Substructure in the Most Massive GEEC Groups: Field-like Populations in Dynamically Active Groups

1.2 MB·English

by  Annie Hou

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed19January2012 (MNLATEXstylefilev2.2)
Substructure in the Most Massive GEEC Groups:
Field-like Populations in Dynamically Active Groups
2
Annie Hou1, Laura C. Parker1, David J. Wilman2, Sean L. McGee3,4, William E. Harris1,
1
0 Jennifer L. Connelly2, Michael L. Balogh4, John S. Mulchaey5, Richard G. Bower3
2
1Department of Physics & Astronomy, McMasterUniversity, Hamilton ON L8S 4M1, Canada
n 2Max-Planck-Institut fu¨rExtraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany
a 3Department Of Physics, Universityof Durham, Durham, UK DH1 3LE
J
4Department of Physics and Astronomy, Univeristy of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

8 5Observatoriesof the Carnegie Institution, 813 Santa Barbara Street, Pasadena, California, USA
1

]
O 19January2012
C
h. ABSTRACT
p The presence of substructure in galaxy groups and clusters is believed to be a sign
- of recent galaxy accretion and can be used not only to probe the assembly history of
o
these structures, but also the evolution of their member galaxies. Using the Dressler-
r
t Shectman (DS) Test, we study substructure in a sample of intermediate redshift
s (z ∼ 0.4) galaxy groups from the Group Environment and Evolution Collaboration
a
[ (GEEC) group catalog. We find that 4 of the 15 rich GEEC groups, with an average
velocity dispersion of ∼525 km s−1, are identified as having significant substructure.

1 The identified regionsoflocalizedsubstructure lie onthe groupoutskirts andin some
v
cases appear to be infalling. In a comparisonof galaxy properties for the members of
6
groupswithandwithoutsubstructure,wefindthatthegroupswithsubstructurehave
7
a significantly higher fraction of blue and star-forming galaxies and a parent colour
6
distribution that resembles that of the field population rather than the overall group
3
. population.Inaddition,weobservecorrelationsbetweenthedetectionofsubstructure
1
and other dynamical measures, such as velocity distributions and velocity dispersion
0
profiles. Based on this analysis, we conclude that some galaxy groups contain sig-
2
nificant substructure and that these groups have properties and galaxy populations
1
that differ from groupswith no detected substructure.These results indicate that the
:
v substructure galaxies,which lie preferentially on the groupoutskirts and could be in-
Xi falling, do not exhibit signs of environmental effects, since little or no star-formation
quenching is observed in these systems.
r
a
Key words: galaxies:statistics-galaxies:kinematicsand dynamics-galaxies:formation
1 INTRODUCTION assume here, also includes separate haloes that are either
merging to form a larger halo; gravitationally bound and
ThecurrenttheoryofstructureformationintheUniverseis infalling onto a pre-existing halo; or in the nearby large-
based on thestandard Λcold dark matter(ΛCDM) cosmo- scale-structure, but not necessarily bound or infalling. In
logical model,inwhichobjectsgrowhierarchically from the general, accreting structure does not have the same kine-
initial matter density perturbations through mergers and matic properties as the host, but whether or not substruc-
accretion(e.g.,Press & Schechter1974;Lacey & Cole1993; ture can be observed depends on how long it remains in-
Springel et al.2005).Inordertotestthetheoryofhierarchi- tact after infall. Early N-body simulations suggested that
cal structure formation, one must investigate the assembly the assimilation of substructure into the host was rapid,
historyofthelargestructuresintheUniverse,namelygalaxy providing no detectable long-lived features (Katz & White
groups and clusters. 1993;Summerset al.1995).However,laterworkhasshown
A naturalconsequenceof a hierarchical Universeis the that the lack of observable substructure in these simula-
existence of substructure within larger systems. Tradition- tionswasduetopoorresolution(Moore et al.1996).Indeed,
ally, substructure has been defined as a kinematically dis- high resolution N-body simulations (e.g., Diemand et al.
tinct sub-halo within a larger parent halo. A broader, more 2008; Springelet al. 2008), demonstrate that several hun-
observationally motivated definition, and one that we will dred thousand sub-haloes can exist in a Milky Way sized
2 Hou et al.
dark matter halo at a redshift of zero. Using semi-analytic ysiswasbasedonasmallsampleofverynearbysystems.In
modelstostudythesubstructurewithinindividualgalaxyto ordertogainabetterunderstandingoftheroleofgroupsin
cluster-sizedhaloes,Taylor & Babul(2004)showedthatac- thegrowth of structure, we must search for substructurein
cretingsystemscouldsurvivewithinthehosthaloformany alargersampleofgalaxygroupswithhighlycompletespec-
orbits,dependingontheorbitalparametersofthesubstruc- troscopy that cover a wide range in redshift. Such studies
tureupon infall. have only become possible with recent deep spectroscopic
These theoretical results suggest that substructure surveysthat have produced large group catalogues, such as
should be a detectable quantity and numerical dark theSloanDigitalSkySurvey(SDSS)(Berlind & et al.2006;
matter simulations of galaxy groups and clusters in a Yanget al. 2007), the Group Environment and Evolution
ΛCDM Universe predict that approximately 30 per cent of Collaboration (GEEC) (Wilman et al.2005;Carlberg et al.
all systems should contain substructure (Knebe& Mu¨ller 2001),andthehigherredshiftextensionofGEEC(GEEC2)
2000). Studies of individual clusters (e.g., Beers et al. (Balogh et al. 2011) optical group catalogs.
1982; Dressler & Shectman 1988; West & Bothun 1990; Inaddition totherole of thegroup environmentin the
Bird 1994a; Colless & Dunn 1996; Burgett & et al. 2004; growth of large scale structure in the Universe, studies of
B¨ohringer et al. 2010) indicate that a large fraction of sys- substructurewithingroupsallowsustoprobegalaxyevolu-
tems show evidence of significant sub-clustering. The pre- tion.Sincegroupshavefewermembersthangalaxyclusters,
dicted theoretical value of 30 per cent is in agreement any substructure present will have a stronger effect on the
with some substructurestudiesof groupsandclusters (e.g., observed group properties (i.e. colours, blue or active frac-
Zabludoff & Mulchaey 1998a; Solanes et al. 1999), but sev- tions). If substructure traces accreting galaxies, one might
eralotherresultshavedemonstratedamuchhigherfraction expectacorrelationbetweenobservedgalaxypropertiesand
of substructure;Bird (1994b) observed that 44 percent1 of substructure.Possible correlations could exist betweensub-
their sample contained substructure, Dressler & Shectman structureandthecoloursofgalaxiesingroups,orwithsub-
(1988) observed 53 per cent and Ramella et al. (2007) find structureandstarformation rates.Oneofthemaingoalsof
an extremely high substructure fraction of 73 per cent. Al- thispaper is to search for such correlations.
thoughtheprecisefraction ofgroupsandclusterswithsub- In this paper we search for substructurein a sample of
structuremaystillbeasourceofdebate,theobservedpres- intermediate redshift galaxy groups from theGEEC Group
ence of any substructure strongly suggests that these sys- Catalog. In Section 2, we discuss the sensitivity and reli-
temsgrowinahierarchicalmannerthroughtheaccretionof ability of the Dressler-Shectman (DS) Test for group-sized
galaxies and smaller groups of galaxies. systemsusingMonteCarlosimulations.InSection3,weap-
Though galaxy clusters are amongst the largest struc- plytheDSTesttotheGEECgroupsanddiscusstheresults
tures in the local Universe, they do not represent the ofouranalysis. InSection4,wediscusstherelationship be-
mostcommonhostenvironmentforgalaxies.Galaxygroups, tween the presence of substructure and other indicators of
whichcontainafewtotensofmembergalaxies,arethehost dynamical state, such as the shape of the group velocity
environment of more than half of the present-day galaxy distribution. In Section 5, we look for correlations between
population(Geller & Huchra1983;Ekeet al.2005).Despite substructure and the properties of members galaxies, such
theimportanceofgroupsinthebuildupoflargegalaxyclus- as colour and star formation rate, and discuss the possi-
ters,therehavebeenfewstudieson theassemblyhistory of bleimplications ofourfindings.InSection6wepresentour
groups themselves. conclusions. Additionally, we include an Appendix, which
One method of probing group assembly histories is to providesdetailed results of our Monte Carlo Simulations.
look at the amount of substructure within these systems. Throughout this paper we assume a ΛCDM cosmology
Thepresenceofsuchstructurewouldindicatethatthegroup with ΩM =0.3, ΩΛ =0.7, and H0 = 75 km s−1 Mpc−1.
has recently accreted galaxies (Lacey & Cole 1993). Stud-
ies have been carried out for galaxy groups in the local
Universe by Zabludoff & Mulchaey (1998a), who observed
2 DETECTING SUBSTRUCTURE IN GROUPS
significant (> 99 per cent confidence level) substructure in
two of their six local groups. An interesting result of their Numerous tests for substructure have been developed and
analysis showed that the substructure was located on the carried out for cluster-sized systems (see Pinkney et al.
outskirts of the systems, that is 0.3-0.4 h−1 Mpc, where 1996, for a thorough review). In a comparison of five 3-
h=H0/(100 km s−1 Mpc−1), fro∼m the core of the group. dimensional (3-D) tests, which use both velocity and spa-
Based on these results, Zabludoff & Mulchaey (1998a) con- tial information, Pinkney et al. (1996) determined that the
cluded that like rich galaxy clusters, some galaxy groups Dressler-Shectman (DS) Test (Dressler & Shectman 1988)
assembledinahierarchicalmannerthroughtheaccretionof wasthemostsensitivetestforsubstructure,forsystemswith
smallerstructuresfrom thefield.Amorerecentstudyoflo- as few as 30 members. In the following section we look at
calgalaxygroupsbyFirth et al.(2006)foundsimilarresults, theDSTest,anddetermineitsreliabilityandrobustnessfor
with roughly half of their sample showing significant sub- smaller group-sized systems.
structure. Although, the findings of Zabludoff & Mulchaey
(1998a) and Firth et al. (2006) provided an important first
2.1 The Dressler-Shectman (DS) Test
step inunveilingtheassembly history ofgroups,theiranal-
Substructuremanifestsitselfasdetectabledeviationsinthe
spatial and/or velocity structure of a system. The aim of
1 11/25galaxiesintheirsamplehavesignificant(>95percent) the DS Test is to compute local mean velocity and velocity
substructurebasedonresultsoftheDressler-Shectmanstatistics. dispersion values,foreach individualgalaxy anditsnearest
Substructure inthe Most MassiveGEEC Groups: Field-likePopulationsin DynamicallyActive Groups 3
neighbours,andthencomparethesetotheglobalgroupval- our own Monte Carlo simulations in order to check the re-
ues. Following thenotation of Dressler & Shectman (1988), liability, sensitivity and robustness of the DS Test, using
we define (ν¯,σ) as the mean velocity and velocity disper- both the critical value and probability (P-value) methods,
sion of theentire group,which is assumed tohaven for group-sized systems. It should be noted that we specifi-
members
galaxies. Then for each galaxy i in the group, we select it callymodelourhostmockgroupsaftertheobservedGEEC
plus a numberof its nearest neighbours, Nnn, and compute group sample.
theirmeanvelocityν¯i andvelocitydispersionσi .From
local local
thesewecomputetheindividualgalaxydeviations,δ ,given
i
as
δ2 = Nnn+1 νi ν 2+ σi σ 2 , (1) 2.2.1 Generating the Mock Groups
i σ2 local− local−
(cid:18) (cid:19)(cid:20)(cid:16) (cid:17) (cid:16) (cid:17) (cid:21) Mock galaxy groups, both with and without substructure,
where 1 i n (i.e. δ is computed for each galaxy aregeneratedusingMonteCarlomethodstoassignmember
members i
in the sy≤stem≤). Dressler & Shectman (1988) originally de- galaxy positions. These mock groups are thenused tocom-
velopedthetestforcluster-sizedsystemsandthenumberof putethefalsenegativeandpositiveratesoftheDSTest,and
nearest neighbours used to compute the δ values was rel- alsodeterminethesensitivityofthetestagainstavarietyof
i
atively high (i.e. Nnn = 11). Since substructure in galaxy input parameters.
groups is likely to have fewer than 11 constituent galax- Theradialpositionsforthemembersofthemockgroups
ies, we take Nnn to be √nmembers following the methodol- arerandomlydrawnfromfitstotheprojectedgroup-centric
ogy of authors who have previously applied the DS Test radial distributions of the galaxies observed in the GEEC
togroup-sizesystems(Silverman1986;Pinkney et al. 1996; groupcatalog(Wilman et al.2005).Thegroupsaredivided
Zabludoff & Mulchaey1998b).Thisensuresthatlargekine- intofourbinsbasedonthenumberofmembersineachgroup
matic deviations of a few neighbouring galaxies do not (Fig.1),andfitstoeach binareused topopulatethemock
get diluted by adding too many unassociated galaxies, and groups. Since the GEEC groups span such a wide range of
thereby lowering the computed νi and σi values in masses and group membership, we elect not to use a single
local local
Equation 1. fit tothe radial distribution of all thegroup galaxies in our
The statistic used in the DS Test is the ∆-value, given sample. Instead, we divide our sample into bins of group
by membership (5 nmembers <10, 10 nmembers <15, 15
≤ ≤ ≤
n <20 and n 20) and fit each distribution
members members
≥
∆= δi. (2) separately. It should be noted that we bin our sample by
i groupmembership,ratherthanmassorvelocitydispersion,
X
asweaimtostudythefalsepositiveandnegativeratesofthe
A system is then considered to have substructure if
DS Test as a function of n . However, the results are
members
∆/n > 1.0 (Dressler & Shectman 1988). This
members similarifwebinbyσ ratherthann .Thehistograms
members
method of using a threshold value to find substructure is
and fitsto the radial distributions of thebinned groups are
referred to as the critical values method.
shown in Fig. 1. Thegeneral form oftheradial distribution
Analternativemethodofidentifyingsubstructurewith
of member galaxies is given by
the DS Test is to use probabilities (P-values) rather than
critical values. The P-values for the DS Test are computed
by comparing the observed ∆-value to ‘shuffled’ ∆-values,
N exp( λR), (4)
whicharecomputedbyrandomlyshufflingtheobservedve- ∝ −
locities and re-assigning these values to the member posi-
tions, a procedure called ‘MC shuffling’. The P-values are
where R is the radial position of the given galaxy and λ =
given by 2.98,1.31,0.902and0.606Mpc−1forthe5 n <10,
members
≤
P = (∆shuffled >∆observed)/nshuffle. (3) 10≤nmembers <15, 15≤nmembers <20 and nmembers ≥20
bins, respectively. From these results it is clear that groups
X
with fewer members have steeper radial distributions and
where∆shuffledand∆observedarebothcomputedusingEqua- smaller maximum group centric radii (Fig. 1).
tion2andnshuffle isthenumberof‘MCshuffles’,andthere- Theredshiftsofthemembergalaxiesinthemockgroups
fore the number of ∆shuffled-values, used to compute the are randomly drawn from Gaussian distributions. The dis-
probability.OnecanseefromEquation3thatsystemswith persions oftheinputGaussians are takentobetheaverage
significantsubstructurewillhavelowP-values,sinceitisun- velocitydispersionoftheaforementionedgroupmembership
likely to obtain the observed ∆-value randomly (Equation bins,whichare:300,350,400and550kms−1.Thesedisper-
2). sionvaluesarechosenforthemocksgroupsinordertobest
mimic the systems in our GEEC sample. We also generate
mock groups with the same input host velocity dispersion
2.2 Monte Carlo Simulations
(σ ) for all values of n and find no significant dif-
host members
Although Pinkney et al. (1996) have carried out an exten- ference in ourresults (see Appendixfor further detail).
sive investigation of the DS Test, their analysis was per- AswillbeshowninSection2.2.2,inordertodetermine
formed on systems with a minimum of 30 members, and thefalsenegativeratesfortheDSTest,wemustincludesub-
themajority of ourintermediate redshift groups havefewer structurewithinthehostgroup.Thepositionsandredshifts
member galaxies (see Section 3.1). Therefore, we perform ofthesubstructuregalaxiesaredrawnfromaGaussian dis-
4 Hou et al.
often greater than 1.0, with values peaking closer to 1.4 for
200 120 larger(i.e.n 80-100)clusters.Althoughitispossi-
members
∼
100 bletobetteridentifysubstructureinrichersystems,suchas
150 clusters, with a highervalue of ∆/n 1.4 - 1.6 (e.g.,
80 members ∼
Girardi et al. 2005; Knebe& Mu¨ller 2000), we findthat for
100 60 group-sized systems this methodology could not simultane-
40 ously producelow false positive and false negative rates.
50 Alternatively, when P-values are used to identify sub-
20
structure, we find that the false positive rates are much
0 0 lower than with the critical values method and also re-
0 2 4 6 0 2 4 6
100 markably stable for a wide range of group members (i.e.
60 5 nmembers 50). From ourmock groupswe findthatfor
80 ≤ ≤
significance levels of 0.01, 0.05 and 0.10, the false positive
40 60 rates are 5, 10 and 15 per cent for all values of nmembers
tested. In other words, the DS Test will falsely identify
40 roughly 5 per cent more substructure than the desired sig-
20 nificancelevel.Althoughtheseratesarehigherthantheex-
20
pected values for a given significance level, they are still
0 0 substantially lower than the rates obtained using the criti-
0 2 4 6 0 2 4 6
cal values method.Also, as long as onechooses significance
levels of 0.01 or 0.05, the rate of false identifications is ac-
ceptablylow.Basedontheseresults,weruleoutthecritical
Figure 1. Histograms of the radial distribution of the galaxies
valuesmethodandonlyperformthefollowinganalysisusing
in the GEEC Group Catalog stacked in bins of nmembers. The
dashedlinecorrespondstoanexponentialfittothedistribution, theprobabilities, P-values, method.
which we use to generate the radial positions of galaxies in our
mockgroups.
2.2.3 Testing for False Negatives
tribution2. The free parameters in our mock groups with Havingdetermined therate offalse identificationsobtained
withtheDSTest,wenowtestfortherateoffalsenegatives,
substructureare:thevelocitydispersionofthesubstructure
or type II errors. For this statistic the false negative rate
(σredshift), spatial dispersion of the substructure (σposition),
measureshowoftentheDSTestfailstodetectsubstructure
location of thesubstructure,in bothposition (ǫposition) and
whenindeeditexists.Thepurposeofconductingthesefalse
velocity (ǫ ) space, the numberof galaxies in the sub-
redshift
negativetestsistwofold:first,theyhelpdeterminetherelia-
structure (n ), the number of galaxies in the host group
sub
bilityofthestatisticandsecond,byvaryingonlyoneofthe
(n ),andvelocitydispersionofthehostgroup(σ ).
members host
freeinputparameters(listedinSection2.2.1)atatime,you
Webrieflyanalyzetheeffectsofeachoftheseparameterson
can determine how sensitive the test is to each parameter.
therobustnessof theDSTest inthefollowing sections, and
The latter places quantitative constraints on the maximum
give a more detailed discussion in the Appendix.
size and location of substructurethat can be identified.
Before we begin looking at the input parameters, we
2.2.2 Testing for False Positives first determine how reliable the test is at identifying ‘ob-
vious’ substructure, that is to say galaxies that are tightly
Usingthemockgroupswithnoinputsubstructuredescribed
correlated and located far from the group centre, both in
inSection2.2.1,wedeterminethefalsepositiverates,ortype
projection on the sky and along the line-of-sight (see Table
I errors, which for the DS Test occur when substructure is
1 for input parameter values). For these mock groups, we
identifiedwhennoneexists.Theonlyparameterwevaryfor
find that substructure is correctly identified in almost all
thesesystemsisthenumberofmembergalaxies(n ).
members cases, using the P-value method and a significance level of
Wefirst computethefalse positiveratesusingthecrit-
0.01, producing false negative rates of 0 or 1 percent.
ical values method. For each value of n we com-
members We then investigate the individual free parameters in
pute the ∆-statistic, (Equations 1 and 2) and then clas-
more detail to determine how each alters the false negative
sify a group as having substructure if ∆/n > 1.0.
members rate. Webriefly discuss the main results here and leave the
With this criterion, we find that for all relevant values of
detailed quantitative analysis, as well as full tables of false
n the false positive rates are extremely high. For
members negative rates, for theAppendix.
example for n = 20, the false positive rate is 81
members ∼ Of the five free parameters, we find that the DS Test
per cent and even for larger systems, n = 100, we
members is most sensitive to the numberof galaxies in the substruc-
find that the rate is equally high. A similar result was ob-
ture (n ) and the location of the peak of the substruc-
sub
servedbyKnebe& Mu¨ller(2000)inastudyofsubstructure
ture’s velocity distribution with respect to the peak of the
in numerically simulated galaxy clusters. They found that
host’s (ǫ ). Previous studies of substructure in galaxy
redshift
forhaloeswithnosubstructurethe∆/n -valueswere
members clusters by Dressler & Shectman (1988) and Pinkney et al.
(1996) showed that the DS Test was unable to find sub-
2 Testswithnon-Gaussianinputsubstructurehavealsobeencar- structure that was ‘superimposed’ with the highest density
ried out and for all reasonable distributions the results do not regionsofthehosts,sincethegalaxieswerespatiallymixed.
differsignificantlyfromtheresultspresentedhere. Pinkneyet al. (1996) even stated that in these cases, any
Substructure inthe Most MassiveGEEC Groups: Field-likePopulationsin DynamicallyActive Groups 5
Table1.Inputparametervaluesforthe‘base’mockgroupsdescribedinSection2.2.3;i.e.MonteCarlogroupswithazerofalsenegative
rate.
nmembers nsub σhost σposition ǫposition σredshift ǫredshift
kms−1 Mpc Mpc kms−1 kms−1
10 4 350 0.01 0.5 100 1300
15 5 400 0.01 0.5 100 1300
20 5 550 0.01 0.5 100 1300
50 10 550 0.01 0.5 100 1300
typeof3-Dtestwouldnotbeabletoaccuratelydetectsub- Taking into account the results of both the false neg-
structure. An important distinction, not made by these au- ative and positive tests, we conclude that for systems with
thors, is that two forms of ‘superposition’ can occur. Sub- n 20, the DS Test can reliably identify real sub-
members
≥
structurecanbesuperimposedwiththehostgroupeitherin structureif theP-values method is employed using a confi-
projected angular position or in redshift space. Our analy- dencelevelofeither0.01or0.05.Forgroupswithn <
members
sis shows that theDSTest is significantly moresensitive to 20,wefindthatthepercentageofgroupswith substructure
ǫredshift than to ǫposition. The test can usually identify sub- identified bythe DS Test should be taken as a lower limit.
structure with superpositions as projected on the sky, but
has a very difficult time with those along the line-of-sight.
From Equation 1, it is clear that only collections of neigh-
3 SUBSTRUCTURE IN THE GEEC GROUPS
bouring galaxies with a different local mean velocity and
velocity dispersion will produce high δ values, no matter 3.1 The GEEC Group Catalog
i
their angular position.
The Group Environment and Evolution Collaboration
In addition we also find that the level of sensitivity of
(GEEC) group catalog is based on a set of 200 inter-
the DS Test to ǫ , the distance between the substruc- ∼
redshift mediate redshift, 0.1 < z < 0.6, galaxy groups initially
ture’sandhost’speakvelocitydistribution,isdependenton
identified in the second Canadian Network for Observa-
thenumberof members in thehost group.Wefind that for
tionalCosmology(CNOC2)redshiftsurvey(Yeeet al.2000;
small groups (i.e. nmembers < 20), the input substructure Carlberg et al.2001).TheCNOC2surveyobserved 4 104
needs to be further than 2σhost from the group centre in galaxies covering four patches,totalling 1.5 deg2 in∼are×a, in
order to be detected. On the other hand, the DS Test can
theUBVR I bandsdowntoalimitingmagnitudeofR =
C C C
identify substructure that is roughly 2σ away from the
host 23.0.Spectraofmorethan6000galaxieswereobtainedwith
peak of the host’s Gaussian velocity distribution in groups
the MOS spectrograph on the Canada-France-Hawaii Tele-
with more than 20 members. For even larger systems, that
scope(CFHT),with48percentcompletenessatR =21.5
C
is clusters with n 50, the input substructure can
members ≥ (Yeeet al. 2000). The GEEC group catalog includes ex-
belocated within 1σ and still be identified.
host tensive follow-up spectroscopy with the Inamori Magellan
Another result from this analysis is that the DS Test Areal Camera and Spectrograph (IMACS) (Connelly, J. et
is sensitive to the number of galaxies that are part of the al., submitted) and Low Dispersion Survey Spectrograph
substructure (nsub). Our simulations show that no matter (LDSS2) on Magellan (Wilman et al. 2005), as well the Fo-
the membership of the host group, the test cannot identify cal Reducer and low dispersion Spectrograph (FORS2) on
substructurewith fewerthenfourmembers.Also,themini- the Very Large Telescope (VLT) (Connelly, J. et al., sub-
mum required number of members within the substructure mitted). We have also obtained multi-wavelength imaging
increases with nmembers. This is due to the fact that we set data, which includes: X-ray observations with the X-ray
Nnn inEquation1to√nmembers.Therefore, moremembers Multi-Mirror Mission-Newton (XMM-Newton) and Chan-
in the host group means that the velocity information of dra X-ray Observatories (Finoguenov et al. 2009), ultravio-
more‘neighbours’will beused tocalculate νilocal andσliocal. let observations with Galaxy Evolution Explorer (GALEX)
Thus,iftherearetoofewgalaxiesinthesubstructure,their (McGee et al.2011),opticalobservationswiththeAdvanced
kinematicdeviationscanbewashedoutbyotherneighbour- Camera for Surveys (ACS) on the Hubble Space Telescope
ing host galaxies. (HST)(Wilman et al.2009),infrared observations with the
We find that for rich galaxy groups, with n Multi-band Imaging Photometer for Spitzer (MIPS) on
members
≥
20, the DS Test can reliably identify true substruc- the Spitzer Space Telescope (Tyler et al. 2011), and near-
ture, as has been shown by several other authors infrared observations with Isaac Newton Group Red Imag-
(e.g., Dressler & Shectman 1988; Pinkney et al. 1996; ing Device (INGRID) on the William Herschel Telescope
Knebe& Mu¨ller 2000). For systems with fewer member (Balogh et al. 2009), Infrared Array Camera (IRAC) on
galaxies, such as poor groups with n <20, the false Spitzer(Wilman et al.2008),andtheSonofISAAC(SOFI)
members
negative rates are very low (< 5 per cent) only for tightly on the New Technology Telescope (NTT) (Balogh et al.
correlatedsubstructuregalaxieswithlargekinematicdevia- 2009). In addition, improved optical imaging was obtained
tions.Inthesepoorgroups,substructurethatismoreloosely in the ugrizBVRI filters from the CFHT Megacam and
associatedwithavelocitypeakclosetothatofitshostgroup CFH12K imagers (Balogh et al. 2009).
is not as easily detected by thetest. Inadditiontothefollow-upobservationsoftheCNOC2
6 Hou et al.
fields, group membership has also been redefined by
Wilman et al. (2005) using more relaxed algorithm param-
- groups with no substructure
eters than those used by Carlberg et al. (2001). The origi- - groups with substructure
- all groups in GEEC sample
nal search parameters were optimized such that the group-
finding algorithm would identify dense, virialized groups,
whiletheWilman et al.(2005)catalogincludesloosergroup
populations that cover a wider range of dynamical states.
Forthisreason, theGEECgroupcatalog isidealforthein-
vestigation of substructure within groups, since we are not
restricted to dense group cores and are able to probe the
surroundinglarge scale structure.
- groups with no substructure
- groups with substructure
- all groups in GEEC sample
3.2 Analysis of the GEEC Groups
We apply the DS Test, as described in Section 2, to a sub-
set of the GEEC groups. Although there are roughly 200
groups in the GEEC catalog, the majority of systems have
fewerthan10members.InSection2.2.3,wedeterminedthat
in order to obtain a reliable measure of substructure, the
minimum number of member galaxies for the DS Test is
n = 20, which leaves us with a subset of 15 groups.
members
These groups are amongst the most massive GEEC groups Figure2.Top:Intrinsicvelocitydispersionσintversusthegroup
with an average velocity dispersion of 525 km s−1. redshiftforthegalaxygroupsinoursample.Solidcirclesindicate
∼
As previously mentioned, due to the relaxed member- groups with no substructure and open triangles indicate groups
ship allocation algorithm parameters, some of the GEEC with identified substructure according to the DS Test, at a 99
groupshaverelativelylargeradialextents,andcanbelarger per cent confidence level. The smaller open circles represent the
than the suggested maximum group virial radius (r200) of dispersionsof allthe groups inthe GEEC catalogue, the major-
1.0 Mpc (Mamon 2007), but for the purposes of detecting ity of which are not used in this analysis. Our nmembers ≥ 20
GEEC sampletend to have higher velocity dispersions.Bottom:
substructure we elect not to apply any radial cuts to our
groupsforourmainanalysis.Ourdefinitionofsubstructure nmembers versus the group redshift for the galaxy groups in our
sample.Symbolsarethesameastheplotabove.
isliberal, inthatweincludestructurethatmaybeinfalling
or structure that is in nearby large scale structure but not
necessarilyboundtothehostgroup.Thus,toensurethatwe
redshift. Groups with and without substructure both span
do not eliminate any possible detection of substructure, we
a wide range of velocity dispersions and group membership
analyzeallgalaxiesidentifiedasgroupmembersbytheFOF-
indicating that there is no apparent redshift bias with re-
algorithmappliedinWilman et al.(2005).Ourdecisionnot
gards to group velocity dispersions or n for the DS
members
to apply radial cuts is furtherjustified given that substruc-
Test.
tureisofteningroupandclusteroutskirts(West & Bothun
Although the minimum membership cut needed to de-
1990;Zabludoff & Mulchaey 1998a).
termine a reliable percentage of groups that contain sub-
For the distribution parameters we estimate νi and
local structure is nmembers = 20, we can still apply the DS Test
ν, from Equation 1, as the group and local (i.e. ith galaxy
to systems with fewer members and establish a lower limit
and its √nmembers nearest neighbours) canonical mean ve- on this fraction. Including groups with as few as ten mem-
locity, and σi and σ, also from Equation 1, as the local
local bers increases our sample size to 63 systems. Applying the
and group intrinsic velocity dispersion, computed following
same methodology described above we find that 11 of our
the method outlined in Wilman et al. (2005). The disper-
63groups( 17percent)areidentifiedashavingsignificant
sionuncertaintiesarecomputedusingthejackknifemethod ∼
(> 99 per cent c.l.) substructure.
(Efron 1982) and are given in Tables 2 and 3.
Of the 15 GEEC groups with n 20 we find
members
≥
that 4 groups, ( 27 per cent) are identified as having sub-
∼ 3.3 GEEC Groups with Substructure
structure at the99 per cent confidencelevel (c.l.). In Table
2,welistgroupproperties,∆/n -values,andP-values WeexaminetheGEECgroupsclassifiedashavingsubstruc-
members
for the groups with substructure, identified as the systems ture by the DS Test in detail to determine if we can iden-
thathaveP-valuesoflessthan1percent.InTable3welist tify theregions of localized substructure.By examining the
the same values, but for groups without substructure, that availableposition andvelocity information,wecanfindcol-
issystemsthathaveP-valuesgreaterthan1percent.Also, lections of galaxies that are kinematically distinct from the
it should be noted that although we list the ∆/n host group.
members
critical values in Tables 2 and 3, we rely on the P-values In the following analysis, we focus on small subgroups
to identify substructure in our groups. In addition, Tables ofgalaxiesthatmaybepartofsomelocalized substructure.
2 and 3 lists the dynamical properties of the groups to be This is done by looking at the δ histogram (Figs. 3(a) -
i
discussedinSections4.1and4.2.InFig.2,weplotboththe 6(a)), velocity histograms (Figs. 3(b)- 6(b)),‘bubble-plots’
intrinsicvelocitydispersionofthegroup(top)andthetotal (i.e.positionplotsofthegroupmembersweightedbyexpδ
i
numberofgroup members(bottom) versusthemeangroup (Dressler & Shectman 1988) (Figs. 3(c) - 6(c)) and group-
Substructure inthe Most MassiveGEEC Groups: Field-likePopulationsin DynamicallyActive Groups 7
Table 2.GrouppropertiesandDSstatisticsfortheGEECgroupswithsubstructure
GEECGroupID nmembers zgroup σ ∆/nmembers P valuea ADTest ShapeofVelocity
kms−1 Classification DispersionProfile
25 28 0.362 491±32 0.693 0 non-Gaussian rising
208 22 0.269 530±45 0.841 0 non-Gaussian rising
226 86 0.359 944±17 1.37 0 non-Gaussian rising
320 29 0.245 463±33 0.751 0.00383 Gaussian rising
aUsing100000‘MCshuffles’.WeidentifygroupswithP values<0.01ashavingsignificantsubstructure.
Table 3.GrouppropertiesandDSstatisticsvaluesfortheGEECgroupswithnosubstructure
GEECGroupID nmembers zgroup σ ∆/nmembers P-valuea ADTest ShapeofVelocity
kms−1 Classification DispersionProfile
4 20 0.201 360±39 0.605 0.524 non-Gaussian flat
38 34 0.511 739±21 0.910 0.0372 non-Gaussian declining
104 27 0.145 365±25 0.659 0.0501 Gaussian flat
110 33 0.156 338±22 0.599 0.413 Gaussian declining
117 27 0.220 261±20 0.412 0.851 Gaussian flat
138 53 0.438 743±29 0.983 0.354 non-Gaussian flat
238 21 0.408 606±52 0.826 0.135 non-Gaussian flat
308 26 0.224 511±35 0.854 0.610 Gaussian declining
334 20 0.323 454±30 0.670 0.0563 Gaussian flat
346 32 0.373 439±20 0.612 0.232 non-Gaussian flat
362 24 0.460 666±43 0.861 0.0817 Gaussian rising
aUsing100000‘MCshuffles’.WeonlyidentifygroupswithP values<0.01ashavingsignificantsubstructure.
centric radial velocity (i.e. czmember czgroup) weighted po- tions, shown in the‘bubble-plots’and similar group-centric
−
sition plots (Figs. 3(d) - 6(d)). radial velocities, shown in the weighted position plots.
WewillnowdiscusseachofthefourGEECGroupswith
The δi and velocity histograms provide an estimate on substructure in detail. Using the methodology described
the amount of substructure and the dynamical state of the above,wesearch forcandidatelocal regions ofsubstructure
groups. The δi histogram gives an overall view of the kine- in our sample. GEEC Group 25 (Fig. 3) has a collection of
matic deviations and the velocity histogram can be used five galaxies, just south-east of the group centre, that all
to identify non-Gaussian features, such as multiple peaks. have high δ values and comparable velocities. Similarly in
i
In order to look for local regions of substructure, one must GEEC Group 208 there are seven galaxies that lie south-
look at both the ‘bubble-plot’ and velocity weighted posi- west of the group centre, with equally high δ values (Fig.
i
tion plots in Figs. 3 - 6. The ‘bubble-plots’ allow for the 4(c)). Though, when we look at these same galaxies in the
visual identification of candidate regions of local substruc- velocityweightedpositionplot(Fig.4(d)),onlyfiveofthese
ture.Sincethesizeofthesymbolsinthe‘bubble-plot’scales sevengalaxieshavecomparableradialvelocities.Thisresult
withagalaxy’sδi value,largesymbolscorrespondtostrong highlights the importance of looking at both the ‘bubble-
local kinematic deviations from the global values. Thus, a plot’and velocity weighted positions plots, as galaxies with
collectionofneighbouringgalaxieswithsimilarlylargesym- large kinematic deviations may be correlated in position-
bols, such as region A in Fig. 5(c), could indicate a kine- space, but not in velocity-space.
matically distinct system. In order to confirm that these In Fig. 5, we show the substructure analysis plots for
candidate regions are truly distinct, one must check that GEEC Group 226 and from the ‘bubble-plot’ we see that
thecandidate substructuregalaxies also havesimilar veloc- therearetwopossiblydistinctregionsoflocalized substruc-
ities, since the sign or direction of the galaxy velocity is ture. The first region lies directly north-east of the group
not taken into account in theDS Test (Equation 1).To de- centre (region A in Fig. 5(c)) and includes the galaxy with
terminethis,welookat thegroup-centricvelocityweighted the highest δ value. All of the members within this given
i
positionplottoseeifthecandidatelocalsubstructuregalax- substructure have similar radial velocities (Fig. 5(d)). The
ies have similar velocities. In Figs. 3(d) to 6(d) the red second region of interest containseleven galaxies that lie in
symbols correspond to positive group-centric velocities (i.e. the very north-east corner of the ‘bubble-plot’ (region B in
czmember czgroup >0),bluesymbolscorrespondtonegative Fig. 5(c)). Again, all of the galaxies within this particular
−
group-centricvelocities(i.e.czmember czgroup <0)andthe substructurehavesimilargroup-centricvelocities,thoughin
−
symbol size scales with the magnitude of the velocity off- theopposite direction of themembers in region A.
set. We only identify galaxies as part of local substructure
if neighbouring galaxies havesimilar large kinematic devia-
8 Hou et al.
Figure3.GEECGroup25.(a):δi histogram.(b):Histogramof Figure 5.Sameas Fig.3butforGEECGroup226andtheve-
thevelocitydistribution,wherethedashed-lineindicatesthebest locityweightedplotnowscalesasexp(czmember−czgroup)/600.
fitting Gaussian velocity dispersion. (c): Dressler&Shectman The dotted box encompasses the first identified region of local
(1988)‘bubble-plot’wherethegalaxysymbolsscalewithexp(δi). substructure (region A) and the long dashed box encompasses
(d): Position plot where the galaxy symbols scale with group- thesecondregionoflocalsubstructure(regionB).
centricvelocity(i.e.exp(czmember−czgroup)/350),bluesymbols
correspondtogalaxieswithnegativegroup-centricvelocities(i.e.
czmember−czgroup <0) andredsymbolscorrespond togalaxies
withpositivegroup-centricvelocities(i.e.czmember−czgroup>0).
Figure 6.SameasFig.3butforGEECGroup320.
Figure 4.SameasFig.3butforGEECGroup208andtheve-
locityweightedplotnowscalesasexp(czmember−czgroup)/400.
Substructure inthe Most MassiveGEEC Groups: Field-likePopulationsin DynamicallyActive Groups 9
Fromthe‘bubble-plot’ofGEECGroup320(Fig.6(c)),
we see two possible regions of substructure;one just north-
west of centre and another further south-west of centre.
The structure near the group centre does not appear to
be very localized, as the velocities, though in the same di-
rection, have significantly different magnitudes (Fig. 6(d)).
The second region of high δ values may actually be two
i
separate structures. The velocity weighted position plot in
Fig. 6(d) reveals that three of the galaxies in the structure
havesimilarnegativegroup-centricvelocities(i.e.cz
member
−
czgroup < 0) and two have similar positive velocities (i.e.
czmember czgroup > 0). Therefore, we identify the collec-
−
tionofthreegalaxies,withthenegativegroup-centricradial
velocities, as thebest candidate of substructurewithin this
system.
In each of the GEEC groups with substructure, it ap-
pearsthatouridentifiedregionsoflocalizedsubstructurelie
on the outskirts or edges of the group, and may either be
infalling onto a pre-existing system or in the nearby large
scale structure,but not necessarily bound or infalling. This
result is in agreement with similar studies of substructure
in local groups (Zabludoff & Mulchaey 1998a) and clusters
(West & Bothun 1990).
It should also be noted that although the DS Test has
beenshowntobereliableforgroup-sizedsystems,thenum-
berofmemberswithinthesubstructurecanaffecttheresults
of the statistic. As discussed in Section 2.2, and shown in
more detail in the Appendix, fewer(more) true members of
substructure can increase(decrease) the rate of false nega-
tives. However,we also show that therateof false positives
is consistently low for all of our mock groups (see Section
2.2).Thus,anydetectionofsubstructureinthesesystemsis
likely tobe real. Figure 7. α−Vr plot for GEEC Groups (a) 25, (b) 208, (c)
region A and the host group of 226, (d) region B and the host
groupof226 (d)and(e) 320 .Theunshaded regions correspond
to bound solutions and shaded regions correspond to unbound
3.4 Is the localized substructure gravitationally
solutions of the virial theorem given by Equation 5. The solid
bound to the group?
line corresponds to the measured value of Vr (i.e. the line-of-
Thelocal regionsofsubstructurewedetectlieonthegroup sightvelocitydifferencebetweenthesubstructureandhostgroup
centres). The dashed lines correspond to one-sigma deviations,
outskirtsandarepossiblyboundandinfalling,ornotbound,
takentobetheerrorsontheintrinsicvelocitydispersion.
butcloseinlargescalestructure.Inordertohelpdistinguish
between these two possibilities, we apply a simple bound
testtoestimatewhetherornottheregionsoflocalized sub-
tweenthetwoobjects.V istheline-of-sightrelativevelocity
structure are gravitationally bound to thehost group. This r
between thetwo bodiesand R istheprojected separation,
is done by computing the limits for bound systems, using p
both of which are measurable quantities.
avariation of thevirial theorem asdiscussed in Beers et al.
The unknown quantity in Equation 5 is the projection
(1982),anddeterminingifthesubstructurefallswithinthese
angle α. Thus, to compute the limit between bound and
limits. Beers et al. (1982) state that for a two-body system
unbound systems, one must work in α V space to de-
onalinearorbit,theNewtonianlimitforgravitationalbind- − r
termine the probability that the system is gravitationally
ing, projected ontothe sky is given by
bound for any given projection angle. This is achieved by
setting 0◦ α 90◦ and solving for V in Equation 5,
r
≤ ≤
Vr2Rp ≤2GMsin2αcosα, (5) producing a distinct line in α−Vr space that clearly sepa-
rates bound and unbound solutions (Fig. 7). One can then
where,
compute the probability of a bound solution, for a given
projection angle, using theα V plot.
Vr =V sinα, Rp =Rcosα, (6) − r
To apply this methodology to our group sample, we
treatouridentifiedregionsoflocalsubstructureasone-body
and where α is the angle between the line joining the and the remaining galaxies as the second-body, which we
two-body system and the plane of the sky (see fig. 7 of refertoas the‘host’ group.Thetotal mass ofthesystem is
Beers et al. 1982), M is the total mass of the entire sys- takentobethevirialmass,M200(i.e.thetotalmasswithina
tem (substructure plus host group), and R and V are the radiusthatenclosesameandensityof200timesthecritical
true(3-dimensional) positional andvelocityseparations be- density of the Universe at the redshift of the galaxy), of
10 Hou et al.
theGEECGroupsascomputedinBalogh et al.(2009)and
Table 4. Groups properties and DS statistics values for the
given by GEECGroupswitha1.0Mpcradiuscut
33/2σ3 1
M200 = G 10H0(1+z)1.5, (7)
GEECGroupID namembers ν σint P-value
kms−1 kms−1
where σ is the measured intrinsic velocity dispersion. The
measured Vr and Rp values are taken to be the distance 110 26 -15.3 350 0.403
betweentheR-bandluminosity-weightedcentresofthelocal 138 23 -226 730 0.792
substructure and the ‘host’ group centre, along the line-of- 226 25 -174 847 0.110
sight (V ) and projected on thesky (R ). 308 25 2.52 512 0.507
r p
InFig.7,weplottheα V plotsforthefivecandidate 346 26 -80.4 434 0.128
r
−
regions of local substructure, as discussed in Section 3.3. aGroupmembershipafterthe1.0Mpcradiuscut
The shaded regions indicate theareas spanned byunbound
solutions, as given by Equation 5, the solid black vertical
line is the measured value of V , and the long-short dashed 4.1 Comparison with the Dynamical
r
vertical linesindicate onesigma deviations, taken tobethe Classification of Velocity Distribution
intrinsic velocity dispersion error.
If a correlation does exist between substructure and re-
Using the methodology described above and Fig. 7, we
cent galaxy accretion, one would expect that the groups
conclude that the identified local substructures in GEEC
withsubstructureshouldalsobedynamicallycomplex,with
Groups 25 and 226 are not bound to the host group, while
perhaps non-Gaussian velocity distributions. In Hou et al.
for GEEC Groups208 and320 thedetected substructureis
(2009),weestablished aclassification schemetodistinguish
likely boundto the host group.
betweendynamicallyrelaxedandcomplexgroups.Usingthe
Anderson-Darling (AD) goodness-of-fit test, we are able to
determine how much a system’s velocity distribution de-
3.5 Substructure within 1 Mpc of the Group viates from Gaussian. This is done by comparing the cu-
Centroid mulative distribution function (CDF) of the ordered data,
which in our case is the observed velocity distribution, to
In the previous section we analyzed a subset of 15 GEEC
the model Gaussian empirical distribution function (EDF)
groups, with n 20, without applying any radial
members ≥ using computing formulas given in D’Agostino & Stephens
cuts. Here we apply a 1.0 Mpc cut, which is the suggested
(1986).TheADstatisticisthenconvertedintoaprobability,
maximum virial radius for groups (Mamon 2007), on the
orP-value,usingresultsdeterminedviaMonteCarlometh-
same subset of groups and re-apply the DS Test. Applying
odsinNelson(1998).Asystemisthenconsideredtohavea
this radial cut, while still requiring a minimum number of
non-Gaussian velocity distribution if its computed P-value
20membergalaxies,reducesoursamplefrom15to5groups
is less then 0.01 corresponding to a 99 per cent c.l.
(GEECGroups110,138,226,308and346).Withthisradial
We now apply this scheme to our sample of 15 GEEC
cut,wefindthatall5groupsareidentifiedasnothavingsub-
groups, with n 20 and no radial cut, to compare
structure (see Table 4) according to the DS Test. The only thedynamicalsmtaemtebewrsit≥hthedetectionofsubstructure3.The
groupthatwaspreviouslyidentifiedashavingsubstructure,
results of our dynamical classification scheme indicate that
priortothe1.0Mpccut,isGEECGroup226.InFig.5,itis
8ofthe15groupsareclassified ashavingnon-Gaussian ve-
evidentthatalthoughtherearegalaxieswithrelativelyhigh
locitydistributions,at the99percentc.l., andarethusdy-
δ values close to the group centre, the members with the
i namically complex (see Tables 2 and 3).Of thefour GEEC
highest δ values lie near the edge of the group. In fact the
i groups with substructure only GEEC Group 320 shows a
most significant feature in the ‘bubble-plot’ (Fig. 5) is on
velocity distribution consistent with being Gaussian. Five
thetop-right corner of theplot, far from the group centre.
groups, GEEC Groups 4, 38, 138, 238, and 346, are identi-
Ifweincludeall of thegroupswith n 10 after
members ≥ fied as being dynamically complex, but do not contain any
a 1.0 Mpc radial cut, we find that 2 out 33 groups ( 6 per
∼ substructureaccording to the DSTest.
cent)ofoursamplecontainssignificantsubstructure.Again,
Pinkney et al. (1996) found that different statistical
we note that for systems with fewer than 20 members, the
tools (i.e. 1-D, 2-D and 3-D tests) probe the dynamical
DS Test can only provide a lower limit on the amount of
state of a system at varying epochs. Using N-body simula-
substructurepresent.
tions, these authors determined that 1-D tests, such as the
AD Test are most sensitive to scenarios when substructure
passesthroughthecoreofthehostgroup(i.e.core-crossing).
During this time substructure can become spatially mixed
4 CORRELATIONS BETWEEN
within the host group, and if the substructure is loosely
SUBSTRUCTURE AND OTHER
boundthenitmaybedifficulttodetectwith3-Dtests,such
INDICATORS OF DYNAMICAL STATE
Having identified the GEEC groups that contain substruc-
ture, we can also look at other dynamical properties, i.e. 3 The dynamical classifications in this paper differ from those
the velocity distributions and velocity dispersion profiles in Houetal. (2009). The reason for this difference is that in
(VDPs),todetermineifthereareanycorrelationswithsub- Houetal.(2009)weapplieda1.0Mpcradius cut tothe GEEC
structure. groups,whereasnoradialcutisappliedinthisanalysis.