone (Fig. 2, left), the shear-peak sta-
tisticpresentsremarkablyconsistentfeatureswiththematched-filter
statistic, revealing the density peaks at the same angles. Unlike the
matched-filtertechnique,herewecannotusethesamelightconedata
(Methods)toperformamocktestbecauseoftheinsufficientresolution.
ThispreventsusfromestimatingtheuncertaintyduetotheLSSbased
onthenumericalsimulationdata.Therefore,toestimatethestatistical
significanceoftheshear-peakstatistic,wecomputedthebaselineusing
thedataperse,assumingthatazimuthalaverageapproachesthemean
shear-peakcountintheblankfield.Ofcourse,sincetheComacluster
is far from a blank field, the baseline obtained in this way is likely to
be overestimated. Thus, this approach is a conservative choice. The
29.0°
28.0°
27.0°
196.0° 195.0°
RA
194.0°
–2
–1
0
1
2
3
4
5
45°
6
Dec.
S/N
315°
1 Mpc
0.010
0.008
0.006
0.004
0.002
–0.002
–0.004
0
225°
135°
N
W
SE
Γ+(θ)
Fig.1|Massreconstructionandmatched-filterstatisticoftheComacluster.
Formassreconstruction,weusedtheconvolutionalneuralnetworkmethod50
afterdeeplearningtrainingwithawide-field(3.5 deg × 3.5 deg)convergence
field.Weverifythatthemassreconstructionresultisconsistentwiththeversion
generatedwiththeconventionalmethod51
.Thebackgroundiscolour-codedwith
thelensingsignal-to-noiseratio(S/N).Themagentastar,pentagonandtriangle
representNGC4874,NGC4889andNGC4839,respectively.Theinnerandouter
yellowsolidcirclesenclosetheradialextent(r = 1and2.8 Mpc)oftheannulus,
wherewedetectedtheICFsignal.Theblacksolidcurveandshadingillustratethe
matched-filterstatistic(Γ+)anditsuncertainty(shotnoise + LSSeffect)inpolar
coordinates(seealsoExtendedDataFig.2).Thematched-filterstatistic
correlateswellwiththemassoverdensity.Throughoutthepaper,weassumeaflat
Lambdacolddarkmattercosmologycharacterizedbyh = 0.7and
Ωm,0 = 1 − ΩΛ,0 = 0.3.
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
claimedasalong(∼18 Mpc)cosmicfilamentonlyundertheassumption
thatthefilamentisalignedalongtheLOSdirection.Currently,thereis
noevidencesupportingsuchafortuitousalignment.TheMACSJ0717
result is different from that of A222/A223 in that the mass detection
extendsfromthemainclustercomprisingtwomergingclusterstothe
southeasternX-raygroupseparated18
fromthemainclusterby1.2 Mpc
andthenfromtherefurtherstretchestowardsthesouthby2.5 Mpc.As
in the A222/A223 system, under the assumption that this mass exten-
sion is aligned along the LOS direction, the structure is interpreted
as a projection of the 18-Mpc-long cosmic filament. An X-ray-based
filamentary structure detection was reported around A2744 (ref. 19).
Although these gas structures show signs of correlations with some
WLmassandgalaxyoverdensities,theWLmassreconstructionalone
does not convincingly reveal the filamentary structure. Currently, no
cosmic-webstructuresextendingtensofmegaparsecs,similartothose
observedinComa,havebeenreportedinA2744.
ThecurrentdiscoveryoftheICFinComahasanimportantimplica-
tionforthecosmologicalstudiesbasedonclustermassfunctions.Asin
Coma,ifasubstantialfractionofthetotalmassisgenerallycontained
in ICFs within a cluster’s virial radius, it becomes imperative to revisit
the definition of the cluster mass. In simulations, cluster masses are
definedasthetotalmasswithinaspherewithradiuscomputedforthe
given density contrast criteria. In observations, typical mass estima-
tionisobtainedundertheassumptionthatthedensityprofilefollows
an analytic description. Given that neither the simulations nor the
observations explicitly account for the ICFs, omitting of these struc-
tures in both approaches may introduce non-negligible bias in the
estimationofcosmologicalparametersbasedonclustermasses.
Methods
Feasibility of ICF detection at low-z
WLstudiesoflow-redshift(z ≪ 0.1)galaxyclustershavebeenconsidered
a difficult task mainly because (1) the lensing efficiency is low and (2)
verywide-fieldimagingdataarerequired.Thelatterisnolongeralimit-
ingfactorintoday’sera,wheremanywide-fieldinstrumentsareavailable.
Theformeriscertainlyaweaknessarisingfromthegeometriceffectof
thelow-redshiftlens.However,aswedemonstratebelow,theweakness
issignificantlyoutweighedbythehighsignal-to-noiseratio(S/N)dueto
alargenumberofsourcegalaxiesperphysicalareaofthelens.Thus,we
argue that the Coma cluster WL provides a considerably better oppor-
tunityforlow-contraststructuredetectionthanathigherredshift.
We define the WL S/N parameter λ as λ = ηβ√n/σLSS , where η is
the purity of the source population, n is the physical source number
density (number of sources per physical area at the lens redshift), β is
the lensing efficiency and σLSS is the noise due to the LSS20
along the
LOS direction. The term σLSS decreases with angular scale and thus is
smaller at lower redshift because the angular size of the filament is
larger. The lensing efficiency is β ≡ ∫
∞
zl
dzdp (z) DlDls/Ds , where p(z) is
thesourceredshiftprobabilitydistribution,zl isthelensredshift,Dl is
theangulardiameterdistancetothelensandDls/Ds istheratioofangu-
lardiameterdistancesfromthelenstothesourceandfromtheobserver
to the source. Extended Data Fig. 1 shows that β (red) increases with
thelensredshift.TheComalensefficiencyislowernearlybytwoorders
of magnitude than the one at zl = 0.5. However, as the lens redshift
decreases,thenumberofsourcegalaxiesperphysicalareaatthelens
redshiftincreasesquickly.Therefore,thetotallensingS/Nperphysical
area of the lens (blue) in fact increases as the lens redshift decreases,
becomingthreetimeshigherattheComaredshiftof∼0.023thanthe
S/N value at zl = 0.5. One caveat that one can recall in this S/N analysis
is the shear calibration. Since the intrinsic lensing signal is weaker at
lowerredshift,therequirementfortheresidualshearcalibrationerror
shouldbemorestringent.
Matched-filterstatistic
A matched filter refers to the template (or kernel) that extracts the
optimal S/N measurement when it is correlated with the signal. Both
theshapeofthesignalandthenoisecharacteristicsareimportantcon-
siderationsindesigningthefilter.Inthisstudy,weadopttheformalism
presentedbyMaturiandMerten4
.
Colberg et al.5
studied the density profiles of filaments from cos-
mological simulations and found that filaments have well-defined
edges characterized by the scale width hc, inside which the density is
approximately constant. Outside the edges, the density drops as h−2
,
wherehistheperpendiculardistancefromthe‘ridge’ofthefilament.
Adoptingtheresult,Maturi&Merten4
usedthefollowinganalyticform
tomodelthefilamentconvergenceprofile:
κ (h) =
κ0
1 + (h/hc)
2
, (1)
where κ0 is the maximum convergence at the ridge. Note that at
the characteristic width hc, the density drops to half the maximum
0.075
0.070
0.065
0.060
0.055
0.050
0.045
0.040
0.035
193.0°
194.0°
195.0°
RA
196.0°
1 Mpc
197.0°
27.0°
28.0°
29.0°
50 100 150 200 250 300 350
θ (deg)
Dec.
Shear-peak
density
(arcmin
–2
)
225°
135° 45°
315°
0.07
0.06
0.05
SE
W
N
N
W
SE
Fig.2|Intraclusterfilamentdetectionbasedonshear-peakstatistic.Left,
theWLshear-peakmapcreatedwiththe5 × 1012
Mʘ NFWhalofilter.Theinner
andouteryellowsolidcirclesrepresentr = 1and2.8 Mpc,respectively.Theblack
solidcurveandshadeindicatetheshear-peakdensityanditsuncertaintyin
polarcoordinates.Circularblankregionsarethestellarmasks.Right,shear-peak
statisticasafunctionofangle.Theblacksolidlinerepresentsthedensityof
shearpeaksinarcmin2
andtheshaderepresents1σ uncertaintyfromthePoisson
statistics.Dashedhorizontallineistheazimuthalmean.Thenorthernand
westernpeaksareinexcellentagreementwiththematched-filterresult(Fig.1).
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
convergenceκ0.TheWLshearγinducedbythefilament(equation(1))
isorientedperpendiculartothefilamentaxisandgivenby
γ = κ(h). (2)
In practice, γ (equation (2)) is obtained from the ellipticities of
sourcegalaxies.Assumingthatourcoordinateoriginliesatoneendof
the filament and θf is the orientation angle of the filament measured
counterclockwisefromthexaxis,γisrelatedtothegalaxies’ellipticity
components ϵ1 and ϵ2 via γ = ϵ1 cos [2 (θf − π/2)] + ϵ2 sin [2 (θf − π/2)]. If
we let γi be the estimate of γ from the ith source galaxy, our
matched-filterstatisticisgivenby
Γ =
1
W
∑
i
γiΨ (xi, yi) , (3)
where Ψ(xi, yi) is the filter (or weight) at the position (xi, yi) of the ith
sourcegalaxyandW = ΣiΨ(xi,yi).ThefilterΨisobtainedbyconsidering
theexpectedshearsignalofthefilamentandthenoiseduetotheLSS.
InFourierspace,theoptimalfilterisgivenasfollows:
̂
Ψ (k) = ̂
τ (k) /Pn (k) , (4)
where ̂
τ (k)istheFouriertransformoftheexpectedshearfromthefila-
ment (equation (2)) and Pn(k) is the noise power spectrum including
the LSS and intrinsic galaxy shape noise. Note that since we let the
estimator (equation (3)) include the proper normalization (that is,
1/W),weomitanormalizationconstantinequation(4).
In WL, the signal comes from the scalar potential and thus pro-
ducesonly‘E-mode’signals.The‘B-mode’signalisobtainedbyrotating
galaxyellipticitiesby45°andshouldbeconsistentwithzeroifthereis
nosignificantresidualsystematics.Inasimilarfashion,wecandefine
the corresponding terms in the matched-filter statistic Γ. Hereafter,
weuseΓ+ todenotetheE-modestatisticandrefertoitasthetangential
componentandΓ× todenotetheB-modestatisticandrefertoitasthe
cross component. Note that the cross component Γ× does not neces-
sarily become zero even in the absence of the systematics because
anycoherentalignmentofgalaxiestilted45°withrespecttothefilter
orientationcanproducenon-zerovalues.
Maturi and Merten4
provide the following analytic form for the
varianceofΓ(equation(3)):
σ2
Γ
(θ) =
1
2W2
∑
i
|γi|
2
Ψ2
(xi, yi) . (5)
Wefindthatequation(5)doesnotproperlyincludetheLSScontri-
butionandleadstoanoverestimationofthefilamentdetectionsignifi-
cance.Thus,inthisstudy,weusethepubliclyavailablekappaTNGlight
cone (convergence) data (http://columbialensing.org)21
constructed
fromthecosmologicalhydro-dynamicalsimulationsIllustrisTNG300-1
(refs. 22–27) to properly estimate the statistical significance of our
filament detection. We select the convergence dataset for the source
redshift at zs = 0.5, since it is the closest match to the effective source
redshift (zeff ≈ 0.7) estimated for the current Coma cluster WL data.
Fromthe1005 × 5 degconvergencefields,wegenerated900subfields
matching the current Coma field size (∼12 deg2
). Then, we produced
mock shear catalogues at the positions of the Coma source galaxies.
Finally, we applied the matched filter to the shear catalogues and
estimated the variance at each angle due to the LSS effect. We added
the two uncertainties from this LSS contribution and the shot noise
13 h 30 min 00 h 00 min 12 h 30 min
+35°
+30°
+25°
+20°
RA (J2000)
Dec.
(J2000)
5 Mpc
NGC 4874
NGC 4889
NGC 4839
NGC 4789
SDSS galaxies
N
SE
W
−6 −4 −2 0 2 4 6
(cz − czA1656)/(1 + zA1656) (×1,000 km s−1)
Fig.4|AlignmentoftheICFswiththelarge-scalefilaments.TheLOSvelocity
fromtheSDSSDR16catalogue13
iscolour-coded.Thesymbolsizeisproportional
totheSDSS-rbandmagnitude.Thesizeofthefilledblackcircleinthelowerleft
cornerrepresentsthebrightnessofNGC4874.Neighbouringgalaxygroups
aremarkedwithcyandiamonds.Theblackdashedr = 2.8 Mpccircleindicates
theHSCcoveragewhereweperformedWLanalysis.Thelightgreenarrows
withinitshowtheorientationsoftheICFsdetectedinthecurrentstudybased
onWLsignals.Magentaarrowsindicatetheapproximatecosmic-webfilament
directionsdetectedwiththegalaxydistributions6,7
.TheWL-basedICFsarewell
alignedwiththegalaxy-basedlarge-scalefilaments.
1.2
1.0
0.6
0.4
0.2
0.01 0.02
hc (Mpc)
K0
hc = 0.29+0.05
–0.05
hc = 1.07+0.43
–0.30
hc = 0.10+0.05
–0.04
0.03 0.2 0.6 1.0
0.8
h
c
(Mpc)
N
SE
W
K0 = 0.0168+0.0024
–0.0023
K0 = 0.0080+0.0018
–0.0015
K0 = 0.0188+0.0055
–0.0044
Fig.3|Posteriordistributionsofthefilamentmodelparametersestimated
fromtheMarkovChainMonteCarlosampling.Innerandoutercontours
representthe68%and95%confidencelimits,respectively.Dashedlinesindicate
themedian.Seetextforinterpretation.
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
(equation(5))inquadraturetocomputethetotaluncertainty.Extended
Data Fig. 2 displays the matched-filter statistic and its uncertainty
derivedfromtheComafield.
To evaluate the performance of the matched-filter technique for
filament detection, we created mock shear catalogues and applied
the method. Extended data Fig. 3 shows two examples of the mock
test results. In the top panel, we assumed that a Coma-like cluster
(M200c = 8 × 1014
Mʘ) at z = 0.02 is placed at the intersection of two fila-
mentsat10°and70°withalinearmassdensityofmf = 1.2 × 1014
Mʘ Mpc−1
.
These mock simulation setup parameters are deliberately chosen to
resemblethepropertiesoftheComaclusteranditsfilaments.Wefind
that the matched-filter statistic successfully identifies the two fila-
mentsandreachesmaximaatthecorrectorientations.Thecross-shear
statistic (Γ×) possesses much lower amplitudes and vanishes at the
orientationofthefilament.Inthebottompanel,thesetupisidentical
to the one in the top panel, except that another Coma-like cluster at
the same redshift is placed at θ = 135° about 1.4 Mpc away from the
field centre. This is to test whether the presence of massive halos can
masquerade as filaments in our matched-filter statistic. The result
shows that although a small bump is detected at θ = 135°, its ampli-
tude is substantially lower than the peaks due to the filaments, which
illustrates that the matched filter is much more sensitive to the
low-density anisotropic linear structure than to the high-density iso-
tropicmasspeak.InthetwoexamplesshowninExtendeddataFig.3,we
omitted,forillustrativepurposes,thenoiseduetotheintrinsicgalaxy
shapedispersionandLSS.Whenweincludethesenoisecontributions,
the significance of the bump due to the second galaxy cluster drops
belowourdetectionthreshold.
Shear-peakstatistic
Besides the matched-filter statistic, another useful method for ICF
detectionproposedbyMaturiandMerten4
istheshear-peakstatistic.
‘Shearpeaks’referstoprojectedoverdenseregionsinaWLmassmap
and their statistic as a function of significance is a powerful probe of
cosmological parameters28–33
. High S/N peaks are found at the loca-
tions of individual massive clusters, whereas true low S/N peaks are
mostlyproducedbytheprojectionofmanylow-masshalosalongthe
LOS direction, rather than by single low-mass halos. Because of their
low S/N nature, a significant fraction of low S/N shear peaks creates
a false positive. Since the presence of ICFs boosts the probability of
low S/N shear-peak detection, we can trace the ICF with their count-
ing statistic.
In this study, we employ an aperture mass filter derived from a
truncatedNavarro–Frenk–White(NFW)profiletominimizetheinflu-
ence of the LOS LSS. The convergence of the projected NFW profile34
is KNFW (x) = 1/(1 + x)
2
,where x = 𝜗𝜗/𝜗𝜗s, 𝜗𝜗 istheangularseparationand 𝜗𝜗s
is the scale radius. Its tangential-shear profile is approximated as
GNFW (x) = 2 ln (1 + x) /x2
− 2/ [x (1 + x)] − 1/(1 + x)
2
,andattheoutskirts,we
applytheGaussiantruncationfunction: G (x) = GNFW (x) exp (−𝜗𝜗
2
/2𝜗𝜗
2
out),
where 𝜗𝜗out isthetruncationradius.
We treated the mass map produced by this aperture filter as if it
wasanastronomicalimageofacrowdedstellarfield.Wedetectedthe
shear peaks using SExtractor35
(https://github.com/astromatic/sex-
tractor) and measured the number of peaks by azimuthally scanning
a pan-shaped region at every degree. The pan-shaped region has an
openingangleof30°andcoversaradialextentfrom1 Mpcto2.8 Mpc.
WemanuallysetthebackgroundleveltozeroinourSExtratorrun.
Datareduction
We used Subaru HSC observations in g and r bands. HSC is an
870-megapixel mosaic CCD camera (116 2k × 4k CCDs) with a pixel
scale of ∼0.17″ and an approximately 1.5° diameter field of view. The
observations were conducted with seven different pointings, which
togetherformahexagonalfootprintwithalargestdimensionexceed-
ing 4.5°. The radius of the largest complete circle within the mosaic
field is approximately 1.9°. The details of the observations are given
inSupplementaryTable1.
Single-frame processing (overscan, bias, flat, dark and so on)
was performed with the HSC Pipeline36
, which was built on the pro-
totype pipeline developed for the Rubin Telescope Legacy Survey of
SpaceTime.ThepipelinealsoincludesrobustcalibrationoftheWorld
CoordinateSystem,whichstorestheastrometricanddistortionsolu-
tions in the ‘Simple Imaging Polynomial’ format. Since our WL pipe-
line uses the SWarp package (https://www.astromatic.net/software/
swarp/), which only understands the TPV format, we converted the
astrometric header of each frame using the sip-to-pv (https://github.
com/stargaser/sip_tpv.git) script37
. These calibrated files were com-
bined using SWarp to create giant (97k × 91k pixels) mosaic images.
We generated two versions of mosaic images. The first version is pro-
ducedusingallavailableframesexceptfordefectiveones.Thisproduct
providesdeepphotometryandisalsousefulforobjectdetection.The
secondmosaiciscreatedfromtheframeswithseeingbetterthan0.85″.
Thisimageisoptimizedforgalaxyshapemeasurement.Supplementary
Fig. 1 displays the colour-composite image created with these large
mosaicimages,withatotaleffectiveareaof∼12deg2
.
Objectdetectionandphotometry
We ran SExtractor for object detection and photometry. We used the
dual-imagemodetoobtainobjectcolourswithconsistentsegmenta-
tioninformation.WeprovidedSExtractorwithaweightimagecreated
by SWarp for the detection and a root-mean-square error image for
the photometry. For object detection, we required objects to satisfy
the criteria DETECT_THRESH = 2 and DETECT_MINAREA = 5. We set
the deblending parameters with the blending threshold DEBLEND_
NTHRESHof64andtheminimalcontrastDEBLEND_MINCONTof10−4
toidentifytheoverlappingobjects.WeusedMAG_ISOforcolouresti-
mation and MAG_AUTO for luminosity measurement. We performed
photometriccalibrationusingtheSDSSDR16(ref.13).
Sourceselection
Weselectsourcegalaxiesasfollows.First,wechooseobjectsbetween
23 < r < 26. Because of the proximity of the Coma cluster, most of the
faintgalaxiesinthisselectionarelikelytobebackgroundsources.We
donotimposeacolourcut,sincethemembergalaxycontaminationis
estimatedtobenegligibleinthismagnituderange.Toconfirmthis,we
comparethenumberdensitydistributionsbetweentheComacluster
andCOSMOS2020(ref.38)fields(SupplementaryFig.2).Inthelatter,
thereisnoComa-likecluster.Therefore,ifourmagnitude-basedsource
selectionincludesanon-negligiblefractionoftheComamembers,the
Comafieldmustshowanexcessintheselectionwindow.Theexcellent
agreementbetweenthetwofieldsverifiesthattheclustergalaxycon-
taminationcanindeedbeignoredwithinthesourceselectionwindow.
The objects with a half-light radius (rh) smaller than ∼0.5″ are
discarded to avoid stellar contamination. Our forward-model shape
measurement utilizes the MPFIT39
module, which reports the status
and stability of the shape fitting and the ellipticity uncertainty. We
only keep the sources with the stable fitting (STATUS = 1) and a small
ellipticityuncertainty(<0.4).
Some spurious sources cannot be identified with the method
described above. They include false detections around bright stars
forming concentric circles and unidentified cosmic rays near the
field edges. As for the former, we deselect the objects by applying
large circular masks on the stars brighter than 13 mag in r band. The
spurious objects near the field edges are not included in our final
source catalogue because we reject the sources with distances of
r > 2.8 Mpc from the Coma cluster centre. We note that there are no
spurious objects on the edges of the six flanking fields facing toward
the cluster centre because the regions overlap the central and other
flankingfields.Thenumberdensityinthefinalsourcecatalogueis∼38
arcmin−2
. Since it is impossible to derive photometric redshifts from
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
onlytwofilters,weutilizethepubliclyavailableGOODS-Sphotometric
redshift catalogue40
to estimate the effective redshift of the source
population. After applying the same source selection criteria to the
GOODS-S photometric redshift catalogue and taking into account
the difference in image depth, we determine the effective source
redshift to be zeff = 0.72. Because of the proximity of the Coma clus-
ter, the critical surface density is not sensitive to the source redshift.
For example, even if we assume zeff = 1, the critical surface density
changes by approximately 1%.
Shearmeasurement
We measured galaxy shapes from the mosaic image. This requires
us to model the point-spread-function (PSF) for each CCD frame
per exposure and to carefully propagate the PSF model at the loca-
tion of the galaxy on the coadd. The PSF model for each CCD frame
was constructed through Principal Component Analysis based on
the observed stars and polynomial interpolation41,42
. At each galaxy
location, we first identify all contributing frames and then stack
their PSF models after applying due rotations. This PSF modelling
scheme enables us to capture the sophisticated PSF variation pat-
terns across the mosaic image, including sudden discontinuities at
the CCD boundaries. The PSF residual (the observed star ellipticity
minus the model PSF ellipticity) correlation function shows that the
correlation amplitude is below 10−6
on angular scales greater than 1′
(left panel of Supplementary Fig. 3).
Once we obtain a secure PSF model at the location of a source
galaxy,weconvolveanellipticalGaussianfunctionwiththePSFandfit
theresultingprofiletotheobject43–47
.SincethePSF-convolvedelliptical
Gaussian profile differs from the observed galaxy profile, model bias
occurs.Inaddition,theellipticitymeasurementbasedonthemaximum
likelihood is biased because of the non-linear relation between pixel
noiseandshear,oftentermed‘noisebias’.Asignificantfractionofgal-
axiesisaffectedbyblendingeffects48
.Toaddressthemixtureofthese
sourcesofshearmeasurementbias,weuseimagesimulationsandcom-
pareinput(true)shearswithoutput(measured)shears.Thesimulation
showsthattheadditivefactor,whichmainlyarisesfromanimperfect
PSF model, is negligible. We find that the star-galaxy ellipticity cross
correlation is at the 10−6
level on angular scales greater than 10′ (right
panel of Supplementary Fig. 3). Both the PSF residual and star-galaxy
correlationdiagnosticsverifythattheresidualWLsystematicerroris
negligible.TheWLpipelineweemployedhereparticipatedinthethird
Gravitational Lensing Accuracy Testing challenge49
and was publicly
validatedtobeoneofthebest-performingmethodsinthisblindtest.
Dataavailability
TherawSubaruHSCimagingdatausedforthecurrentstudyarepub-
licly available. The processed mosaic images and data points in the
article figures are available on request from the authors. Source data
areprovidedwiththispaper.
Codeavailability
Our custom data processing codes are available on request from the
authors.
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Acknowledgements
M.J.J. acknowledges support for the current research from the
National Research Foundation (NRF) of Korea under the programmes
2022R1A2C1003130 and RS-2023-00219959.
Authorcontributions
K.H. reduced the data, measured WL signals and filaments and wrote
the manuscript. M.J.J. designed the research, created the reduction
pipeline, coded the filament detection filter and wrote the manuscript.
S.C. provided the mass reconstruction based on a convolutional
neural network. H.C. identified the filaments based on the Coma
galaxy distribution.
Competinginterests
The authors declare no competing interests.
Additionalinformation
Extended data is available for this paper at
https://doi.org/10.1038/s41550-023-02164-w.
Supplementary information The online version
contains supplementary material available at
https://doi.org/10.1038/s41550-023-02164-w.
Correspondence and requests for materialsshould be addressed to
M. James Jee.
Peer review information Nature Astronomy thanks Smriti Mahajan and
the other, anonymous, reviewer(s) for their contribution to the peer
review of this work.
Reprints and permissions informationis available at
www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.
Springer Nature or its licensor (e.g. a society or other partner) holds
exclusive rights to this article under a publishing agreement with
the author(s) or other rightsholder(s); author self-archiving of the
accepted manuscript version of this article is solely governed by the
terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Springer Nature Limited
2024
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
ExtendedDataFig.1|WLS/Nperphysicalareavariationwiththelens
redshift.Redsolidlineisthelensingefficiencyβ.BluesolidlineistheWLS/Nper
physicalarea(λ)normalizedbythevalueat z = 0.5.Whilethelensingefficiency
isreducedapproximatelytwoordersofmagnitudeasthelensredshiftdecreases
fromz=0.5totheComaredshift(z=0.023),thenetWLS/Nperphysicalareaat
thelensredshiftincreasesapproximatelybyafactorofthree.Thisnetgainisdue
tothecombinedeffectofthehigherscoredensity nandlowerLSSnoise σLSS per
physicalareaattheComaredshift.Hereweassumethatthepurity η isthesame
acrossthelensredshift.Infact, η isalsoexpectedtobehigherattheComa
redshiftbecauseoftheproximity.
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
ExtendedDataFig.2|Matched-filterdetectionoftheICFsintheComa
cluster.Black(red)solidlinerepresentsthetangential(cross)-shearcomponent.
Darkshadeindicatestheshotnoise(equation5).Lightshadeincludesboththe
shotnoiseandthenoiseduetotheLSSeffect.ThreeICFs(N,SEandW)are
detectedwithasignificancelevelhigherthan3σ.Thecross-componentcrosses
zeroattheselocations.
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
ExtendedDataFig.3|Matched-filterdetectionwithamockfilament-cluster
configuration.TopLeft:MockconvergencemapwithtwofilamentsandanNFW
halodisplayedinlogscale.Mockfilamentsareorientedat10°and70°withan
NFWhaloatthecentre.Thelinearmassdensityofthefilamentmf =1.2×1014
M☉Mpc−1
andthehalomassM200 =8×1014
M⊙ aremotivatedbyourmeasurements
inComa.WhiskersshowtheresultingWLshear.Innerandouteryellowcircles
indicater = 1and2.8Mpc,respectively.TopRight:Black(red)solidlineindicates
thetangential(cross)-component Γ+(Γ×).Thetangential-shearcomponentis
alsoshownintheleftpanel(blacksolid)inpolarcoordinates.Bottom:Sameas
thetoppanelsexceptthatanotherM200 =8×1014
M⊙ haloisplaced(whitearrow)
atθ=120°,∼1.2Mpcapartfromthecentre.Thetangentialcomponent Γ+ is
sensitivetothefilamentarymassstructureandpeaksatthecorrectangles.
Althoughtheoff-centrehalogivesrisetoasmallpeakatθ=120°,itsheightis
muchweakerthanthosearisingfromtherealfilamentarystructures.Herewe
showtheversionthatdoesnotincludeintrinsicshapenoiseforillustration
purposes.Withtheinclusionoftheshapenoise,thetangential-componentpeak
duetothehaloisbelowourdetectionthreshold.
Nature Astronomy
Article https://doi.org/10.1038/s41550-023-02164-w
Extended Data Table 1 | Physical Properties of the Intracluster Filaments

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Weak-lensing detection of intracluster filaments in the Coma cluster

  • 1. Nature Astronomy natureastronomy https://doi.org/10.1038/s41550-023-02164-w Article Weak-lensingdetectionofintracluster filamentsintheComacluster Kim HyeongHan 1 , M. James Jee 1,2 , Sangjun Cha 1 & Hyejeon Cho 1,3 Theconcordancecosmologicalmodelpredictsthatgalaxyclustersgrow attheintersectionoffilamentsthatstructurethecosmicwebandextend tensofmegaparsecs.Althoughthishypothesishasbeensupportedbythe baryoniccomponents,noobservationalstudyhasdetectedthedarkmatter componentoftheintraclusterfilaments(ICFs),theterminalsegmentofthe large-scalecosmicfilamentsattheirconjunctionwithindividualclusters. Wereportweak-lensingdetectionofICFsintheComaclusterfieldfromthe ∼12-deg2 HyperSuprime-Camimagingdata.Thedetectionisbasedontwo methods,thematched-filtertechniqueandtheshear-peakstatistic.The matched-filtertechniqueyieldsdetectionsignificancesof6.6σand3.6σfor thenorthernandwesternICFsat110°and340°,respectively.Theshear-peak statisticyieldsdetectionsignificancesof3.1σand2.8σfortheseICFs.Both ICFsarehighlycorrelatedwiththeoverdensitiesintheweak-lensingmass reconstructionandarewellalignedwiththeknownlarge-scale(>10 Mpc) cosmicfilamentsassociatedwiththeComasupercluster. An intracluster filament (ICF) is a terminal segment of a cosmic-web filament, which, as numerical simulations show1–3 , often penetrates wellinsidethevirialradiusofthecluster.WedetectedICFsintheComa cluster(z = 0.023; A1656)withthe12-deg2 high-qualitySubaruHyper Suprime-Cam (HSC) wide-field imaging data based on the two shear-based approaches (Methods): the matched-filter technique4 (Fig. 1) and the shear-peak statistic (Fig. 2). We were able to measure theweak-lensing(WL)signalfromtheICFsbecause(1)thesurfacemass density of the filament escalates toward the galaxy cluster1,5 , thus increasingitsdensitycontrastagainstthebackground,and(2)alarge number of source galaxies per physical area of the lens boost the WL statistical power, due to the proximity of the Coma cluster (Methods and Extended Data Fig. 1). Results Matched-filterstatistic Figure 1 (see also Extended Data Fig. 2) shows the matched-filter sta- tistic Γ+ in polar coordinates together with the reconstructed mass distributionoftheComacluster.TherearethreeoutstandingΓ+ peaks withsignificanceabove3σat∼110°(justcounterclockwisefromNorth (N) in Fig. 1), ∼240° (at Southeast (SE)) and ∼340° (near West (W)). WeestimatethesignificancesoftheN,SEandWfeaturestobe6.6σ,4.3σ and3.6σ,respectively,consideringboththeshotnoiseandlarge-scale structure (LSS) along the line-of-sight (LOS). As seen in the mock test (MethodsandExtendedDataFig.3),thecrossmatched-filterstatistic (Γ×)alsovanishesattheseangles.AmongthethreeICFcandidates,theN andWfeaturesareincoincidencewiththeshear-peak-baseddetection. We find that the matched-filter statistic result is consistent with the features identified in the two-dimensional mass reconstruction (Fig. 1). The correlation between the matched-filter statistic peaks andmassoverdensitiescanbeclearlyseen.Thenorthernandwestern regionsatr > 1 Mpcarecharacterizedbyoverdensitiesformingradially alignedlinearstructureswhereastheSEregiondoesnotpossesssuch acoherentstructure.Thelinearstructureat∼30°isalsoingoodagree- ment with the location of the matched-filter peak. However, since its matched-filtersignificanceisrelativelylow(∼2.5σ),weclassifyitasan ICFcandidateinthispaper. As there is a strong concentration of mass on the northern ICF (∼2.3 Mpc away from the Coma cluster centre at ∼110°), we investi- gated whether this mass clump is a main contributor to the detec- tion.Whenwelimitouranalysistotheannulusatrbetween1 Mpcand 2 Mpc, excluding this overdense region, we still find the peak at the Received: 7 June 2023 Accepted: 3 November 2023 Published online: xx xx xxxx Check for updates 1 Department of Astronomy, Yonsei University, Seoul, Korea. 2 Department of Physics and Astronomy, University of California Davis, Davis, CA, USA. 3 Center for Galaxy Evolution Research, Yonsei University, Seoul, Korea. e-mail: mkjee@yonsei.ac.kr
  • 2. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w northern and western peaks possess significances of 3.1σ and 2.8σ, respectively. The southeastern peak has a significance of 2.0σ, which ismuchlowerthanthematched-filterresult(4.3σ).Thefeatureat∼30° is consistent with the baseline and not significant in this shear-peak statistic. Discussion WemeasuredthepropertiesoftheICFsfromourMarkovChainMonte Carlo sampling using the parametric model (equation (1)), and the result is presented in Extended Data Table 1. In Fig. 3, we display the posterior distributions of the normalization κ0 and the characteristic width hc. Although we do not consider the SE peak at θ = 240° a solid detection, we include it in the analysis to illustrate that its properties differfromthoseoftheothertwo.ThenorthernandwesternICFshave acharacteristicwidthofhc = 0.29 +0.05 −0.05 Mpcand 0.10 +0.05 −0.04 Mpc,respec- tively, and a normalization constant (that is, the peak density) of κ0 = 0.0168 +0.0024 −0.0023 and 0.0188 +0.0055 −0.0044,respectively.Ontheotherhand, inthecaseoftheSEfilamentcandidate,thenormalizationconstantis afactoroftwolower(0.0080 +0.0018 −0.0015)thanthoseoftheothertwo.Also, its characteristic width is much larger (hc = 1.07 +0.43 −0.30 Mpc) than the other two. The properties of the SE feature suggest that perhaps the signalmaycomefrommultipleoverlappingfilaments,ifitisafilament. Assumingacylindricalsymmetrywithin4hc,themeandensitiesofthe northern and western ICFs are 103 and 115 times the critical density (343 and 383 times the background density) at the Coma redshift, respectively. To compare the ICFs with the larger filaments traced by galaxies around the Coma cluster, we retrieved the galaxy catalogue within the r = 10° (∼16.8 Mpc) radius of NGC 4874 from the Sloan Digital Sky SurveyDataRelease16(SDSSDR16)13 .Figure4displaysthedistribution ofgalaxiesaroundtheComacluster.Weshowthedirections(magenta arrows)ofthefourlarge-scalefilamentsintheliterature6,7 detectedwith galaxyoverdensities.TheorientationofthewesternICFiswellaligned withthefilamentdirectionintheliteratureanditiswell-tracedbythe galaxies at similar redshifts to the Coma cluster within this field. The northernICForientationisalsoconsistentwiththefilamentdirection in the literature. Its presence is not clear in galaxy overdensity within theHSCfield(r < 2°).Interestingly,theSEpeakat∼240°,whichweclas- sified as an ICF candidate, is also aligned with the filament suggested bythegalaxyoverdensity. ThedashedcircleinFig.4illustratestherelativelysmallfieldsize of the HSC imaging data. If galaxies are assumed to Poisson-sample thedarkmatterdistribution,itisdifficulttotracetheICFwithgalaxies alonebecausetheregionisalreadycrowdedwiththeComaclustergal- axies,aswellasthegalaxiesbelongingtothefilaments.Inthisregard, the matched-filter WL analysis may serve as a useful (and perhaps better) tool to identify the ICFs, because the filter is designed to be sensitivetothinlinearmassdistributions. A recent study based on the state-of-the-art cosmological hydro-dynamicalsimulation14 findsthatthemeancharacteristicwidths of the short (L < 9 Mpc) and long (L > 20 Mpc) cosmic filaments are 0.25 ± 0.03 Mpcand0.24 ± 0.03 Mpc,respectively,atz = 0.Thecharac- teristicwidthofthenorthernICFinComaapproximatelycorresponds tothesemeanvalues,whereasthatofthewesternICFisatthelowend of the distribution. Also, from the result of this study14 , we estimate the mean densities for the short and long filaments within the cylin- drical volume at r < 4hc to be 67 and 33 times the background density, respectively. Considering the large filament-to-filament variation14 and the three-fold filament density increase at the cluster junction1,5 , we find that the properties of the ICFs in Coma are at the high end of thedistributionbutnotexceptional. The current study differs from the previous studies reporting filamentdetectionsinA222/A223(ref.15)andMACSJ0717(refs.16,17), whichwereprimarilybasedonweaklensing.TheA222/A223detection was a mass bridge between the two massive clusters, which can be same orientation with a similar significance (∼6σ). As demonstrated in our mock test (Extended Data Fig. 3), isotropic mass distributions are not likely to masquerade as significant filament detection in the matched-filterstatistic. One of the extensively studied filaments of the Coma cluster in the literature is the western filament in the direction of the Leo cluster (A1367), which, together with A1656, comprises the Coma supercluster6–12 . The orientation of the western ICF is highly con- sistent with this filament. It is also remarkable that the central mass substructures within r < 1 Mpc form a short (∼1 Mpc) filament well aligned with this ICF. Shear-peakcountstatistic Figure2showstheshear-peakmapandtheazimuthalshear-peakden- sityvariation.Althoughitisdifficulttodetectshear-peakdensityexcess from the two-dimensional map alone (Fig. 2, left), the shear-peak sta- tisticpresentsremarkablyconsistentfeatureswiththematched-filter statistic, revealing the density peaks at the same angles. Unlike the matched-filtertechnique,herewecannotusethesamelightconedata (Methods)toperformamocktestbecauseoftheinsufficientresolution. ThispreventsusfromestimatingtheuncertaintyduetotheLSSbased onthenumericalsimulationdata.Therefore,toestimatethestatistical significanceoftheshear-peakstatistic,wecomputedthebaselineusing thedataperse,assumingthatazimuthalaverageapproachesthemean shear-peakcountintheblankfield.Ofcourse,sincetheComacluster is far from a blank field, the baseline obtained in this way is likely to be overestimated. Thus, this approach is a conservative choice. The 29.0° 28.0° 27.0° 196.0° 195.0° RA 194.0° –2 –1 0 1 2 3 4 5 45° 6 Dec. S/N 315° 1 Mpc 0.010 0.008 0.006 0.004 0.002 –0.002 –0.004 0 225° 135° N W SE Γ+(θ) Fig.1|Massreconstructionandmatched-filterstatisticoftheComacluster. Formassreconstruction,weusedtheconvolutionalneuralnetworkmethod50 afterdeeplearningtrainingwithawide-field(3.5 deg × 3.5 deg)convergence field.Weverifythatthemassreconstructionresultisconsistentwiththeversion generatedwiththeconventionalmethod51 .Thebackgroundiscolour-codedwith thelensingsignal-to-noiseratio(S/N).Themagentastar,pentagonandtriangle representNGC4874,NGC4889andNGC4839,respectively.Theinnerandouter yellowsolidcirclesenclosetheradialextent(r = 1and2.8 Mpc)oftheannulus, wherewedetectedtheICFsignal.Theblacksolidcurveandshadingillustratethe matched-filterstatistic(Γ+)anditsuncertainty(shotnoise + LSSeffect)inpolar coordinates(seealsoExtendedDataFig.2).Thematched-filterstatistic correlateswellwiththemassoverdensity.Throughoutthepaper,weassumeaflat Lambdacolddarkmattercosmologycharacterizedbyh = 0.7and Ωm,0 = 1 − ΩΛ,0 = 0.3.
  • 3. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w claimedasalong(∼18 Mpc)cosmicfilamentonlyundertheassumption thatthefilamentisalignedalongtheLOSdirection.Currently,thereis noevidencesupportingsuchafortuitousalignment.TheMACSJ0717 result is different from that of A222/A223 in that the mass detection extendsfromthemainclustercomprisingtwomergingclusterstothe southeasternX-raygroupseparated18 fromthemainclusterby1.2 Mpc andthenfromtherefurtherstretchestowardsthesouthby2.5 Mpc.As in the A222/A223 system, under the assumption that this mass exten- sion is aligned along the LOS direction, the structure is interpreted as a projection of the 18-Mpc-long cosmic filament. An X-ray-based filamentary structure detection was reported around A2744 (ref. 19). Although these gas structures show signs of correlations with some WLmassandgalaxyoverdensities,theWLmassreconstructionalone does not convincingly reveal the filamentary structure. Currently, no cosmic-webstructuresextendingtensofmegaparsecs,similartothose observedinComa,havebeenreportedinA2744. ThecurrentdiscoveryoftheICFinComahasanimportantimplica- tionforthecosmologicalstudiesbasedonclustermassfunctions.Asin Coma,ifasubstantialfractionofthetotalmassisgenerallycontained in ICFs within a cluster’s virial radius, it becomes imperative to revisit the definition of the cluster mass. In simulations, cluster masses are definedasthetotalmasswithinaspherewithradiuscomputedforthe given density contrast criteria. In observations, typical mass estima- tionisobtainedundertheassumptionthatthedensityprofilefollows an analytic description. Given that neither the simulations nor the observations explicitly account for the ICFs, omitting of these struc- tures in both approaches may introduce non-negligible bias in the estimationofcosmologicalparametersbasedonclustermasses. Methods Feasibility of ICF detection at low-z WLstudiesoflow-redshift(z ≪ 0.1)galaxyclustershavebeenconsidered a difficult task mainly because (1) the lensing efficiency is low and (2) verywide-fieldimagingdataarerequired.Thelatterisnolongeralimit- ingfactorintoday’sera,wheremanywide-fieldinstrumentsareavailable. Theformeriscertainlyaweaknessarisingfromthegeometriceffectof thelow-redshiftlens.However,aswedemonstratebelow,theweakness issignificantlyoutweighedbythehighsignal-to-noiseratio(S/N)dueto alargenumberofsourcegalaxiesperphysicalareaofthelens.Thus,we argue that the Coma cluster WL provides a considerably better oppor- tunityforlow-contraststructuredetectionthanathigherredshift. We define the WL S/N parameter λ as λ = ηβ√n/σLSS , where η is the purity of the source population, n is the physical source number density (number of sources per physical area at the lens redshift), β is the lensing efficiency and σLSS is the noise due to the LSS20 along the LOS direction. The term σLSS decreases with angular scale and thus is smaller at lower redshift because the angular size of the filament is larger. The lensing efficiency is β ≡ ∫ ∞ zl dzdp (z) DlDls/Ds , where p(z) is thesourceredshiftprobabilitydistribution,zl isthelensredshift,Dl is theangulardiameterdistancetothelensandDls/Ds istheratioofangu- lardiameterdistancesfromthelenstothesourceandfromtheobserver to the source. Extended Data Fig. 1 shows that β (red) increases with thelensredshift.TheComalensefficiencyislowernearlybytwoorders of magnitude than the one at zl = 0.5. However, as the lens redshift decreases,thenumberofsourcegalaxiesperphysicalareaatthelens redshiftincreasesquickly.Therefore,thetotallensingS/Nperphysical area of the lens (blue) in fact increases as the lens redshift decreases, becomingthreetimeshigherattheComaredshiftof∼0.023thanthe S/N value at zl = 0.5. One caveat that one can recall in this S/N analysis is the shear calibration. Since the intrinsic lensing signal is weaker at lowerredshift,therequirementfortheresidualshearcalibrationerror shouldbemorestringent. Matched-filterstatistic A matched filter refers to the template (or kernel) that extracts the optimal S/N measurement when it is correlated with the signal. Both theshapeofthesignalandthenoisecharacteristicsareimportantcon- siderationsindesigningthefilter.Inthisstudy,weadopttheformalism presentedbyMaturiandMerten4 . Colberg et al.5 studied the density profiles of filaments from cos- mological simulations and found that filaments have well-defined edges characterized by the scale width hc, inside which the density is approximately constant. Outside the edges, the density drops as h−2 , wherehistheperpendiculardistancefromthe‘ridge’ofthefilament. Adoptingtheresult,Maturi&Merten4 usedthefollowinganalyticform tomodelthefilamentconvergenceprofile: κ (h) = κ0 1 + (h/hc) 2 , (1) where κ0 is the maximum convergence at the ridge. Note that at the characteristic width hc, the density drops to half the maximum 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 193.0° 194.0° 195.0° RA 196.0° 1 Mpc 197.0° 27.0° 28.0° 29.0° 50 100 150 200 250 300 350 θ (deg) Dec. Shear-peak density (arcmin –2 ) 225° 135° 45° 315° 0.07 0.06 0.05 SE W N N W SE Fig.2|Intraclusterfilamentdetectionbasedonshear-peakstatistic.Left, theWLshear-peakmapcreatedwiththe5 × 1012 Mʘ NFWhalofilter.Theinner andouteryellowsolidcirclesrepresentr = 1and2.8 Mpc,respectively.Theblack solidcurveandshadeindicatetheshear-peakdensityanditsuncertaintyin polarcoordinates.Circularblankregionsarethestellarmasks.Right,shear-peak statisticasafunctionofangle.Theblacksolidlinerepresentsthedensityof shearpeaksinarcmin2 andtheshaderepresents1σ uncertaintyfromthePoisson statistics.Dashedhorizontallineistheazimuthalmean.Thenorthernand westernpeaksareinexcellentagreementwiththematched-filterresult(Fig.1).
  • 4. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w convergenceκ0.TheWLshearγinducedbythefilament(equation(1)) isorientedperpendiculartothefilamentaxisandgivenby γ = κ(h). (2) In practice, γ (equation (2)) is obtained from the ellipticities of sourcegalaxies.Assumingthatourcoordinateoriginliesatoneendof the filament and θf is the orientation angle of the filament measured counterclockwisefromthexaxis,γisrelatedtothegalaxies’ellipticity components ϵ1 and ϵ2 via γ = ϵ1 cos [2 (θf − π/2)] + ϵ2 sin [2 (θf − π/2)]. If we let γi be the estimate of γ from the ith source galaxy, our matched-filterstatisticisgivenby Γ = 1 W ∑ i γiΨ (xi, yi) , (3) where Ψ(xi, yi) is the filter (or weight) at the position (xi, yi) of the ith sourcegalaxyandW = ΣiΨ(xi,yi).ThefilterΨisobtainedbyconsidering theexpectedshearsignalofthefilamentandthenoiseduetotheLSS. InFourierspace,theoptimalfilterisgivenasfollows: ̂ Ψ (k) = ̂ τ (k) /Pn (k) , (4) where ̂ τ (k)istheFouriertransformoftheexpectedshearfromthefila- ment (equation (2)) and Pn(k) is the noise power spectrum including the LSS and intrinsic galaxy shape noise. Note that since we let the estimator (equation (3)) include the proper normalization (that is, 1/W),weomitanormalizationconstantinequation(4). In WL, the signal comes from the scalar potential and thus pro- ducesonly‘E-mode’signals.The‘B-mode’signalisobtainedbyrotating galaxyellipticitiesby45°andshouldbeconsistentwithzeroifthereis nosignificantresidualsystematics.Inasimilarfashion,wecandefine the corresponding terms in the matched-filter statistic Γ. Hereafter, weuseΓ+ todenotetheE-modestatisticandrefertoitasthetangential componentandΓ× todenotetheB-modestatisticandrefertoitasthe cross component. Note that the cross component Γ× does not neces- sarily become zero even in the absence of the systematics because anycoherentalignmentofgalaxiestilted45°withrespecttothefilter orientationcanproducenon-zerovalues. Maturi and Merten4 provide the following analytic form for the varianceofΓ(equation(3)): σ2 Γ (θ) = 1 2W2 ∑ i |γi| 2 Ψ2 (xi, yi) . (5) Wefindthatequation(5)doesnotproperlyincludetheLSScontri- butionandleadstoanoverestimationofthefilamentdetectionsignifi- cance.Thus,inthisstudy,weusethepubliclyavailablekappaTNGlight cone (convergence) data (http://columbialensing.org)21 constructed fromthecosmologicalhydro-dynamicalsimulationsIllustrisTNG300-1 (refs. 22–27) to properly estimate the statistical significance of our filament detection. We select the convergence dataset for the source redshift at zs = 0.5, since it is the closest match to the effective source redshift (zeff ≈ 0.7) estimated for the current Coma cluster WL data. Fromthe1005 × 5 degconvergencefields,wegenerated900subfields matching the current Coma field size (∼12 deg2 ). Then, we produced mock shear catalogues at the positions of the Coma source galaxies. Finally, we applied the matched filter to the shear catalogues and estimated the variance at each angle due to the LSS effect. We added the two uncertainties from this LSS contribution and the shot noise 13 h 30 min 00 h 00 min 12 h 30 min +35° +30° +25° +20° RA (J2000) Dec. (J2000) 5 Mpc NGC 4874 NGC 4889 NGC 4839 NGC 4789 SDSS galaxies N SE W −6 −4 −2 0 2 4 6 (cz − czA1656)/(1 + zA1656) (×1,000 km s−1) Fig.4|AlignmentoftheICFswiththelarge-scalefilaments.TheLOSvelocity fromtheSDSSDR16catalogue13 iscolour-coded.Thesymbolsizeisproportional totheSDSS-rbandmagnitude.Thesizeofthefilledblackcircleinthelowerleft cornerrepresentsthebrightnessofNGC4874.Neighbouringgalaxygroups aremarkedwithcyandiamonds.Theblackdashedr = 2.8 Mpccircleindicates theHSCcoveragewhereweperformedWLanalysis.Thelightgreenarrows withinitshowtheorientationsoftheICFsdetectedinthecurrentstudybased onWLsignals.Magentaarrowsindicatetheapproximatecosmic-webfilament directionsdetectedwiththegalaxydistributions6,7 .TheWL-basedICFsarewell alignedwiththegalaxy-basedlarge-scalefilaments. 1.2 1.0 0.6 0.4 0.2 0.01 0.02 hc (Mpc) K0 hc = 0.29+0.05 –0.05 hc = 1.07+0.43 –0.30 hc = 0.10+0.05 –0.04 0.03 0.2 0.6 1.0 0.8 h c (Mpc) N SE W K0 = 0.0168+0.0024 –0.0023 K0 = 0.0080+0.0018 –0.0015 K0 = 0.0188+0.0055 –0.0044 Fig.3|Posteriordistributionsofthefilamentmodelparametersestimated fromtheMarkovChainMonteCarlosampling.Innerandoutercontours representthe68%and95%confidencelimits,respectively.Dashedlinesindicate themedian.Seetextforinterpretation.
  • 5. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w (equation(5))inquadraturetocomputethetotaluncertainty.Extended Data Fig. 2 displays the matched-filter statistic and its uncertainty derivedfromtheComafield. To evaluate the performance of the matched-filter technique for filament detection, we created mock shear catalogues and applied the method. Extended data Fig. 3 shows two examples of the mock test results. In the top panel, we assumed that a Coma-like cluster (M200c = 8 × 1014 Mʘ) at z = 0.02 is placed at the intersection of two fila- mentsat10°and70°withalinearmassdensityofmf = 1.2 × 1014 Mʘ Mpc−1 . These mock simulation setup parameters are deliberately chosen to resemblethepropertiesoftheComaclusteranditsfilaments.Wefind that the matched-filter statistic successfully identifies the two fila- mentsandreachesmaximaatthecorrectorientations.Thecross-shear statistic (Γ×) possesses much lower amplitudes and vanishes at the orientationofthefilament.Inthebottompanel,thesetupisidentical to the one in the top panel, except that another Coma-like cluster at the same redshift is placed at θ = 135° about 1.4 Mpc away from the field centre. This is to test whether the presence of massive halos can masquerade as filaments in our matched-filter statistic. The result shows that although a small bump is detected at θ = 135°, its ampli- tude is substantially lower than the peaks due to the filaments, which illustrates that the matched filter is much more sensitive to the low-density anisotropic linear structure than to the high-density iso- tropicmasspeak.InthetwoexamplesshowninExtendeddataFig.3,we omitted,forillustrativepurposes,thenoiseduetotheintrinsicgalaxy shapedispersionandLSS.Whenweincludethesenoisecontributions, the significance of the bump due to the second galaxy cluster drops belowourdetectionthreshold. Shear-peakstatistic Besides the matched-filter statistic, another useful method for ICF detectionproposedbyMaturiandMerten4 istheshear-peakstatistic. ‘Shearpeaks’referstoprojectedoverdenseregionsinaWLmassmap and their statistic as a function of significance is a powerful probe of cosmological parameters28–33 . High S/N peaks are found at the loca- tions of individual massive clusters, whereas true low S/N peaks are mostlyproducedbytheprojectionofmanylow-masshalosalongthe LOS direction, rather than by single low-mass halos. Because of their low S/N nature, a significant fraction of low S/N shear peaks creates a false positive. Since the presence of ICFs boosts the probability of low S/N shear-peak detection, we can trace the ICF with their count- ing statistic. In this study, we employ an aperture mass filter derived from a truncatedNavarro–Frenk–White(NFW)profiletominimizetheinflu- ence of the LOS LSS. The convergence of the projected NFW profile34 is KNFW (x) = 1/(1 + x) 2 ,where x = 𝜗𝜗/𝜗𝜗s, 𝜗𝜗 istheangularseparationand 𝜗𝜗s is the scale radius. Its tangential-shear profile is approximated as GNFW (x) = 2 ln (1 + x) /x2 − 2/ [x (1 + x)] − 1/(1 + x) 2 ,andattheoutskirts,we applytheGaussiantruncationfunction: G (x) = GNFW (x) exp (−𝜗𝜗 2 /2𝜗𝜗 2 out), where 𝜗𝜗out isthetruncationradius. We treated the mass map produced by this aperture filter as if it wasanastronomicalimageofacrowdedstellarfield.Wedetectedthe shear peaks using SExtractor35 (https://github.com/astromatic/sex- tractor) and measured the number of peaks by azimuthally scanning a pan-shaped region at every degree. The pan-shaped region has an openingangleof30°andcoversaradialextentfrom1 Mpcto2.8 Mpc. WemanuallysetthebackgroundleveltozeroinourSExtratorrun. Datareduction We used Subaru HSC observations in g and r bands. HSC is an 870-megapixel mosaic CCD camera (116 2k × 4k CCDs) with a pixel scale of ∼0.17″ and an approximately 1.5° diameter field of view. The observations were conducted with seven different pointings, which togetherformahexagonalfootprintwithalargestdimensionexceed- ing 4.5°. The radius of the largest complete circle within the mosaic field is approximately 1.9°. The details of the observations are given inSupplementaryTable1. Single-frame processing (overscan, bias, flat, dark and so on) was performed with the HSC Pipeline36 , which was built on the pro- totype pipeline developed for the Rubin Telescope Legacy Survey of SpaceTime.ThepipelinealsoincludesrobustcalibrationoftheWorld CoordinateSystem,whichstorestheastrometricanddistortionsolu- tions in the ‘Simple Imaging Polynomial’ format. Since our WL pipe- line uses the SWarp package (https://www.astromatic.net/software/ swarp/), which only understands the TPV format, we converted the astrometric header of each frame using the sip-to-pv (https://github. com/stargaser/sip_tpv.git) script37 . These calibrated files were com- bined using SWarp to create giant (97k × 91k pixels) mosaic images. We generated two versions of mosaic images. The first version is pro- ducedusingallavailableframesexceptfordefectiveones.Thisproduct providesdeepphotometryandisalsousefulforobjectdetection.The secondmosaiciscreatedfromtheframeswithseeingbetterthan0.85″. Thisimageisoptimizedforgalaxyshapemeasurement.Supplementary Fig. 1 displays the colour-composite image created with these large mosaicimages,withatotaleffectiveareaof∼12deg2 . Objectdetectionandphotometry We ran SExtractor for object detection and photometry. We used the dual-imagemodetoobtainobjectcolourswithconsistentsegmenta- tioninformation.WeprovidedSExtractorwithaweightimagecreated by SWarp for the detection and a root-mean-square error image for the photometry. For object detection, we required objects to satisfy the criteria DETECT_THRESH = 2 and DETECT_MINAREA = 5. We set the deblending parameters with the blending threshold DEBLEND_ NTHRESHof64andtheminimalcontrastDEBLEND_MINCONTof10−4 toidentifytheoverlappingobjects.WeusedMAG_ISOforcolouresti- mation and MAG_AUTO for luminosity measurement. We performed photometriccalibrationusingtheSDSSDR16(ref.13). Sourceselection Weselectsourcegalaxiesasfollows.First,wechooseobjectsbetween 23 < r < 26. Because of the proximity of the Coma cluster, most of the faintgalaxiesinthisselectionarelikelytobebackgroundsources.We donotimposeacolourcut,sincethemembergalaxycontaminationis estimatedtobenegligibleinthismagnituderange.Toconfirmthis,we comparethenumberdensitydistributionsbetweentheComacluster andCOSMOS2020(ref.38)fields(SupplementaryFig.2).Inthelatter, thereisnoComa-likecluster.Therefore,ifourmagnitude-basedsource selectionincludesanon-negligiblefractionoftheComamembers,the Comafieldmustshowanexcessintheselectionwindow.Theexcellent agreementbetweenthetwofieldsverifiesthattheclustergalaxycon- taminationcanindeedbeignoredwithinthesourceselectionwindow. The objects with a half-light radius (rh) smaller than ∼0.5″ are discarded to avoid stellar contamination. Our forward-model shape measurement utilizes the MPFIT39 module, which reports the status and stability of the shape fitting and the ellipticity uncertainty. We only keep the sources with the stable fitting (STATUS = 1) and a small ellipticityuncertainty(<0.4). Some spurious sources cannot be identified with the method described above. They include false detections around bright stars forming concentric circles and unidentified cosmic rays near the field edges. As for the former, we deselect the objects by applying large circular masks on the stars brighter than 13 mag in r band. The spurious objects near the field edges are not included in our final source catalogue because we reject the sources with distances of r > 2.8 Mpc from the Coma cluster centre. We note that there are no spurious objects on the edges of the six flanking fields facing toward the cluster centre because the regions overlap the central and other flankingfields.Thenumberdensityinthefinalsourcecatalogueis∼38 arcmin−2 . Since it is impossible to derive photometric redshifts from
  • 6. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w onlytwofilters,weutilizethepubliclyavailableGOODS-Sphotometric redshift catalogue40 to estimate the effective redshift of the source population. After applying the same source selection criteria to the GOODS-S photometric redshift catalogue and taking into account the difference in image depth, we determine the effective source redshift to be zeff = 0.72. Because of the proximity of the Coma clus- ter, the critical surface density is not sensitive to the source redshift. For example, even if we assume zeff = 1, the critical surface density changes by approximately 1%. Shearmeasurement We measured galaxy shapes from the mosaic image. This requires us to model the point-spread-function (PSF) for each CCD frame per exposure and to carefully propagate the PSF model at the loca- tion of the galaxy on the coadd. The PSF model for each CCD frame was constructed through Principal Component Analysis based on the observed stars and polynomial interpolation41,42 . At each galaxy location, we first identify all contributing frames and then stack their PSF models after applying due rotations. This PSF modelling scheme enables us to capture the sophisticated PSF variation pat- terns across the mosaic image, including sudden discontinuities at the CCD boundaries. The PSF residual (the observed star ellipticity minus the model PSF ellipticity) correlation function shows that the correlation amplitude is below 10−6 on angular scales greater than 1′ (left panel of Supplementary Fig. 3). Once we obtain a secure PSF model at the location of a source galaxy,weconvolveanellipticalGaussianfunctionwiththePSFandfit theresultingprofiletotheobject43–47 .SincethePSF-convolvedelliptical Gaussian profile differs from the observed galaxy profile, model bias occurs.Inaddition,theellipticitymeasurementbasedonthemaximum likelihood is biased because of the non-linear relation between pixel noiseandshear,oftentermed‘noisebias’.Asignificantfractionofgal- axiesisaffectedbyblendingeffects48 .Toaddressthemixtureofthese sourcesofshearmeasurementbias,weuseimagesimulationsandcom- pareinput(true)shearswithoutput(measured)shears.Thesimulation showsthattheadditivefactor,whichmainlyarisesfromanimperfect PSF model, is negligible. We find that the star-galaxy ellipticity cross correlation is at the 10−6 level on angular scales greater than 10′ (right panel of Supplementary Fig. 3). Both the PSF residual and star-galaxy correlationdiagnosticsverifythattheresidualWLsystematicerroris negligible.TheWLpipelineweemployedhereparticipatedinthethird Gravitational Lensing Accuracy Testing challenge49 and was publicly validatedtobeoneofthebest-performingmethodsinthisblindtest. Dataavailability TherawSubaruHSCimagingdatausedforthecurrentstudyarepub- licly available. The processed mosaic images and data points in the article figures are available on request from the authors. Source data areprovidedwiththispaper. Codeavailability Our custom data processing codes are available on request from the authors. References 1. Cautun, M., van de Weygaert, R., Jones, B. J. T. & Frenk, C. S. Evolution of the cosmic web. Mon. Not. R. Astron. Soc. 441, 2923–2973 (2014). 2. Kuchner, U. et al. Mapping and characterization of cosmic filaments in galaxy cluster outskirts: strategies and forecasts for observations from simulations. Mon. Not. R. Astron. Soc. 494, 5473–5491 (2020). 3. Rost, A. et al. The ThreeHundred: the structure and properties of cosmic filaments in the outskirts of galaxy clusters. Mon. Not. R. Astron. Soc. 502, 714–727 (2021). 4. Maturi, M. & Merten, J. Weak-lensing detection of intracluster filaments with ground-based data. Astron. Astrophys. 559, A112 (2013). 5. Colberg, J. M., Krughoff, K. S. & Connolly, A. J. Intercluster filaments in a ΛCDM Universe. Mon. Not. R. Astron. Soc. 359, 272–282 (2005). 6. Mahajan, S., Singh, A. & Shobhana, D. Ultraviolet and optical view of galaxies in the Coma supercluster. Mon. Not. R. Astron. Soc. 487, 4336–4347 (2018). 7. Malavasi, N. et al. Like a spider in its web: a study of the large-scale structure around the Coma cluster. Astron. Astrophys. 634, A30 (2020). 8. Williams, B. A. & Kerr, F. J. The distribution of the spiral galaxies in the direction of the Coma/A 1367 supercluster. Astron. J. 86, 953–980 (1981). 9. Fontanelli, P. The Coma/A1367 filament of galaxies. Astron. 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Kaiser, N. & Squires, G. Mapping the dark matter with weak gravitational lensing. Astrophys. J. 404, 441 (1993). Acknowledgements M.J.J. acknowledges support for the current research from the National Research Foundation (NRF) of Korea under the programmes 2022R1A2C1003130 and RS-2023-00219959. Authorcontributions K.H. reduced the data, measured WL signals and filaments and wrote the manuscript. M.J.J. designed the research, created the reduction pipeline, coded the filament detection filter and wrote the manuscript. S.C. provided the mass reconstruction based on a convolutional neural network. H.C. identified the filaments based on the Coma galaxy distribution. Competinginterests The authors declare no competing interests. Additionalinformation Extended data is available for this paper at https://doi.org/10.1038/s41550-023-02164-w. Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41550-023-02164-w. Correspondence and requests for materialsshould be addressed to M. James Jee. Peer review information Nature Astronomy thanks Smriti Mahajan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Reprints and permissions informationis available at www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. © The Author(s), under exclusive licence to Springer Nature Limited 2024
  • 8. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w ExtendedDataFig.1|WLS/Nperphysicalareavariationwiththelens redshift.Redsolidlineisthelensingefficiencyβ.BluesolidlineistheWLS/Nper physicalarea(λ)normalizedbythevalueat z = 0.5.Whilethelensingefficiency isreducedapproximatelytwoordersofmagnitudeasthelensredshiftdecreases fromz=0.5totheComaredshift(z=0.023),thenetWLS/Nperphysicalareaat thelensredshiftincreasesapproximatelybyafactorofthree.Thisnetgainisdue tothecombinedeffectofthehigherscoredensity nandlowerLSSnoise σLSS per physicalareaattheComaredshift.Hereweassumethatthepurity η isthesame acrossthelensredshift.Infact, η isalsoexpectedtobehigherattheComa redshiftbecauseoftheproximity.
  • 10. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w ExtendedDataFig.3|Matched-filterdetectionwithamockfilament-cluster configuration.TopLeft:MockconvergencemapwithtwofilamentsandanNFW halodisplayedinlogscale.Mockfilamentsareorientedat10°and70°withan NFWhaloatthecentre.Thelinearmassdensityofthefilamentmf =1.2×1014 M☉Mpc−1 andthehalomassM200 =8×1014 M⊙ aremotivatedbyourmeasurements inComa.WhiskersshowtheresultingWLshear.Innerandouteryellowcircles indicater = 1and2.8Mpc,respectively.TopRight:Black(red)solidlineindicates thetangential(cross)-component Γ+(Γ×).Thetangential-shearcomponentis alsoshownintheleftpanel(blacksolid)inpolarcoordinates.Bottom:Sameas thetoppanelsexceptthatanotherM200 =8×1014 M⊙ haloisplaced(whitearrow) atθ=120°,∼1.2Mpcapartfromthecentre.Thetangentialcomponent Γ+ is sensitivetothefilamentarymassstructureandpeaksatthecorrectangles. Althoughtheoff-centrehalogivesrisetoasmallpeakatθ=120°,itsheightis muchweakerthanthosearisingfromtherealfilamentarystructures.Herewe showtheversionthatdoesnotincludeintrinsicshapenoiseforillustration purposes.Withtheinclusionoftheshapenoise,thetangential-componentpeak duetothehaloisbelowourdetectionthreshold.
  • 11. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02164-w Extended Data Table 1 | Physical Properties of the Intracluster Filaments