Friends-of-friends galaxy group finder with membership refinement. Application to the local Universe

2.1 MB·

by  E. Tempel

Astronomy&Astrophysicsmanuscriptno.tempel (cid:13)cESO2016
January20,2016
Friends-of-friends galaxy group finder with membership refinement
Application to the local Universe
E.Tempel1,R.Kipper1,2,A.Tamm1,M.Gramann1,M.Einasto1,T.Sepp1,2,andT.Tuvikene1
1 TartuObservatory,Observatooriumi1,61602Tõravere,Estonia
e-mail:[email protected]
2 InstituteofPhysics,UniversityofTartu,Ravila14c,51010Tartu,Estonia
6 ABSTRACT
1
0 Context.Groupsformthemostabundantclassofgalaxysystems.Theyactastheprincipaldriversofgalaxyevolutionandcanbeused
2 astracersofthelarge-scalestructureandtheunderlyingcosmology.However,thedetectionofgalaxygroupsfromgalaxyredshift
surveydataishamperedbyseveralobservationallimitations.
n
Aims. We improve the widely used friends-of-friends (FoF) group finding algorithm with membership refinement procedures and
a
applythemethodtoacombineddatasetofgalaxiesinthelocalUniverse.Amajoraimoftherefinementistodetectsubgroupswithin
J
theFoFgroups,enablingamorereliablesuppressionofthefingers-of-Godeffect.
9
Methods.TheFoFalgorithmisoftensuspectedofleavingsubsystemsofgroupsandclustersundetected.Weusedagalaxysample
1 builtofthe2MRS,CF2,and2M++surveydatacomprisingnearly80000galaxieswithinthelocalvolumeof430Mpcradiusto

detect FoF groups. We conducted a multimodality check on the detected groups in search for subgroups. We furthermore refined
]
group membership using the group virial radius and escape velocity to expose unbound galaxies. We used the virial theorem to
O
estimategroupmasses.
C Results.Theanalysisresultsinacatalogueof6282galaxygroupsinthe2MRSsamplewithtwoormoremembers,togetherwiththeir
. massestimates.AbouthalfoftheinitialFoFgroupswithtenormoremembersweresplitintosmallersystemswiththemultimodality
h
check.Aninterestingcomparisontoourdetectedgroupsisprovidedbyanothergroupcataloguethatisbasedonsimilardatabuta
p completelydifferentmethodology.Twothirdsofthegroupsareidenticalorverysimilar.Differencesmostlyconcernthesmallestand
-
o largestoftheseothergroups,theformersometimesmissingandthelatterbeingdividedintosubsystemsinourcatalogue.
r
Keywords. catalogs–galaxies:groups:general–large-scalestructureoftheUniverse–methods:dataanalysis
t
s
a
[
1. Introduction threeareprovidedbyredshiftsurveys.Mostimportantly,redshift
2
measurements cannot distinguish peculiar motions of galaxies
vGalaxiesmayresideinanextraordinaryvarietyofenvironments
from their drift along the Hubble flow. The resulting stretching
7ofdifferentscaleandnature.Moreover,agalaxycanbeembed- ofgalaxygroupsintheredshiftspace,thefingers-of-Godeffect1,
1dedindifferentenvironmenttypesatthesametime–considera makes it difficult to mark group boundaries in the radial direc-
1
pairofgalaxies,eachwithitssatellitesystem,inhabitingalarge-
1 tion.
scalefilamentwithinasupercluster.
0 Over the years, the community has developed an arsenal of
. Theexactdefinitionforagalaxygrouporacluster(weuse algorithmstoovercometheincompletenessofdataforgroupde-
1
theterm‘group’forboththroughout)tendstovaryfromauthor tection,which,inonewayoranother,makeassumptionsabout
0
toauthorand,evenworse,fromsystemtosystem.Nevertheless, thegravitationalpotentialandthe3Dshapeofgroups.Oldetal.
6
1wecantakeitforgrantedthatthegroupistheprimarylevelof (2014,2015)comparedtheperformanceofmanyofthesemeth-
:environmentforanygivengalaxyandhasthemostdirecteffect odsonmockobservationaldata.Atrivialbutnonethelessimpor-
vontheevolutionofthegalaxy.Italsoisthemainreceiveroffeed- tantconclusionwasmade:therecoveryofgrouppropertiesmost
Xiback from the galaxy’s gravitational potential, radiation, galac- criticallydependsontheaccuracyofmembershipdetermination.
ticwinds,AGNjets,etc.Thismutualrelationshipsuggeststhat
From the scientific point of view, registries of galaxy sys-
r
agalaxygroupcataloguesprovideanindispensabletoolforstudy- tems in the local Universe are of particular importance. In our
inggalaxyevolution.Ontheotherhand,galaxygroupsandclus-
cosmological neighbourhood, fainter and smaller galaxies are
tersarethelargestgravitationallyboundsystems(bythetypical
visible, more and higher quality data are available for any fur-
definition)andaretracersandcharacterisersofthecosmicweb
theranalysis,redshift-independentdistanceestimatorsareavail-
ofvoids,sheets,filaments,andsuperclusters.Therefore,galaxy
able for many sources, etc. The Two Micron All Sky Survey
groupcataloguesessentiallyprovidehandymeansforestimating
and its extensions (2MASS; Jarrett et al. 2000; Skrutskie et al.
various cosmological parameters, their evolution and interrela- 2006; Lavaux & Hudson 2011; Huchra et al. 2012) offer a so
tion,andforvalidatingcosmologicalsimulations.
far unrivalled dataset of galaxies in the local Universe that al-
The problem is that no straightforward procedure exists for
determining a galaxy group from observational data. Out of 1 The term coined at the IAU Symposium 79 in 1977 in Tallinn by
the six real- and velocity-space coordinates required to decide Tully & Fisher (1978); the effect itself was first noted by Jackson
whetheragalaxydoesordoesnotbelongtoagivengroup,only (1972).
Articlenumber,page1of10
A&Aproofs:manuscriptno.tempel
��� redshiftz=0...0.1(upto430Mpc).Thisselectionrestrictsour
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whichcombineselementsfromthe2MRS,the6DFGalaxySur-
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�� �� ��� ��� ��� vey(Jonesetal.2009),andtheSloanDigitalSkySurvey(York
�������� et al. 2000). Of the 64745 galaxies of the 2M++, we added
Fig. 1. Observed magnitude distribution for 2MRS, CF2, and 2M++ 31271galaxies3 downtoKs <12.54,whichextendsthesample
datasets in our final galaxy sample. Here, only those CF2 and 2M++ wellbeyondthe2MRSmagnitudelimit.
galaxiesareconsideredthatarenotpresentinthe2MRScatalogue.The Our final galaxy dataset includes 78378 galaxies. The ob-
correspondingnumbersareshowninthelegend. served magnitude distribution for the 2MRS, CF2, and 2M++
subsamples is shown in Fig. 1. The dataset is incomplete for
galaxies with K > 11.75. This should be taken into account
s
lows cataloguing galaxies across most of the celestial sphere. when strictly flux- or volume-limited samples are needed (e.g.
Using these data, Kochanek et al. (2003) compiled a catalogue for constructing galaxy luminosity functions or calculating the
ofgalaxyclustersusingthe‘matched-filter’algorithm,inwhich luminosity density field). The incompleteness is not a serious
clusters are identified as overdensities with respect to a back- problem in the catalogue construction because the member-
grounddistribution.Daietal.(2007)appliedthesamealgorithm ship was individually refined for each group (see Sect. 3.2).
tocompileacatalogueofgalaxyclustersandstudytheirX-ray Moreover, the dataset is not complete for the nearby Universe,
properties and baryon fractions (Dai et al. 2010), while Crook where many dwarf galaxies cross the magnitude threshold, but
etal.(2007)andLavaux&Hudson(2011)appliedvariationsof are missed by the 2MASS survey because of their low surface
thepopular‘friends-of-friends’(FoF)algorithmtodetectgalaxy brightness(Karachentsevetal.2013).Thebestgroupcatalogue
groups.Díaz-Giménezetal.(2012)presentedaphotometriccat- forthenearby(d (cid:46) 40Mpc)Universeisprobablytheonecon-
alogueofcompactgroupsof2MASSgalaxiesandstudiedtheir structedbyMakarov&Karachentsev(2011).
properties, especially the properties of their first-ranked galax- Figure2showsthedistributionofgalaxiesintheplaneofthe
ies.Mostrecently,Lavaux&Jasche(2016)usedaBayesianap- sky. While the CF2 and 2MRS galaxies are distributed all over
proach to extract structures from the galaxy distribution, while the sky, those of the 2M++ are not. The completeness of the
Tully (2015a) introduced the power of scaling relations to con- 2M++ sample is fully described in Lavaux & Hudson (2011).
straingalaxygroupsandappliediton2MASSgalaxiestocon- Figure3showstheluminositiesofgalaxiesandtherelativecon-
structagroupcatalogue(Tully2015b). tributionsbythe2MRS,CF2,and2M++subsamplesasafunc-
In this paper, we present a catalogue of galaxy groups in tion of distance. The 2MRS provides the bulk of the galaxies
the nearby Universe. The groups and clusters have been recov- inthenearbyregionandissupplementedbytheCF2,whilethe
ered by applying the FoF method, improved according to the 2M++ becomes dominant farther away. These two catalogues
lessons learned from studies of the substructure of groups with combinedprovidearepresentativegalaxysampleupto400Mpc.
the mclust package (Einasto et al. 2010, 2012; Ribeiro et al. Withahighernumberdensityofgalaxieswegainmorereliable
2013). Our product is mainly based on the 2MASS Redshift groupswithmorereliableproperties,whichmeansabetterinput
Survey. This enables a straight comparison with the latest cat- for any subsequent analysis. For example, we intended to use
alogues that rely on the same data, but are fundamentally dif- the prepared dataset to extract galaxy filaments from the local
ferent group detection principles. In addition to cross-checking UniverseusingtheBisousmodel(Tempeletal.2014a).Forthe
the group finder algorithms, this comparison also allows us to filamentdetection,ahighnumberdensityofgalaxiesispreferred
characterisethe2MASSdataasabasisforgalaxygroupstudies. whilethevaryingcompletenessintheskyisnotaconcern.
Throughout this paper we assume the Planck cosmology Considering the above, the group construction and the re-
(Planck Collaboration et al. 2015): the Hubble constant H0 = sultingcataloguearepresentedseparatelyfortwocases:thefull
67.8kms−1Mpc−1,thematterdensityΩm =0.308,andthedark dataset and the pure 2MRS, the latter being more suitable for
energydensityΩΛ =0.692. studieswherecompletenessisofcriticalimportance.
2. Galaxydata 3. Groupdetectionandmembershiprefinement
TodelineategalaxygroupsinthelocalUniverse,weusedgalaxy 3.1. Conventionalfriends-of-friendsgroupfinder
datafromtheextragalacticdistancedatabase(EDD2;Tullyetal.
One of the simplest and therefore most widely used algorithms
2009). The sample encompasses three datasets. As the main
for group detection is the FoF percolation method5, as first re-
source,weusedtheTwoMicronAllSkySurvey(Skrutskieetal.
ported by Turner & Gott (1976), Huchra & Geller (1982), and
2006) Redshift Survey (2MRS) galaxies brighter than 11.75
magnitudes in the Ks band (for a description of the catalogue, 3 The actual number at the time of our download; the original paper
seeHuchraetal.2012).Weonlyusedgalaxiesthataresecurely givesadifferentnumber.
offtheGalacticplane:Galacticlatitude|b|>5◦.Sincethegalaxy 4 Wenotethatthe2M++magnitudesaredefinedslightlydifferently
sample becomes extremely sparse farther away, we only used from the 2MRS magnitudes (see Lavaux & Hudson 2011, for de-
galaxieswithacosmicmicrowavebackground(CMB)corrected tails). Fortunately, our group construction algorithm does not depend
ongalaxyluminosities.
2 http://edd.ifa.hawaii.edu. 5 Alsoknownassingle-linkageclusteringamongstatisticians.
Articlenumber,page2of10
E.Tempeletal.:Friends-of-friendsgalaxygroupfinderwithmembershiprefinement
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Fig.4.Meanseparationbetweengalaxiesintheplaneofthesky(thick
lines)andin3Dspace(thinlines)asfunctionsofredshift.Tofindthe
skyprojectiondistances,thenearestneighbourwassoughtwithinavol-
umedefinedbythefixedlinkinglengthratiosoftheFoFalgorithm(see
textfordetails).Dashedlinescorrespondtothewholesample,dotted
lines to the 2MRS galaxies alone. Solid blue line shows the transver-
sallinkinglengthasusedinourgroupfindingalgorithm.Inthenearby
Fig. 2. Sky distribution of galaxies in the 2MRS, CF2, and 2M++
region,thetransversallinkinglengthisroughly0.1timesthemeansep-
datasets.OftheCF2and2M++datasets,onlygalaxiesnotpresentin
arationofgalaxiesofthegivensamples.Wenotethatthegalaxysample
the2MRScatalogueareshown.SeeFig.3inLavaux&Hudson(2011) reachesredshiftz=0.1;forillustrativereasons,thefigureonlypresents
fortheskycoverageinthe2M++dataset.
thenearerpart.
Tempeletal.(2014b)proposedthatforredshift-basedcata-
logues,thelinkinglengthshouldbecalibratedaccordingtothe
meandistancetothenearestgalaxy(i.e.themeanseparation)in
theplaneofthesky.Thedistanceshouldbemeasuredconsider-
ingthenearest(inskyprojection)neighbourwithinacylindrical
volumedefinedbythesamefixedb /b ratioasusedinthesub-
|| ⊥
sequentFoFanalysis.
Figure4showsthatthemeandistancetothenearestgalaxy
in the plane of the sky corresponds well to the actual 3D mean
separationbetweengalaxies.However,theactual3Dseparation
cannotbedirectlyusedtocalibratethelinkinglengthbecauseof
Fig.3.Galaxyabsolutemagnitudeasafunctionofdistancein2MRS, redshift space distortions. To overcome this problem, distances
CF2, and 2M++ datasets. Here, the CF2 and 2M++ datasets include in the radial direction need to be multiplied by the same b||/b⊥
onlygalaxiesthatarenotpresentin2MRScatalogue.Solidlinesshow ratio as is used for FoF analysis during the calculation of the
thefractionofgalaxiesinthecompletesampleasafunctionofdistance. meanseparation.Theresultwouldbeeffectivelyidenticaltoour
currentapproach.
For flux-limited surveys, the FoF linking length should in-
Zeldovich et al. (1982). We used the FoF method previously to crease with distance because fainter galaxies are not detected
detectgalaxygroupsfromSDSSredshift-spacecatalogues(Tago fartheraway.Tempeletal.(2014b)scaledthelinkinglengthac-
etal.2008,2010;Tempeletal.2012,2014b). cordingtonearbygroupsandfoundacorrectionfunctiontotake
Recently,Oldetal.(2014,2015)inspectedindetailtheabil- thedroppingoutoffaintergroupmemberswithincreasingdis-
ity of various group detection algorithms to recover the actual tanceintoaccount.Thisscalingwithdistanceiswellexpressed
groupsandgroupmassesusingsimulatedgalaxycatalogues.The with an arctangent law. For the current sample the dependence
resultsindicatedthatusingthestandardcalibrationforthelink- of the linking length (in the transversal direction) on z can be
inglength(seebelow),theFoFmethodrecoversgalaxygroups expressedas
reasonablywell.
WhentheFoFmethodisappliedtoredshift-spacecatalogues b⊥(z) =0.25[1+5arctan(z/0.05)], (1)
of galaxies, the only free parameters are the linking lengths in Mpc
radial (b , along the line of sight) and in transversal (b , in
|| ⊥
the plane of the sky) directions. These linking lengths are of- which is also plotted in Fig. 4. We used the linking length in
tencalibratedaccordingtosimulations(seee.g.Ekeetal.2004; physical and not in comoving units. However, the difference is
Robothametal.2011);valuesclosetob ≈ 0.1andb ≈ 1.0in negligibleforthegivenredshiftrange.
⊥ ||
unitsofmeanseparationbetweengalaxiesaretypicallyused.A This scaling correlates very well with the mean separation
detailedanalysisofhowlinkinglengthvaluesaffectthedetected up to redshift 0.04 (see Fig. 4), while farther away the mean
galaxygroupshasbeenconductedbyDuarte&Mamon(2014). separationincreasesfasterthanthearctanlaw.Thediscrepancy
Theysuggestedthatb ≈ 0.07andb ≈ 1.1(orevenhigherin emergeswhenalltheothermembersofthegroupremainunde-
⊥ ||
radialdirections,dependingonthegoalofthestudy)shouldbe tected as a result of the flux limit, and for a given galaxy, the
used. nearestgalaxyisfoundfromsomeneighbouringgroup.
Articlenumber,page3of10
A&Aproofs:manuscriptno.tempel
Compared to Duarte & Mamon (2014), our linking length
1
intransversaldirectionsisslightlyhigher(0.1vs0.07timesthe
mean separation up to redshift 0.04). Nevertheless, we contin-
ued to use our value for the following reasons: it has worked
well in our previous catalogues and in the comparison project f5
0.
(Old et al. 2014, 2015); we conducted a subsequent member-
shiprefinement;andfollowingDuarte&Mamon(2014),wecan
concludethatatthegivenlevel,theeffectoflinkinglengthdif-
ferencesontheresultsaremarginal. 0
10 20 30 40 50 60
The remaining question in our FoF method implementation Simulated group richness
isthechoiceoftheradiallinkinglengthb .Sofar,noclear-cut
||
recipeexists.Withtoolowavaluewewouldmissgroupmem- Fig. 5. Fraction of correct unimodality detections in intrinsically uni-
modal Gaussian mock groups as a function of group richness. For
bers with high peculiar velocities and thus also underestimate
groups with 8–20 members, the mclust algorithm returns an incorrect
groupmasses.Toohighavaluewouldcontaminatethedetected
multimodalitydetectioninabout10–20%ofthecases.
groups with outliers and merge separate groups. In our previ-
ouspapers,wehavefoundthebalanceusingb /b = 10,while
|| ⊥
forexampleDuarte&Mamon(2014)proposedthatb /b ≈16
|| ⊥ numberofsubgroupsandusingtheEM(expectationmaximisa-
or even higher should be used. In the following, we conserva-
tion)algorithm,mclust findsthemostprobablelocations,sizes,
tivelyraiseourpreviouslyusedvaluetob /b =12togainmore
|| ⊥ and shapes for each subgroup. Additionally, mclust gives the
groupmembersintheradialdirection.Apotentialcontamination
probabilityofeachgalaxyofbeingwithineachsubgroup.Inthe
would be reduced later with the membership refinement proce-
end, each galaxy is assigned to a single group according to the
dure.
highestprobability.Weonlyappliedthemclustanalysisonsys-
Afurthercomplicationwiththelinkinglengthisthatinprin-
temswithatleastsevengalaxies.
ciple,itdependsontheunderlyingenvironmentdensity(seee.g.
Sinceingalaxyredshiftsurveys,groupsarenotsphericalbut
Eke et al. 2004; Robotham et al. 2011). However, because the elongatedalongthelineofsightduetotheFoGeffect,wefixed
dependency is weak and can thus only slightly affect the FoF
oneaxiswiththelineofsightduringtheclusteringanalysis.The
group detection, we did not adjust the linking length according
othertwoaxesweresetperpendicularwiththelineofsightand
todensity,butreliedonthemembershiprefinementinthisaspect
eachother,whiletheorientationintheskyplanewasleftfree.
aswell.
We ran mclust with different expected numbers of subsys-
Figure4showsthatthemeanseparationisroughlythesame
tems (from one to ten) to determine the most probable value.
for2MRSandthewholedatasetuptoredshift0.04.Hence,we
ThelatterwasthenchosenusingtheBayesianinformationcrite-
canuse thesame FoFlinkinglength valuesand scalingin both
rion(BIC),whichiswidelyusedinstatisticsandisimplemented
cases.
inthemclustpackage.
TheclusteringalgorithmwasappliedoneachFoFgroupsep-
3.2. Friends-of-friendsgroupmemberrefinement arately. If the algorithm detected subcomponents, we ran the
same algorithm on each subcomponent to test whether even
TheconventionalFoFgroupfinderissimpleandworksreason-
moresubstructurecouldbefound.Inmostcases,thefirstrunwas
ablywellinmostsituations,butitalsohasitsdrawbacks.Iftwo
sufficient;amoredetailedanalysisonlyaffectslargeFoFclusters
groupsaremergingortheysimplyhappentolietooclosetoeach
wheretheinstantdetectionofsubsystemsiscomplicated.
other,theFoFalgorithmmaydetectthemasasinglesystem.Ad-
The multimodality analysis might detect subgroups as a re-
ditionally, FoF groups can become “hairy”, meaning that near
sultofpurespatialcoincidenceofgalaxies,especiallyinsmaller
theouteredgesofgroupsthesurroundingfieldgalaxiesarecon-
groups. To estimate the level of this uncertainty, we performed
sideredasgroupmembers.Galaxyfilamentsconnectedtogroups
the following test. For each group richness, we generated 1000
canalsobemistakenforgroupmembersbytheFoFalgorithm.
Gaussiangroupswhosedistributionwaselongatedalongoneco-
As pointed out by Old et al. (2014, 2015), even a simple
ordinateaxistomimictheFoGeffect.Foreachsimulatedgroup
membershiprefinementafteraninitialFoFgroupdetectioncan
we ran the mclust algorithm as we did for the observed sample
significantlyenhancethereliabilityofthegroups.Herewecon-
andestimatedthefractionoffalsedetectionsofmultimodalsys-
ductedtherefinementintwosteps.First,weusedamultimodal-
tems. The results are shown in Fig. 5. For systems with about
ity analysis (see Sect. 3.2.1) to detect multi-component groups
ten membergalaxies, the falsedetection rate isthe highest, be-
andtosplitthemintoindependentsystems.Second,weusedes-
ingaround20%.Forgroupswith20membersormore,thisfrac-
timates of the virial radius and the escape velocity to exclude
tion falls below 10%. This estimate agrees with the one made
group members that are not physically bound to groups (see
byRibeiroetal.(2013).Wethereforeconcludethatcomparedto
Sect.3.2.2).
the expected observational selection effects, the additional un-
certainty of group membership arising from the multimodality
3.2.1. Grouprefinementusingmultimodalityanalysis checkissmall.
To check the multimodality of groups found by the FoF algo-
rithm, we used a model-based clustering analysis assuming a 3.2.2. Groupmembershiprefinementusingvirialradiusand
Gaussiandistributionforthenumberdensityofgroupmembers. escapevelocity
Themethodisimplementedinthestatisticalcomputingenviron-
ment R6 in the package mclust (Fraley & Raftery 2002; Fraley Asthefinalstepinourgroupconstruction,weremovedallgalax-
et al. 2012). For the clustering analysis we fixed the expected iesthatwereapparentlynotboundtothesystems,eitheraccord-
ing to the virial radius or to the escape velocity of the group.
6 https://www.r-project.org. Thus a galaxy was excluded from its group if its distance from
Articlenumber,page4of10
E.Tempeletal.:Friends-of-friendsgalaxygroupfinderwithmembershiprefinement
l
l l l
l 0
l l l 5 l
- l ll l l
l l
Dec (deg)13 ll ll l ll lll l l Dec (deg)52 lllllllllllllllllllllllllllllllllll l Fabshnyigodw.trh6ineg.hinEFt-xohRaFaAmn-dapDllpgeeaoconrif(etuhltspwm,por.eergsGpapaelaalcnaxtxieyvlyseg)lrypoa)onuasdpistsirdoe(eindntssehcleitafefrttde--
Dec (lower panels) coordinates. The conven-
-
l tionalFoFmethodseesbothsystemsassingle
131 131.5 132 132.5 133 211 212 213 214 groups, while the multimodality analysis has
l l splitthemintosubsystems,indicatedwithdif-
ferentcolours(seeSect.3.2.1fordetails).Grey
redshift0.0350.04 lll llllllllll l ll ll l ll redshift0.050.06 ll ll l l lllllllllllllllllllll llll ctdaeworslusiortaeshinxsnshypetgholssaewtuhirnobeeettpshhdfiyraeensitrstnaseetlmShnbgeety;rcotgbtthu.haleu3plesae.ex2mini.sg2eeiutas.miblaTagtblxhhreFioaereotusrshFpidwgiopdhiesetrrn-teecheofiocartnetnnibemnodmeenoplcoevabtnneenetgdd--,
l l cause of the two central galaxies, which were
0.03 l ll llllll iTdheentfiifigeudreasiloluustltireartsesinththaetsmubesmebqeuresnhtipanraelfiysnies-.
131 131.5 132 132.5 133 211 212 213 214 ment may be of critical importance for richer
RA (deg) RA (deg) groupsdetectedwithFoFalgorithm.
the group centre in the plane of the sky was greater than the 1 ll ll
ll
virial radius. The group centre was calculated as the geometri- ll ll
8
calcentreofallgalaxiesinthegroupwithoutanyluminosityor 0. ll
ll
massweighting.Asthevirialradiuswetookr200,theradiusof 0.6 ll ll
a sphere in which the mean matter density is 200 times higher f
4
thanthemeanoftheUniverse.Thevalueofr isentirelyde- 0. ll
200
terminedbythevirialmass,whichweestimatedusingthevirial 0.2 ll
theoremassuminganNFWmassdensityprofileasdescribedin ll ll
0 ll ll ll
Tempeletal.(2014b)andinAppendixB.Inbrief,weusedthe
2 5 10 50 100
velocitydispersionandtheprojectedgravitationalradiustoesti- Group richness
mateagroup’smassviathevirialtheorem.Themassestimation
is thus fully described by the theory and does not require any Fig.7.Fractionofgroupsthatweresplitintomultiplecomponentsdur-
inggroupmembershiprefinement,shownasafunctionoftheinitialFoF
scalingparameters.Theunderlyingcalculationsofgroupveloc-
grouprichness.
itydispersionsandsizesintheplaneoftheskyaredescribedin
AppendixB.
Similarly,agalaxywasremovedfromitsgroupiftheveloc-
and membership refinement procedure on the excluded mem-
ityofthegalaxywithrespecttothegroupcentrewashigherthan
bers.Withthisiterativeapproach,wedetectedsmallgroupsthat
theescapevelocityatitssky-projecteddistancefromthegroup
hadremainedundetectedduringthemultimodalityanalysis,but
centre.Theescapevelocityofagrouprelatestothegravitational
were revealed during the membership refinement according to
potentialΦthrough
thevirialradiusandescapevelocity.
v2 (r)=−2Φ(r), (2)
esc
4. Groupfinderinaction
where r is distance from the group centre. Gravitational poten-
tial is directly related to the assumed dark matter density pro- Now we applied the galaxy group construction algorithm ex-
file(seee.g.Łokas&Mamon2001).Wenotethatourapproach plained in the previous section to galaxy redshift surveys of
is conservative: the sky-projected distance generally underesti- thelocalUniverse.Weconstructedgalaxygroupsseparatelyfor
matesthe3Ddistance,thuswetendtooverestimatetheescape two datasets: the 2MRS and the combined 2MRS, CF2, 2M++
velocity,leavingsomeoutliersinthegroupratherthanremoving datasets, detecting 6282 and 12106 groups, respectively, with
realmembers. two or more members. Since the combined dataset is roughly
Thememberrefinementforgroupswasdoneiterativelysince twiceaslargeasthe2MRSdataset,thesimilardifferenceofthe
thegroupvelocitydispersionandsizeobviouslydependonthe numberofthedetectedgroupsisexpected.Thefractionofgalax-
groupmembership.Formostofthegroups,therefinementcon- iesingroupsinthe2MRSaloneandinthecombineddatasetis
vergedafterafewiterations.Sincegroupmassescannotbeesti- 45%and50%,respectively.Adescriptionofthecorresponding
matedforsmallgroups,weappliedtheoutlierdetectiononlyon groupcataloguesisgiveninAppendixA.
groupswithatleastfivemembergalaxies. In general, the FoF method is reliable (see e.g. Old et al.
Insomecasestheexcludedmembersformseparatecompact 2014, 2015) and statistically, further refinement affects a rela-
systemsofafewmembersattheboundariesoflargergroups.To tivelysmallfractionofgroups.OftheinitialFoFgroups,roughly
detectthesesystemsasgroups,wereranthefullgroupdetection 2% were detected as multi-component systems in the given
Articlenumber,page5of10
A&Aproofs:manuscriptno.tempel
Fig. 8. Upper panel: galaxy group richness (number of galaxies in a
group) as a function of redshift. Lower panel: redshift distribution of
groupsforthe2MRSsampleandforthecombineddataset.Thelackof
richergroupsfartherawayisduetothefluxlimitofthedata.
datasets.Asexpected,theseweremostlyamongthelargestsys-
tems (see Fig. 7). On the other hand, about half of the systems
withatleasttengalaxieswereaffected–hence,themultimodal-
ityanalysisisanimportantadditiontothetraditionalFoFalgo-
rithmforlargersystems.Outlieridentificationusingvirialradius
andescapevelocitywasnecessaryforabout10%ofthesystems.
Onceagain,systemswithmoremembersbenefitedfromthere-
finementmore.
A visual inspection confirms that galaxy systems split into
smaller groups by the multimodality analysis contain apparent
substructure.Similarly,arandomcheckrevealsthattheremoved
outliers appear not to be tightly connected to the groups. Fig-
ure6showsexamplesofthesecases.Fromtheright-handpanels Fig.9.GalaxydistributioninthelocalUniverseaccordingtothecom-
wecandeducethattheFoFalgorithmconsidersthegivengalaxy bined dataset, presented in comoving supergalactic cartesian coordi-
systemasasinglegroupbecauseofthetwogalaxiesatthecentre nates.Theobserverislocatedinthecentreofthefigure,markedwith
ofthefigure.Themembershiprefinement(seealsoSect.3.2.2) ablackpoint.Intheupperpanel,theobservedgalaxydistributionwith
suggeststhatthesetwogalaxiesdonotbelongtoanyofthesub- redshift-based distances is shown. Galaxies in groups with more than
groups.Figure6alsoshowsthatthemultimodalityanalysiscan fivemembersareshownasbluepoints,othergalaxiesasredpoints.To
emphasisetheFoGeffect,isolatedgalaxiesandgalaxypairsareshown
separatenearby(potentiallymerging)groupsthatareclearlydis-
tinctintheskyplaneand/orintheredshiftspace. withslightlysmallerpoints.Intheupperpanelelongatedstructures(fin-
gersofGod)areclearlyvisiblealongthelineofsight–thegalaxydis-
Figure8showstherichness(numberofgalaxiesinagroup)
tributionpointstowardsthecentreofthefigure.Inthelowerpanelthe
of the detected groups as a function of distance. Farther away, same galaxies are plotted after the FoG effect was suppressed as de-
galaxysystemsappeartobesmaller.Thisisanaturalresultfora scribedinthetext.
flux-limitsurveysincethenumberdensityofgalaxiesdecreases
rapidly with increasing distance. The lower panel of the figure
shows that nearby, the 2MRS sample provides almost as many
groups as the combined dataset, while the farther end of the
groupsampleisalmostsolelyprovidedbythecombineddataset.
Figure9illustratestheFoGeffect.Intheupperpanel,theob- the same FoG suppression method on individual galaxy groups
serveddistributionofgalaxiesisplottedwiththeobserverinthe can be found in Fig. 6 in Tempel et al. (2012). This suppres-
centre of the data cube, at the origin of coordinates. The radial sion cannot fully recover the true positions of galaxies in the
elongationofstructuresisclearlyvisible,causedbypeculiarmo- radialdirection,butreducestheaverageerrorofthedistancees-
tionsofgalaxiesingroups.Tosuppresstheseartefacts,weused timates significantly. The FoG-corrected galaxy distribution is
velocitydispersionandprojectedsizetospherisegalaxygroups usefulforseveralapplications,forexample,toconstructthelu-
as described in Appendix B. The lower panel in Fig. 9 shows minosity density field (see Liivamägi et al. 2012) and to detect
galaxy distribution after the spherisation. Compared to the up- galaxy filaments (Tempel et al. 2014a). The latter is also one
per panel, the FoG effect is greatly reduced. An illustration of purposeofthepresentcatalogue.
Articlenumber,page6of10
E.Tempeletal.:Friends-of-friendsgalaxygroupfinderwithmembershiprefinement
40 Number of counterparts 40 Number of counterparts Fig.10. Distributionofmatchinggroupsasa
1 to Tully groups 1 to FoF groups functionofgrouprichnessinTully(2015b)and
inourFoFcatalogue.Intheleftpanel,counter-
groups310 1 02>2 groups310 1 2 0 >2 pFaorFtscfaotraleoagcuheT,uinllythgeroruigphatrepasnoeulghvticferovmertshae.
Number of 12010 012> 2ccc ooocuuuonnnutttneeetrrrepppraaaprrratttrssts Number of 12010 012> 2ccc ooocuuuonnnutttneeetrrrepppraaaprrratttrssts Docwaniitffetah,elomtrwegonuorte,eloi(mnsreeamsetccohtoereerxsrtemasfrpoaetorcgnhmedenosetroreiangldlrtyoehutreaipcicslhsowe)m.ri,tpGgharrrzooiesuuropponss,
+1 + 1
1 1 with zero matches poorer systems. The inset
00 00 piediagramsshowthefractionsofgroupswith
1 1 agivenamountofcounterparts.Table1shows
10 100 10 100 thenumbersandfractionsofgroupscontained
NTully NFoF ineachsector.
Table1.GroupmatchingbetweenTully(2015b)andFoF(thiswork)
catalogues.ThematchisbasedeitherontheTullyortheFoFcatalogue,
asdescribedinthetext.Thenumberandfractionofgroupswithzero,
0
10 l l l l oshnoew, tnw.o or more matches in the respective comparison catalogue are
l l l
l lll
l llll l Tully(2015b) FoF(thiswork)
NFoF10 llllllllllllllllllllllll llllllll lllllll lllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l ll S0123+ammmmmaaaptttaccclethhhceehsses N14gr0441ou8839p7474s F17r7273ac....5311ti%%%%on N5gr128ou833p6876s F9r4320ac....6121ti%%%%on
llllllllll lll llll lllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll ll ll l ll l
llllllllllll lllllllllllll lllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll Total 6202 100% 6267 100%
llllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l l
lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l l lSimilar groups
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllll lDifferent groups agreementisachievedwithintherestricteddistanceinterval.Be-
lowwepresentthecomparisonusingthefull2MRSsample.
10 100
N To conduct the comparison, we found a match between the
Tully
two catalogues, referring to them as Tully and FoF catalogues
Fig. 11. Group richness in Tully (2015b) and in our (FoF) catalogue. below (but we recall that here the FoF groups are refined with
ForeachTullygrouponlythebestmatchingFoFgroupisshown.More asubsequentanalysis).IntheTullycatalogueweonlyconsider
than half of the groups lie on the line indicating a one-to-one match.
groupswithtwoormoremembers.Thematchingwasmadeac-
Similargroupsareshownwithredcolour.Seetextforthedefinitionsof
cordingtothemembershipofgalaxies.Foreachgroupthebest-
bestmatchandsimilarity.Aslightscatterisimposedongrouprichness
matchinggroupintheothercatalogueistheonewiththelargest
forclarity.
numberofcommonmembers.Thismatchdependsonthebasis
catalogue. For example, we consider the case of a group in the
TullycataloguethatconsistsoftwogroupsintheFoFcatalogue.
5. ComparisonwiththecatalogueofTully
WhenwematchitonthebasisoftheTullycatalogue,weobtain
onematch(withthegroupwithmoremembersintheFoFcata-
We compared our results with those derived by Tully (2015b).
logue).WhenwematchitonthebasisoftheFoFcatalogue,the
More thorough comparisons of recent grouping algorithms and
sameTullygroupismatchedwithbothFoFgroups.
their performance can be found elsewhere (Old et al. 2014,
Figure 10 illustrates the group matching. In the left-hand
2015).
panel,thematchisbasedontheTullygroups,intheright-hand
ThecataloguebyTully(2015b)isthelatestsofarandrelies panelonour(FoF)groups.Foramajorityofgroupsinbothcat-
on the same 2MRS dataset as was used in our analysis. On the alogues only a single match is found from the other catalogue.
other hand, our catalogue was constructed using a completely Onlyafewgroupsaresplitintotwoormoregroupsintheother
differentapproach.IncontrasttoourFoFalgorithm,thegroups catalogueinbothcases.Inslightlymorecases,nomatchisfound
in Tully (2015b) were constructed using a halo-based method. atall–mostlygroupswithveryfewmembers.Table1givesthe
This means that a dark halo is ascribed to each galaxy accord- number of groups in both catalogues that have zero, one, two
ingtoscalingrelations.Allgalaxieslyingwithintheboundaries ormorematchesinthecomparisoncatalogue.Iftherearemore
of the halo are considered to belong to the same system, after thanonematchforasinglegroup,thebestmatchisconsidered
which new halo parameters are calculated and the group mem- tobetheonewithmoremembers.
bership is updated. This procedure is repeated iteratively until
Figure 11 shows the richness of groups in the Tully cata-
convergence.
logue with respect to the richness of the best-matching group
Tully (2015b) constructed his group catalogue for the full in the FoF catalogue. More than half of the groups fall on the
2MRS sample, but noted that groups are only reliable within one-to-onecorrespondenceline,whichmeansthattheyareiden-
recession velocities 3000 to 10000 kms−1 (44–146 Mpc). We tical in both catalogues. Very similar groups are represented in
carried out the comparison only considering groups within this redinFig.11.Forsimilaritywerequiredthat80%ofthemem-
distanceintervalaswellasusingthefull2MRSsample.Quali- bersinthematchinggroupsarethesame,thatis,thenumberof
tatively,theresultsaresimilarinbothcases,whileslightlybetter galaxies in groups satisfy N[G ∩G ] ≥ (cid:107)0.8(N[G ∪
Tully FoF Tully
Articlenumber,page7of10
A&Aproofs:manuscriptno.tempel
l lll 45 l
dec (deg)---13.51314 llllllllllll llllllllllllllll ll dec (deg)--1514.5 llll lllllll l dec (deg)4344 ll lllllllllllllllllllllllllllllllllllllllllllllll Fcspeaoivtgsae.iltro1iaog2lnu.sgeEraooxruefapmsTshpuoillnwelynoof(ui2nrt0hRF1re5oAebF-)gDcrteoahcutaapt(lsuodpgiinpusseetor.hlepvGaeganrlioeanluxtspoy)
redshift-14.50.020.0220.0240.026 lllllllllllll ra (ldelgl)lllllllllllll ll redshift-15.50.0240.0250.0260.0270.028 llll lrall ll(dlllelllglllll)l redshift0.0250.030.03542 ll lllllllllllllllllllrlalllll lll(lllllldllllllegll)llllllllllllllllll llllllll aegggbctoshunaarrreueoooctgdlreohuuugFdrrnpppeeeogp.ssiddFnmtaSsisstnnhohaegeteilipmrohfgfaloatuat,onb-urtrDsryaeapipactrlteelFasahosctcmouciagien(nFotlal.sgowlolkToglagTweiiuxurutrheohrtileTeseslru.ymusspaprGelen.elcabyrpmdaenTeertx/eyglheabooalrsleerscmnooey)rragugnsopcrhpuatselotrieessopomeessertesprhamdopseadyaihnfiaonretoraencsasawdttoietetlgeTonmeysnFudtt.nheaalloIoiloniatFnnyne-ttt
250.5 251 251.5 252 252.5 253 36 36.5 37 37.5 38 172 173 174 175
ra (deg) ra (deg) ra (deg) separablesubcomponentsandpossibleoutliers.
topic.Tully(2015b)alsoaddressedthisissueandseparatedthe
systemsintotwocomponentsbyhandinsixcases(seeFig.7in
Tully2015b,foranexample).
Tully(2015b)estimatedmassesofgroupsusingtwodifferent
methods:asinferredfromgalaxyluminosities,andascalculated
fromthevirialtheorem.Groupmasseswereestimatedusingthe
virial theorem in our catalogue as well, but the details of the
practical application of the theorem are slightly different. See
Tully(2015b)andTempeletal.(2014b)fordescriptionsofthe
twotechniques.
Figure13comparesourgroupmassestimateswiththoseby
Tully(2015b).Ourestimatesagreewellwiththevirialtheorem
Fig. 13. Comparison of group masses as estimated in this work and
predictionsinTully(2015b).Asexpected,theluminosity-based
by Tully (2015b). We have used only the virial theorem, while Tully
mass estimate has a larger scatter. We conclude that regarding
(2015b) used the virial theorem (left panel) and galaxy luminosities
thedifferencesinthevirialtheoremapplication,themassesare
(right panel). Here, only identical groups (blue points) and similar
groups(redpoints)withatleastfourmembersareshown.Thevirial- sufficientlyconcordant.
theorem-basedmassestimatesagreewellwitheachother.
6. Conclusions
G ])(cid:107),whereN[G ]indicatesthenumberofgalaxiesin
FoF Tully/FoF
Tully/FoFgroup.Includingsimilargroups,morethantwothirds WepresentedanimprovedFoFgalaxygroupfinderwithgroup
ofallgroupsarethesameinbothcatalogues.Takingintoaccount membershiprefinement.InadditiontotheconventionalFoFal-
thatthesetwocatalogueswereconstructedusingcompletelydif- gorithm,weconductedamultimodalityanalysistosplitmerging
ferenttechniques,thecorrespondenceisremarkable. groupsand/orsubsystemsthatareclearlydistinguishableinthe
From the group comparison analysis, we conclude the fol- sky plane or in the redshift space. The multimodality analysis
lowing:mostofthegroupsareidenticalinbothcataloguesanda affectedabouthalfofthesystemswithatleasttengalaxies.We
majorityofthemareverysimilar.Thegroupsthatarenotiden- refinedthegroupsfurtherusingvirialradiusandescapevelocity
ticalareslightlylargerinTully’scataloguethanintheFoFcata- ofthegroupstodetectgravitationallyunboundgalaxies.
logue(mostlybecauseofmembershiprefinement).Omittingthe WeappliedourmethodongalaxiesinthelocalUniverseus-
meaningless discussion about the true nature of galaxy groups, ingtwodatasets:the2MRSsampleandacombined2MRS,CF2,
wecanneverthelessconsiderthisapositiveresultbecauseforthe and 2M++ dataset. The combined dataset increases the num-
FoGsuppressionwewishtoconsidereachsubgroupseparately, ber density of galaxies farther away. The group catalogues for
keeping the modification of the observed galaxy distribution as both datasets are publicly available and can be accessed from
slightaspossible. http://cosmodb.to.ee.
Figure 12 illustrates the division of single Tully groups Wecomparedourdetectedgroupswithanotherrecentgroup
into multiple groups in our FoF catalogue. Three examples are catalogue based on the 2MRS data by Tully (2015b). Half of
shown.SubcomponentsoftheTullygroupsarereasonablywell the groups were found to be identical in both catalogues and
separatedinourFoFcatalogue.Additionally,severalgalaxiesin two thirds are very similar. Considering that these two cata-
Tullygroupsdonotbelongtoanygroupinourcatalogue:galax- logueswereconstructedusingcompletelydifferentapproaches,
iesintheoutskirtsintheplaneoftheskyand/orseparatedinthe the agreement is remarkable. It ensures that most of the de-
redshift space. We stress that the separation of subcomponents tected systems are actual galaxy groups and that both methods
is not always desired; the required level of the substructure de- aremeaningful.Wenotethatthecataloguesdifferindetails;the
tectionlargelydependsonthegoalofthestudy.Tosuppressthe preferenceofoneovertheotherdependsontheaimofthestudy.
FoG (one goal of the present work), subcomponent distinction Out of the non-identical groups, those in our catalogue tend to
shouldbepreferred.Ingeneral,thedetectionofmulticomponent beslightlysmallerandcontainlesssubstructure,thusbeingmore
groupsassinglesystemsisawell-knownandanoftendiscussed favourableforstudieswheretheFoGsuppressionisrequired.
Articlenumber,page8of10
E.Tempeletal.:Friends-of-friendsgalaxygroupfinderwithmembershiprefinement
Wealsocomparedthegroupmassesinourcatalogueandin AppendixA: Descriptionofthecatalogues
Tully(2015b).Groupmassesestimatedusingthevirialtheorem
The catalogue of galaxy groups consists of two tables for both
agreeverywellinbothcatalogues,eventhoughthepracticalap-
plicationofthevirialtheoremhasbeendifferent. datasets(2MRSaloneandcombined).Thefirsttablelistsgalax-
ies that were used to generate the group catalogues, the sec-
As a forthcoming application, we will use our constructed
ond describes the group properties. The catalogues are avail-
cataloguetodetectgalaxyfilamentsfromthelocalUniverseus-
able at http://cosmodb.to.ee. The catalogues will also be
ing the Bisous model (Tempel et al. 2014a). The data have al-
madeavailablethroughtheStrasbourgAstronomicalDataCen-
ready been used in Libeskind et al. (2015), where galaxy fila-
tre(CDS).
mentsinthelocalUniversewereshowntobewellalignedwith
theunderlyingvelocityfieldconstructedusingtheCF2data.
AppendixA.1: Galaxycatalogues
Acknowledgements. Thisworkwassupportedbyinstitutionalresearchfunding
IUT26-2,IUT40-2andthegrantETF9428oftheEstonianMinistryofEducation
The galaxy catalogues contain the following information (col-
and Research. T.T. acknowledges financial support by the Estonian Research
umnnumbersaregiveninsquarebrackets):
CouncilgrantPUTJD5.
1. [1]pgcid–identificationnumberinPGC(principalgalaxy
catalogue);
References 2. [2]groupid–group/clusteridgiveninthepresentpaper;
3. [3]ngal – richness (number of members) of the
Crook,A.C.,Huchra,J.P.,Martimbeau,N.,etal.2007,ApJ,655,790 group/clusterthegalaxybelongsto;
Dai,X.,Kochanek,C.S.,&Morgan,N.D.2007,ApJ,658,917 4. [4]groupdist – comoving distance to the group/cluster
Dai,X.,Bregman,J.N.,Kochanek,C.S.,&Rasia,E.2010,ApJ,719,119 centre to which the galaxy belongs, in units of Mpc, calcu-
Díaz-Giménez, E., Mamon, G. A., Pacheco, M., Mendes de Oliveira, C., & latedasanaverageoverallgalaxieswithinthegroup/cluster;
Alonso,M.V.2012,MNRAS,426,296
5. [5]zobs–observedredshift(withouttheCMBcorrection);
Duarte,M.&Mamon,G.A.2014,MNRAS,440,1763
6. [6]zcmb–redshift,correctedtotheCMBrestframe;
Einasto,M.,Tago,E.,Saar,E.,etal.2010,A&A,522,A92
7. [7]zerr–erroroftheobservedredshift;
Einasto,M.,Vennik,J.,Nurmi,P.,etal.2012,A&A,540,A123
Eke,V.R.,Baugh,C.M.,Cole,S.,etal.2004,MNRAS,348,866 8. [8]dist – comoving distance in units of Mpc (calculated
Fraley,C.&Raftery,A.E.2002,JournaloftheAmericanStatisticalAssociation, directlyfromtheCMB-correctedredshift);
97,611 9. [9]dist_cor – comoving distance of the galaxy after sup-
Fraley,C.,Raftery,A.E.,Murphy,T.B.,&Scrucca,L.2012,mclustVersion4 pressingthefinger-of-godeffect(seeAppendixB);
forR:NormalMixtureModelingforModel-BasedClustering,Classification, 10. [10–11]raj2000, dej2000–rightascensionanddeclina-
andDensityEstimation
tion(deg);
Huchra,J.P.&Geller,M.J.1982,ApJ,257,423
11. [12–13]glon, glat – Galactic longitude and latitude
Huchra,J.P.,Macri,L.M.,Masters,K.L.,etal.2012,ApJS,199,26
(deg);
Jackson,J.C.1972,MNRAS,156,1P
Jarrett,T.H.,Chester,T.,Cutri,R.,etal.2000,AJ,119,2498 12. [14–15]sglon, sglat – supergalactic longitude and lati-
Jones,D.H.,Read,M.A.,Saunders,W.,etal.2009,MNRAS,399,683 tude(deg);
Karachentsev,I.D.,Makarov,D.I.,&Kaisina,E.I.2013,AJ,145,101 13. [16–18]xyz_sg – supergalactic cartesian coordinates in
Kochanek,C.S.,White,M.,Huchra,J.,etal.2003,ApJ,585,161 units of Mpc based on dist_cor (fingers of god are sup-
Lavaux,G.&Hudson,M.J.2011,MNRAS,416,2840 pressed);
Lavaux,G.&Jasche,J.2016,MNRAS,455,3169 14. [19]mag_ks – Galactic-extinction-corrected K magnitude
Libeskind,N.I.,Tempel,E.,Hoffman,Y.,Tully,R.B.,&Courtois,H.2015, s
asgiveninsourcecatalogue;
MNRAS,453,L108
15. [20]source–sourceofthegalaxy:1for2MRS,2forCF2,
Liivamägi,L.J.,Tempel,E.,&Saar,E.2012,A&A,539,A80
3for2M++.
Łokas,E.L.&Mamon,G.A.2001,MNRAS,321,155
Macciò,A.V.,Dutton,A.A.,&vandenBosch,F.C.2008,MNRAS,391,1940
Makarov,D.&Karachentsev,I.2011,MNRAS,412,2498
AppendixA.2: Descriptionofgroupcatalogues
Navarro,J.F.,Frenk,C.S.,&White,S.D.M.1997,ApJ,490,493
Old,L.,Skibba,R.A.,Pearce,F.R.,etal.2014,MNRAS,441,1513 Thecataloguesofgroups/clusterscontainthefollowinginforma-
Old,L.,Wojtak,R.,Mamon,G.A.,etal.2015,MNRAS,449,1897
tion(columnnumbersaregiveninsquarebrackets):
PlanckCollaboration,Ade,P.A.R.,Aghanim,N.,etal.2015,ArXive-prints
[arXiv:1502.01589] 1. [1]groupid–group/clusterid;
Ribeiro,A.L.B.,deCarvalho,R.R.,Trevisan,M.,etal.2013,MNRAS,434, 2. [2]ngal–richness(numberofmembers)ofthegroup;
784
3. [3–4]raj2000, dej2000–rightascensionanddeclination
Robotham,A.S.G.,Norberg,P.,Driver,S.P.,etal.2011,MNRAS,416,2640
ofthegroupcentre(deg);
Skrutskie,M.F.,Cutri,R.M.,Stiening,R.,etal.2006,AJ,131,1163
Tago,E.,Einasto,J.,Saar,E.,etal.2008,A&A,479,927 4. [5–6]glon, glat – Galactic longitude and latitude of the
Tago,E.,Saar,E.,Tempel,E.,etal.2010,A&A,514,A102 groupcentre(deg);
Tempel,E.,Tago,E.,&Liivamägi,L.J.2012,A&A,540,A106 5. [7–8]sglon, sglat–supergalacticlongitudeandlatitude
Tempel,E.,Stoica,R.S.,Martínez,V.J.,etal.2014a,MNRAS,438,3465 ofthegroupcentre(deg);
Tempel,E.,Tamm,A.,Gramann,M.,etal.2014b,A&A,566,A1 6. [9]zcmb – CMB-corrected redshift of the group, calculated
Tully,R.B.2015a,AJ,149,54 asanaverageoverallgroup/clustermembers;
Tully,R.B.2015b,AJ,149,171 7. [10]groupdist – comoving distance to the group centre
Tully, R. B. & Fisher, J. R. 1978, in IAU Symposium, Vol. 79, Large Scale
(Mpc);
StructuresintheUniverse,ed.M.S.Longair&J.Einasto,31–45
8. [11]sigma_v–rmsdeviationoftheradialvelocities(σ in
Tully,R.B.,Rizzi,L.,Shaya,E.J.,etal.2009,AJ,138,323 v
physicalcoordinates,inkms−1);
Tully,R.B.,Courtois,H.M.,Dolphin,A.E.,etal.2013,AJ,146,86
Turner,E.L.&Gott,III,J.R.1976,ApJS,32,409 9. [12]sigma_sky–rmsdeviationoftheprojecteddistancesin
York,D.G.,Adelman,J.,Anderson,Jr.,J.E.,etal.2000,AJ,120,1579 theskyfromthegroupcentre(σsky inphysicalcoordinates,
Zeldovich,I.B.,Einasto,J.,&Shandarin,S.F.1982,Nature,300,407 inMpc),σ definestheextentofthegroupinthesky;
sky
Articlenumber,page9of10
A&Aproofs:manuscriptno.tempel
10. [13]r_max–distance(inMpc)fromgroupcentretothefar- whered∗ istheinitialdistance(calculateddirectlyfromgalaxy
gal
thestgroupmemberintheplaneofthesky; redshift) to the galaxy, d is the distance to the group cen-
group
11. [14]mass_200–estimatedmassofthegroupassumingthe tre,andH istheHubbleconstant.Forgalaxypairs,wedemand
0
NFWdensityprofile(inunitsof1012M(cid:12)); thattheirsizealongthelineofsightdoesnotexceedthelinking
12. [15]r_200–radius(inkpc)ofthesphereinwhichthemean lengthd (z)usedtodefinethesystem
LL
densityofthegroupis200timeshigherthantheaverageof
13. t[h1e6]Umnaigv_ergsreo;up–observedmagnitudeofthegroup,i.e.the dgal = dgroup+(cid:18)dg(cid:63)al−dgroup(cid:19)|v d−LLv(z|/)H , (B.5)
1 2 0
sumoftheluminositiesofthegalaxiesinthegroup. if|v −v |/H >d (z).
1 2 0 LL
Herezisthemeanredshiftofagalaxypair.
AppendixB: Basicpropertiesofgalaxygroups ThesuppressionofFoGredshiftdistortionsasdefinedabove
wasinitiallyusedtocalculatetheluminositydensityfieldusing
For every galaxy group we calculate several basic properties.
SDSS data (see Liivamägi et al. 2012) and has later been suc-
The main properties are the velocity dispersion and the size in
cessfully used to prepare the data for galaxy filament detection
theplaneofthesky,usedforestimatingthevirialmassandra-
(Tempeletal.2014a).
dius of the groups and for the suppression of the FoG redshift
distortions.DetailsaboutthesecalculationsaregiveninTempel
et al. (2014b). For convenience a condensed description is pro-
videdbelow.
Thegroupvelocitydispersionσ2 iscalculatedwiththefor-
v
mula
1 (cid:88)n
σ2 = (v −v )2, (B.1)
v (1+z )(n−1) i m
m i=1
wherez andv arethemeanredshiftandvelocityofthegroup;
m m
v are the velocities for individual group members. Summation
i
isoverallgalaxieswithameasuredvelocitywithinthegroup.
Thegroupextentintheskyplaneisdefinedas
1 (cid:88)n
σ2 = (r)2, (B.2)
sky 2n(1+z )2 i
m i=1
where r are the projected distances (in comoving coordinates)
i
fromthegroupcentreintheplaneofthesky.
Both quantities, velocity dispersion σ2 and group extent
v
σ2 , are defined in physical units. This is an obvious choice
sky
sinceweusethesequantitiestocalculatethephysicalproperties
ofgroups,thevirialmassandradius.
Group masses are estimated using the virial theorem from
whichwecanderivetheequation
R (cid:32) σ (cid:33)2
M =2.325×1012 g v M , (B.3)
vir Mpc 100kms−1 (cid:12)
whereR isthegravitationalradius,whichforafixedmassden-
g
sity profile only depends on the group extent in the sky σ2 .
sky
ToestimategroupmassesweassumeanNFWprofile(Navarro
etal.1997)usingmass-concentrationrelationasderivedinMac-
ciò et al. (2008). As a result, the NFW profile only depends on
the mass. See Tempel et al. (2014b) for details about gravita-
tionalradiusandmasscalculations.Undertheassumptionofan
NFWprofile,thegroupvirialradiusisuniquelydefinedwiththe
virial mass. The virial radius is defined as the radius in which
the mean density is 200 times higher than the mean density in
theUniverse.
TosuppresstheFoGredshiftdistortionsweusethermssizes
of groups in the sky (σ ) and their rms radial velocities (σ ).
sky v
Both are given in physical units as defined above. To suppress
redshiftdistortions,wecalculatenewradialdistancesforgalax-
iesusingtheformula
(cid:16) (cid:17) σ
d =d + d∗ −d sky , (B.4)
gal group gal group σ /H
v 0
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