astro-ph/9512111 18 Dec 1995 galaxies b eing lo cated in sub clusters We discuss this evi b etter around other brightest clusterThere members is evidence for a b ound p opulation of bright galaxies suggest rays and lo cated b etweeninciding the in two p osition dominant with galaxies ato we secondary form p a eak single detectedvelocity smo oth in space structure X On with the a central contrary the p eak fainter co galaxies tend A Biviano Abstract Received accepted tributions able in the central distributionthe of Coma these cluster A faint continuous galaxies velocity a gradient prob is found galaxies surrounded by two galaxycentral groups dominant mostly galaxies p opulated NGC with and NGC are Unveiling Send oprint requests to ple of cluster available for a cluster ofgalaxy galaxies redshifts We in have the dened Coma a cluster sam the largest presently available membership criterion based on the galaxy velocity when wavelet and adaptive kernel techniques the France and the Universityof of Canada Hawaii the Centre NationalHawaii de telescop e la op erated Recherche Scientique by of the National PSPC cal analyses p ossible Usingsucient this number of sample galaxies and p er the sample to make statisti erwise plete samples within a region of h Coma Your thesaurus co des are will b e inserted byAA hand manuscript later no Observatoire de la CotedAzurLab BP oratoire dAstrophysique F Spatiale Nice CNRSCentro Cedex Traverse de du Astrofsicada France Siphon UniversidadeDAEC Les do Observatoire Trois Porto de Lucs Rua Paris BP doInstitut UniversiteDenis Camp o Diderot dAstrophysique F Alegre CNRS de Marseille UA Paris CedexSterrewacht CNRS Leiden France Porto F UniversitePierre Postbus et Portugal Meudon Marie Cedex Niels Curie France Bohrweg bis Bd Arago RA F Leiden Paris The France Netherlands Based Altogether A striking coincidence of features structure signature traced Xray Such to brighter on or of identify this We 1 F Durret observations on a galaxies members complete to b by image and of data the have the the than tidal interactions kinematics Coma hidden of set galaxy faint assembled and F Durret b the structure 26 allows 2 collected cluster 5 hot galaxy p opulation the 3 D Gerbal cluster magnitude of intracluster us a Coma by with the structure and structures at to large rather we 1 26 is found in the dis dene Mp c radius with a the well 5 have and Research Council 2 dataset O Le Fevre CanadaFrance than main b o dy of gas applying separated seems nearly colour reanalyzed using a rotation The ROSAT of bright to com oth two the b e in in 3 C Lob o cant detection of sub clustering in the cluster core used limited to NGC tering and o ccurs around Fitchett many brightal galaxies Webster and and Mellier is et not al only suggested that sub clus preted as an indicationluminosity of segregation among partial the dynamical galaxies relaxation in Coma inter at a p ossibleof sub clustering Coma around theclaimed giant signicant galaxy substructure NGC in the and SouthWest hinted region of giant galaxies in its core to this considered as the prototypeclusters of irregular clusters Suppp ort earance made of this cluster the Its prototype high of richness well relaxed richnessclusters class since the and rst determination smo oth of ap catalogue its has mass b by een Zwicky one of the most studied galaxy a namical system Ro o d Sastry classied Coma as The Introduction in ant galaxies During thewhich s most the of claims the for clusterther sub mass clustering by was prop osing linked an tothese unconventional these dynamical two two mo del galaxies gi Valtonen in and Byrd Ro o d went hinted even to far a p ossible sub clustering around to Key cluster dence in terms of an ongoing accretion of groups onto the binary the Coma b ecame challenge However Coma cluster words view came from the 2 in Coma 4 A Mazure cluster contrast the Leestatistics the as Galaxies clusters individual Coma early picture more of galaxies number in the b ecause to as cluster and the 5 of in and E Slezak in the cluster NGC and discovery Coma more most the of to provide the rst the s frequent nearby as presence ? some ASTROPHYSICS a by Ro o d of ASTRONOMY well core Gerbal et cluster 6 facts Baier AND NGC of relaxed a started signi couple Virgo Ab ell dy

A Biviano et al Unveiling hidden structures in the Coma cluster

Nevertheless in the same p erio d Dressler Shect sults from our work have b een presented in Biviano et al

man did not nd a signicant signal for sub cluster Gerbal et al and Durret et al

ing in Coma and most dynamical analyses still assumed

Shortly b efore this pap er was submitted we received

a smo oth cluster structure Kent Gunn The

a preprint from CD which also carried out a structural

White Merritt Hughes It was in fact

analysis of the Coma cluster with rather dierent tech

not until the s that the complicated structure of the

niques while we agree on some of their results we do not

Coma cluster b ecame widely accepted thanks to new tech

come to the same conclusions on what concerns the struc

niques applied to the galaxy distribution Escalera et al

ture of the central cluster region

and to the detection of these structures in the X

In x we describ e the optical and Xray data used for

ray band with the Spacelab Xray telescop e Watt et

our analysis we analyse the structure of the central region

al and particularly with ROSAT Briel et al

of the Coma cluster as describ ed by the galaxy and X

White et al Vikhlinin et al

ray distributions in x and the cluster kinematics in x

Sub clustering implies an incomplete virialization of the

in x we extend our analysis to the external regions the

cluster with ongoing mergers of groups onto the main

relevant discussion is provided in x nally we summarize

b o dy of the cluster the dynamical youth of the Coma clus

our results and give our conclusions in x

ter is also indicated by the kinematical dierence b etween

the starforming galaxies and the old galaxy p opulation

The data

So dreet al Zabludo Franx Gavazzi et al

Colless Dunn hereafter CD the existence

Optical data

of a p opulation of EA sp ectrum galaxies likely to have

We have taken p ositions blue magnitudes and bluered

suered a burst of star formation within the last Gyr

colors of galaxies in the Coma region from the catalogue of

Caldwell et al is also suggestive of ongoing

Go dwin Metcalfe Peach hereafter GMP This

accretion of galaxies onto the cluster Finally unlike most

catalogue is nominally complete up to an isophotal mag

clusters Coma lacks a co oling ow Edge et al and

nitude b we note these isophotal magnitudes

has a radio halo Hanisch these features have b een

265

b hereafter in a square degree area centered on

interpreted in terms of an ongoing collision of two equally

h m  0

sized sub clusters McGlynn Fabian Edge et al

1950 1950

Tribble Fabian et al We have assembled a total number of galaxies with

redshifts in the Coma region dened by GMP redshifts

Coma can now b e considered as the prototype of rich

for galaxies have b een obtained by ourselves through

clusters endowed with sub clusters and thus not fully re

observations with the CFHT in May Biviano et al

laxed However the very presence of substructures log

a another redshifts have b een kindly provided

ically implies the existence of a main body on which

by M Colless in advance of publication CD nally

these features are sup erimp osed it has b ecome custom

another redshifts have b een taken from the literature

ary to identify this main b o dy with the group surround

Bothun et al Caldwell et al Davies et al

ing NGC mainly b ecause this galaxy lies on the main

da Costa et al de Vaucouleurs et al

p eak of the diuse cluster Xray emission see eg White

Gavazzi Giovanelli Haynes Homan et al

et al in particular this is the p oint of view of CD

Huchra et al Huchra et al Huchtmeier

However the velocity of NGC is oset from the av

Richter Karachentsev Kopylov Kent

erage velocity of the cluster and although not uncommon

Gunn Leech et al Lucey et al Palumbo

among brightest cluster members this is an unexp ected

et al Sullivan et al van Haarlem et al

result if the galaxy is at rest at the b ottom of the p oten

Wegner et al White et al Zabludo et al

tial well of the cluster Therefore it is also p ossible that

For the compilation of redshifts from the literature

NGC rather lies at the b ottom of the gravitational

we have made use of the ZCAT catalogue Huchra et al

well of its own group similarly to what is observed for

When several redshift measurements were available

other central dominant galaxies Bird

for the same galaxy we have chosen the most accurate one

The large number of galaxy velocities now available

In Table is indicated the completeness in velocity as a

in the Coma cluster eld including our new redshift

function of the limiting magnitude in the GMP region and

dataset Biviano et al a and the high resolution of

in the inner region circle of radius with resp ect

the ROSAT PSPC Xray image allows us to examine the

to all galaxies in the eld cols and resp ectively

structure and kinematics of the central part of the Coma

1

cluster within h Mp c where h is the Hubble constant For the purp ose of our analysis we have extracted sev

1 1

in units of km s Mp c with the aim of understand eral samples from a combination of the GMP photometric

ing if a main cluster body actually exists indep endently catalogue and our redshift catalogue In order to reach a

from the two central sub clusters In this pap er we also high value of completeness in velocities and still have a

address the issue of sub clustering and ongoing infall onto suciently large number of galaxies in the sample most of

the cluster in a larger cluster region Some preliminary re our analyses have b een p erformed on a circular region of

A Biviano et al Unveiling hidden structures in the Coma cluster

The central region of Coma structure

Table Completeness in velocity as a function of limiting

magnitude N and N represent the number of galaxies with

v

Methods of analysis

velocities and the total number of galaxies resp ectively

In order to visualize the distribution of galaxies on all

Magnitude range N N

v

scales at once we have used the metho d of adaptive ker

GMP region region

nels eg Silverman The adaptive kernel technique

is widely used in the astrophysical literature eg Pisani

b

Merritt Gebhardt Here we have also

b

used this technique to draw maps of various moments of

b

b

the galaxy velocity distribution see Figs and

b

The adaptive kernel technique requires an initial ker

b

nel size this size is then mo died according to the lo cal

b

density of p oints Unless otherwise stated we used an ini

b

1

tial kernel size equal to ie h Mp c at the

b

distance of the cluster since this is close to the intrin

sic scale of many structures in the Coma cluster Mellier

et al Escalera et al and also happ ens to b e

radius at the distance of the Coma cluster

nearly equal to the optimal kernel size Silverman

1

corresp ond to h Mp c We choose a circular region to

for the sample C which is the most used sample in our

avoid introducing any preferential direction

analysis

From these samples we have extracted the cluster

The signicance of the detected structures is estimated

members The membership assignment is based on the

through a b o otstrap resampling analysis See App endix A

galaxy velocity when available galaxies with velocities in

for further details

1

the range km s plus one galaxy with a

For the Xray data we have used the wavelet anal

1

velocity of km s are assumed to b elong to Coma

ysis which easily removes noise and allows by its multi

or on the lo cation of the galaxy in the colourmagnitude

scale approach to detect at a level b oth the p oint

band dened by Mazure et al for more details on

sources and the extended sources A thorough description

this membership assignement see Biviano et al b

of the metho d we have used is given in Slezak et al

We have dened and lab eled the samples and subsam

see also Greb enev et al and in App endix B The

ples that we have used as follows

wavelet metho d has already b een applied to the investiga

tion of b oth the galaxy and gas distributions in the Coma

sample C contains the galaxies members of the clus

all

cluster Escalera et al Gerbal et al Vikhlinin

ter in the GMP region up to the completeness magni

et al

tude b

sample C contains members of the cluster within the

circle of radius centered on the GMP center up

The galaxy distribution

to b

We display in Fig upp er panel an adaptive kernel den

subsample C contains C members with b

br ig ht

sity map of all the cluster members in the circle of

subsample C contains C members with b

f aint

radius ie sample C this and the following adaptive

kernel maps have pixels The signicance level of

subsample C contains C members with

f aint19

the features visible in this map has b een evaluated through

b

a b o otstrap resampling technique the densitymap at

Finally the subscript v indicates the subsamples of

condence level see App endix A is also plotted lower

galaxies with available velocities

panel most features of the original map are still visible

The numbers of galaxies with and without velocities

in this map

in these samples are listed in Table see next section

A complex structure is observed with a main p eak cor

resp onding to the central dominant galaxy NGC an

extension to the East corresp onding to the brightest clus

Xray data

ter member NGC and a less signicant extension to

the SouthEast in the direction of another bright galaxy

Xray images of Coma obtained with the ROSAT PSPC

NGC these structures have already b een p ointed out

were kindly made available to us by S White b efore their

by Mellier et al and Escalera et al This map

release in the Garching public archive We combined two

therefore naturally suggests the presence of sub clustering

of these images taken in the hard energy band

keV totalling an exp osure time of ab out s The A classical test for estimating the signicance level of

2

image sizes were pixels with a pixel size of the presence of sub clustering is that of Dressler Shect

1

ie h kp c at the distance of Coma man In this test one computes the lo cal mean ve

A Biviano et al Unveiling hidden structures in the Coma cluster

lo cities and velocity disp ersions of all p ossible groups of

neighboring galaxies and the deviations s of these lo cal

values from the global cluster mean velocity and velocity

disp ersion see also App endix A Large values indicate

a high probability for the cluster to contain substructures

p

Bird suggests that using N instead of galax v

1000

ies in the evaluation of the parameters where N is the

v

total number of galaxies with available velocities max

imizes the sensitivity of the test to signicant structures

while reducing sensitivity to noise uctuations

We have run this test mo died according to the sug

gestion of Bird on our sample C which contains

0 v

galaxies with available velocities and found a prob

ability of that substructures are present based

on Montecarlo simulations In order to visualize

these substructures we have plotted an adaptive kernel map notice that this is quite comparable to the weighted

-1000

wavelet metho d developed by Escalera et al We

caution the reader that it is not our intention to improve the statistical test for detection of substructure developed

-1000 0 1000

by Dressler Shectman the only purp ose of our

technique is to allow a D visualisation of the values of the

parameter used to identify susbtructures This is done

following the pro cedure describ ed in App endix A Iso

contours for the sample C are shown in Fig v

1000

1000 0

0 -1000

-1000 0 1000

-1000

Fig Upp er panel adaptive kernel density map of all the

b elonging to the Coma cluster within a circle of ra

galaxies -1000 0 1000

dius sample C In this gure and in the following ones

co ordinates are in arcseconds with resp ect to the cluster cen

tre dened in GMP North is to the top and East to the left

iso density contours are spaced by galaxiesarcsec

Fig Dressler Schectman map for sample C The av

v

The galaxies NGC NGC and NGC at resp ec

erage in this map is the rst contour starts at a value of

tive p ositions and are indicated

and following contours are spaced by an interval of

by xs The p osition of a secondary maximum detected in the

in Note that contours b eyond a distance of from the

Xray map is indicated by an asterisk at p osition

center are meaningless b ecause the C sample only contains

v

Lower panel adaptive kernel density map at condence

galaxies within this radius Symbols are the same as in Fig

level see App endix A

One may see on this gure that there are two main

p eaks in the distribution corresp onding to two regions

A Biviano et al Unveiling hidden structures in the Coma cluster

where galaxy velocities strongly dier from the average

Table Number of cluster members in the various subsam

velocity eld note that contours b eyond from the

ples after the elimination of galaxies in two fore and back

center are meaningless b ecause the sample C only con

v

ground groups N and N represent the number of galaxies

v

tains galaxies within this radius We have selected the

with velocities and the total number of galaxies resp ectively

galaxies lo cated within the contours delimiting the two

Sample N N

main p eaks these galaxies are listed in Table The

v

galaxies in the rst p eak have an average velocity of

C

all

1

km s and the galaxies in the second p eak have

C

1

an average velocity of km s Notice that

C

br ig ht

these two values are close to the b oundaries of the range

C

f aint

of velocities taken for galaxies b elonging to Coma The

C

f aint

velocity disp ersions of these two groups are more in the

range of those of p o or clusters than of groups see eg

The structure of Coma as visible from Fig upp er

Mazure et al Ramella et al however it is

panel remains complex despite the elimination of the

p ossible that the rst group is in fact made of galaxy

1

groups of galaxies in the foreground and background and

pairs and that the galaxy with a velocity of km s

raises the natural question of whether there really is a

is not a member of the second group but an isolated back

Coma cluster ie an underlying main structure As we dis

ground galaxy By excluding these galaxies the test of

cuss in x there are reasons to b elieve that faint galaxies

Dressler Shectman gives a probability of

may b e more faithful tracers of the main cluster b o dy p o

for the presence of substructures on the remaining

tential For this reason we have split our sample C into the

galaxies and the map do es not show any other signif

two subsamples C and C previously describ ed

icant feature So there are go o d reasons to b elieve that

br ig ht f aint

We have chosen the magnitude b to separate these

these groups are in the fore and background of the Coma

two samples b ecause this magnitude corresp onds to the

cluster In the following we have excluded these galax

dip in the Coma cluster luminosity function Biviano et

ies from our samples The number of galaxies remaining

al b and thus naturally separates bright from faint

in the subsamples dened in x after the elimination of

galaxies in Coma Moreover the number of galaxies with

these galaxies are listed in Table

available redshifts in the two subsamples is approximately

the same

It turns out that the structures seen in the distribu

Table Eleven galaxies b elonging to the foreground and

background groups

tion of bright galaxies are quite dierent from those seen

in the distribution of faint galaxies as can b e seen by plot

Group GMP Velocity b xy

ting the adaptive kernel maps of the C Fig and

br ig ht

number km s arcsec

C Fig samples resp ectively

f aint

As seen in these two gures the relative imp ortance

of the group surrounding NGC is strongly empha

sized in the bright galaxy distribution while the two p eaks

around the two giant central galaxies are no longer present

in the faint galaxy distribution The app earance of the

map shown in Fig is more regular with a single den

sity maximum lo cated b etween the p osition of the two

central galaxies This secondary p eak is lo cated at GMP

co ordinates and therefore at distances from

NGC and NGC of and resp ectively

While there still is an overdensity around NGC it is

less prominent than b efore this overdensity continuously

In Fig we have displayed the adaptive kernel density

decreases and the secondary p eak overdensity increases

map and the density map at condence level for the

when the fraction of faint galaxies is increased ie going

sample C after the elimination of these galaxies the

from sample C to C and to C

map app ears slightly smo other than b efore compare with

br ig ht f aint19 f aint

Fig but the most relevant features are unchanged In By lo oking at the density map at condence level

particular the two p eaks around the two central dom lower panel of Fig one can see that the maximum

inant galaxies are still visible It is not surprising that in the faint galaxy distribution has not a very well de

these p eaks were not detected by the Dressler Shect termined p osition and tends to shift towards NGC

man test since the velocity distribution of galaxies We have estimated the uncertainty on the p osition of

within these groups is not very dierent from the overall this p eak by running b o otstrap resamplings on the

cluster velocity distribution C sample and estimating the p osition of the highest f aint

A Biviano et al Unveiling hidden structures in the Coma cluster

1000 1000

0 0

-1000 -1000

-1000 0 1000 -1000 0 1000

1000 1000

0 0

-1000 -1000

-1000 0 1000 -1000 0 1000

Fig Upp er panel adaptive kernel map of all the galaxies Fig Upp er panel adaptive kernel map of the galaxies b e

b elonging to the Coma cluster within a circle of radius longing to the Coma cluster with magnitudes b sample

sample C after the eliminati on of the galaxies b elonging C The contour spacing and the symbols are the same

br ig ht

to the background and foreground groups The contour spac as in Fig Lower panel adaptive kernel density map at

ing and the symbols are the same as in Fig Lower panel condence level see App endix A

adaptive kernel density map at condence level see Ap

p endix A

ondary maximum detected in the Xrays see x not

asso ciated with any of the two central dominant galaxies

p eak in each b o otstrap sample the disp ersion in the p o

strongly argues in favour of the reality of this p eak

sitions of the highest p eaks is This large disp ersion

is probably due to the presence of two density p eaks the Magnitudes therefore app ear as an ecient to ol of dis

one visible in Fig upp er panel and the very strong crimination the cluster app earance changes when select

p eak around NGC outstanding in the bright galaxy ing samples of luminous or faint galaxies Bright cluster

distribution and not totally erased in the faint galaxy dis galaxies are mainly lo cated around the brightest mem

tribution The striking p ositional coincidence b etween the b ers while faint ones delineate a smo other single p eaked

density p eak of the faint galaxy distribution and a sec structure

A Biviano et al Unveiling hidden structures in the Coma cluster

through the wavelet transform corresp onding to wavelet

scales of and ie and

1

h kp c at the distance of the cluster resp ectively are

1000 displayed in Figs to

0

-1000

-1000 0 1000

1000

Fig Xray image obtained after removing the noise and the artefacts see App endix B

0

In the two rst images Figs we nd signicant

unresolved ie not larger than one pixel features

These generally have optical counterparts which would

-1000 corresp ond to Xray emitting galaxies We nd galax

ies in our eld see Table Our analysis is mo del inde

p endent and allows the detection of Xray sources The

-1000 0 1000 metho d used by Dow White a tting pro cedure

gives actual measurements of the Xray luminosities but

they only detect galaxies in Xrays and give upp er lim

its for the others Note that NGC and NGC are

Fig Upp er panel adaptive kernel map of the galaxies b e

rather strong Xray emitters see Table The strong X

longing to the Coma cluster with magnitudes b sample

ray source visible on Figs lab elled with a Q is a

C The contour spacing and the symbols are the same

f aint

quasar

as in Fig Lower panel adaptive kernel density map at

Structures are also observed around the p ositions of

condence level see App endix A

the two central galaxies at larger wavelet scales see

Figs These detections clearly indicate the existence

of two Xray emitting groups around these two galaxies in

The Xray distribution

addition to the Xray emission due to the galaxies them

selves Vikhlinin et al have already found these

We have p erformed a wavelet analysis on the whole Xray

groups in the same ROSAT image by applying a wavelet

image of Coma but for the purp ose of comparison with

transform but at a single medium scale

the optical sample C we concentrate here only on the

The present analysis reveals two other features of par

00

central part of this image within a radius of

ticular interest

The reconstructed Xray image ie that obtained after

subtracting the noise and artefacts following a technique A third maximum lab elled A which is clearly vis

describ ed in App endix B is displayed in Fig The four ible in Figs b etween the two maxima asso ciated

wavelet images obtained from the noisesubtracted image with NGC and NGC this feature is not re

A Biviano et al Unveiling hidden structures in the Coma cluster

Fig Same as Fig at a scale of pixels

Fig Wavelet image at a scale of pixel The isophotes

are drawn from to by steps of The X and Y scales

are drawn in units of ROSAT PSPC pixels of The two

brightest galaxies NGC and NGC are indicated by

xs Other lab els are A for the secondary maximum B for the

lament b etween the two brightest galaxies and Q for a quasar

in the eld The p ositions of bright galaxies are marked by

crosses see Table

Fig Same as Fig at a scale of pixels

lated to any particular galaxy and was also noted by

White et al It is lo cated at GMP co ordinates

which almost coincides with the p osition

of the density maximum in the faint galaxy distribu

tion the distance b etween the two p eaks is only

This Xray maximum is indicated by an asterisk in the

adaptivekernel maps

Fig Same as Fig at a scale of pixels

A lamentary structure lab elled B b etween Aand the galaxy NGC is visible in Figs

A Biviano et al Unveiling hidden structures in the Coma cluster

The velocity gradient

Table Optical counterparts to Xray features detected with

the wavelet technique Col galaxy name col magnitude

The sample C is dominated by the two galaxy

br ig htv

in the GMP catalogue col log L in the hard keV

X

groups around the central dominant galaxies this can b e

energy band from Dow White

seen by splitting the sample in two subsamples one with

1

Galaxy b log L

velocities v km s and therefore closer to the ve

X

1

name

lo city of NGC and the other with v km s

NGC

There are and galaxies in the two subsamples resp ec

NGC

tively The adaptive kernel density maps of these two sub

NGC A

samples which are magnitude complete are shown

NGC

in Fig upp er and lower panel resp ectively for the low

NGC

and high velocity sample

IC

On the other hand the sample C do es not show

f aintv

IC

evidence for the presence of the two groups even if we con

NGC

sider separately the two subsamples at velocities resp ec

NGC

1

NGC

tively lower and higher than km s Instead there is

NGC

evidence for a continuous velocity gradient in the opp osite

direction to the gradient b etween the two central galaxies

this is shown in the adaptive kernel map of the average

velocity of this sample Fig note that we have used

These two features can actually b e seen directly on the

an initial kernel size three times as large as that used in

reconstructed picture Fig

the other maps ie in this case in order to increase

the signaltonoise in this map see App endix A for a more

thorough explanation Such a gradient has also b een no

Comparison of optical and Xray maps

ticed by CD see also Durret et al Since this

gure is drawn from a sample dened in a circular region

The distributions of the galaxies and Xray gas are re

no preferential direction has b een articially introduced

markably similar In particular the two brightest galax

Since the velocity eld of the C sample of galax

f aintv

ies are surrounded by galaxy groups that are also seen

ies is complex we have lo oked for the direction along

in the Xray maps and the faint galaxy p opulation has

which the strongest correlation is obtained b etween the

a single density p eak which is also found as a secondary

velocities and the co ordinates along this direction in or

maximum in the Xray maps feature A The gas and

der to have a quantitative estimate of the p osition an

galaxies seem therefore to b e swimming in the same

gle and statistical signicance of this gradient The p osi

gravitational p otential However there may exist features



tion angle of the maximal correlation is dened an

present on Xray maps which are absent on optical maps

ticlo ckwise from North with a rather large uncertainty

The resp onse to the gravitational eld of these two kinds of



of estimated by p erforming b o otstrap resam

matter which have very dierent intrinsic physical prop

plings of the data This large uncertainty could b e due

erties is dierent Notice also that hydrodynamical sim

to the existence of two sup erp osed gradients one in the

ulations predict emitting pro cesses from the plasma not

EastWest and the other in the NorthSouth directions

directly related to the p otential well Evrard Ro et

as suggested by Fig The velocity gradient along the

tiger et al As we discuss b elow see x feature

 1 1

axis at p osition angle is km s arcsec

B may b e an example of such pro cesses

1 1

km s h Mp c as deduced from a regression

analysis b etween velocities and co ordinates along this axis

The statistical signicance of this gradient computed

The central region of Coma kinematics

by the nonparametric Kendall correlation co ecient b e

As we have seen in x the faint galaxies trace a tween velocities and p ositions is Its reality is further

much more regular singlep eaked structure than the bright conrmed by the analysis of the more complete sample

galaxies which are mostly group ed around the two bright C the direction of the maximal correlation is al

f aint19v

 

est galaxies We now make use of the velocity data for in most the same and the statistical signicance

vestigating the kinematics of these two p opulations For is even higher despite the fact that the number of

this purp ose we use the C and the C samples galaxies is lower in this sample the gradient along the

br ig htv f aintv

 1 1

As we have velocities only for of the galaxies in the axis at p osition angle is km s arcsec

1 1

C sample we have checked the results concerning km s h Mp c This gradient is much larger

f aintv

the kinematics of the faint galaxy p opulation on the sam than the one found b efore suggesting that incompleteness

ple C which has of its galaxies with known in the sample C has led to an underestimation of the

f aint19v f aintv

redshifts true gradient intensity

A Biviano et al Unveiling hidden structures in the Coma cluster

1000 1000

0 0

-1000 -1000

-1000 0 1000

-1000 0 1000

Fig Mean velocity adaptive kernel map for faint galaxies

C sample Contour levels are spaced by km s

1000 f aintv

and lab elled with their mean velocity value An initial kernel

size three times as large as that used in the previous maps has

b een used here in order to increase the signaltonoise in this gure Symbols are the same as in Fig

0

7500

-1000 7200

-1000 0 1000

6900

Fig Adaptive kernel density map of the galaxies in the

sample C with v km s upp er panel and with

br ig htv

v km s lower panel The contour spacing and the

symbols are the same as in Fig 6600 Consistently with the lack of any coherent features in

-400 -200 0 200 400 600 800

the average velocity maps of the sample C and C

v br ig htv

we nd no signicant gradients on these samples nor do

we detect any signicant gradient outside this inner circle

Fig Running velocity prole heavy line of the

of radius consistent with previous ndings Gre

C sample along the gradient direction the dashed

f aintv

gory Gregory Tit

lines indicate the upp er and lower condence bands as ob

Fig shows the running velocity prole for galax

tained via b o ostrap resamplings the thin line in the mid

ies in the sample C vs their p ositions along the di

f aintv

dle is the average of the b o ostrap resamplings The two bright



rection of the velocity gradient p osition angle the

est galaxies of Coma are indicated by squares errorbars de

condence bands are estimated via b o otstrap

note the observational uncertainties on their velocities

resamplings The running velocity prole along the axis

A Biviano et al Unveiling hidden structures in the Coma cluster

Table Characteristics of the velocity distributions

Sample mean disp ersion skewness kurtosis Tail Index Omnibustest

km s km s probability

C

v

C

br ig htv

C

f aintv

C

allv



at p osition angle of as well as the running velocity

prole of the C sample are similar and are not

19v f aint 0.25 displayed here It must b e noticed that neither NGC 0.2

nor NGC are lo cated on the running velocity curve 0.15 and their relative velocity gradient has an opp osite direc

0.1 tion to the gradient of the main cluster b o dy 0.05 0

Velocity distributions 4000 6000 8000

The histograms and characteristics of the velocity samples

C C and C are displayed in Fig and Ta

v br ig htv f aintv

ble The values indicated in Table are calculated with a 0.3 biweight analysis see eg Beers et al and keeping

0.2 into account the errors on velocities and the reduction to

the cluster reference frame Danese et al All mean 0.1

velocities and values of are compatible with one another velocity and ve The values we nd for the mean cluster 0

4000 6000 8000

lo city disp ersion are not dierent from those calculated by

CD

1

The velocity of NGC is km s a value

1

than the average cluster velocity by km s

larger 0.3

1

The velocity of NGC is km s smaller 1

0.2

than the mean velocity of C by km s These results

v

signicant at levels larger than The two central

are 0.1

dominant galaxies are essentially in a symmetrical situ

1

ation within km s relatively to the C mean

v 0

4000 6000 8000

velocity

In Table we also list the values for the skewness the

kurtosis and the Tail Index relative to the Gaussian dis

tribution and the probability of rejection of gaussianity

Fig Histogram of velocities of the sample C upp er

according to an omnibus test for the various samples The v

panel C middle panel and C lower panel b e

br ig htv f aintv

Tail Index see eg Beers et al is a robust measure

fore heavyline histograms and after shaded histograms the

of the tails in a distribution b eing lower than unity when

subtraction of the average velocity gradient from the observed

the tails are underp opulated relative to a Gaussian The

velocities of galaxies in the C sample which is also part

f aintv

omnibus test makes use of b oth the skewness and the kur

of the C sample The number of bins is approximately equal

v

tosis to provide the probability that a given distribution

to the squarero ot of the number of galaxies in each sample

is signicantly not gaussian see eg DAgostino

Using a range of statistical tests CD have shown

that the velocity distribution of the whole GMP eld de

parts signicantly from a gaussian This is conrmed by

tions with dierent mean velocity in the dataset probably our analysis see Table sample C On the other

allv

the two groups around the central dominant galaxies see hand the galaxy velocity distribution in the central clus

Fig in x On the other hand the C velocity ter region sample C is only slightly nongaussian This

f aintv v

distribution is signicantly nongaussian mainly b ecause nongaussianity mainly arises from the faint galaxy p opu

of its skewness It is remarkable that if we subtract the lation In fact the C velocity distribution is not sig

br ig htv

average gradient see x from the observed velocities nicantly dierent from a Gaussian even if the low value

of this sample the resulting velocity distribution is closer of the Tail Index suggests the sup erp osition of two p opula

A Biviano et al Unveiling hidden structures in the Coma cluster

Table Prop erties of BCMs and their groups

GMP Other name x y b v N N v v

BCM v BCM

number arcsec mag km s km s

NGC

NGC

NGC

NGC

NGC

NGC

NGC

NGC

NGC

NGC

ZW

ZW

IC

to a gaussian the omnibus test rejects gaussianity with a probability of only This is illustrated in Fig

4000

The outer regions of Coma

Other groups 2000

Mellier et al claimed the existence of a p opulation

of galaxies b ound to several of the brightest members of

0

the Coma cluster We have rep eated here their analysis

using our larger dataset see also Biviano et al

We have selected galaxies with b BCMs here

-2000

after for Brightest Cluster Members which are lo cated

near a density enhancement as visible in an adaptive ker

nel map of the C sample Fig The names of these all

-4000

BCMs p ositions magnitudes and velocities are listed in

Table While some of the p eaks visible in Fig may

-4000 -2000 0 2000 4000

not corresp ond to real structures the purp ose here is to

select all possible groups and to run a statistical test for

the presence of two p opulations within these groups

We have constructed groups centered on these

Fig Adaptive kernel density map of all the cluster mem

BCMs by taking all the galaxies closer than from each

b ers in the GMP region sample C The xs indicate all

all

BCM the radius of has b een chosen as a compro

cluster members brighter than b in this eld Contour

spacing is the same as in Fig but contours in the central

mise b etween the need of selecting galaxies close enough

region have b een omitted for clarity

to the BCMs and still having sucient statistics Note

that with such a radius the groups of NGC and

NGC would b e sup erp osed we have chosen to assign

to the NGC group the galaxies falling in the su

of the BCM are listed in col of Table these aver

p erp osition zone since from Fig NGC seems to sit

ages are computed without including BCMs The average

on a larger density p eak

group velocities are equal to the BCM velocities within

the errors however these errors are quite large In order to In Table we list in col the ratio b etween the num

check for the existence of a p opulation of galaxies b ound b er of galaxies with available velocities N and the total

v

to the BCMs we have merged together the velocities rel number of galaxies N in each group BCMs excluded

ative to the velocities of the BCMs of the galaxies Since we do not have any galaxy with available velocity

assigned to the groups BCMs excluded The null in the vicinity of BCMs our analysis is eectively re

hypothesis that we are testing is that this distribution is stricted to putative groups We also give the aver

the same as that of all the cluster galaxy velocities relative age velocities for groups with enough galaxy velocities

to the cluster mean This should b e the case if the sample available these average velocities relative to the velocity

A Biviano et al Unveiling hidden structures in the Coma cluster

of galaxies in the vicinity of BCMs is a random sample of The distribution of starforming galaxies

the cluster p opulation

As noted by many authors So dre et al Zabludo

A KolmogorovSmirnov test see eg Stephens

Franx CD Donas et al Gavazzi et al

do es not reject the hypothesis that the group galaxy

the starforming and the quiescent galaxy p opula

velocities relative to their BCM velocities are drawn

tions in Coma have markedly dierent velocity distribu

from the same parent distribution of the velocities rel

tions We have separated these two p opulations by their

ative to the cluster average velocity in the sample C

allv

colours resp ectively larger or equal to and smaller than

However there is a dierence b etween the velocity distri

b r In the sample C there are blue clus

all

butions of the group galaxies and of the C galaxies

allv

ter members of which with measured velocities and

when only galaxies with b are considered there

red cluster members of which with measured

are and galaxies brighter than this magnitude in

velocities The density proles and velocity distributions

the group and the C sample resp ectively This dif

allv

of the red and blue Coma cluster members are shown in

ference is signicant at the condence level ac

Fig The density prole of the blue galaxies is at

cording to the KolmogorovSmirnov test In fact the ve

ter than that of the red galaxies in the center yet the

lo city disp ersion of the group galaxies brighter than

two proles are similar b eyond corresp onding to

1

b with resp ect to the velocities of their BCMs is

h Mp c from the center the velocity distributions

1

only km s We conclude that the p opulation b ound

of the two p opulations are dierent probability ac

to the BCMs discovered by Mellier et al is made

cording to a KolmogorovSmirnov test b oth b ecause of

of bright galaxies only A similar result was found in x

a dierent mean and a dierent disp ersion the velocity

for the central region of Coma bright galaxies tend to lie

disp ersion of the blue galaxies is larger than that of

in sub clusters and faint galaxies trace the overall cluster

the red galaxies

p otential

The sample C b eing rather incomplete we have

allv

p erformed a similar analysis on the complete sample

of galaxies brighter than b and found approximately

the same results

The region of NGC

Caldwell et al have identied earlytype

galaxies with an abnormal sp ectrum in the Coma clus

ter Given the p eculiarity of their sp ectrum most of these

Let us now concentrate on the well known group around

galaxies are thought to have suered a starburst episo de

the giant galaxy NGC The presence of this group

Gyr ago Caldwell et al A p ossible explanation

makes the velocity distribution of the C sample signif

allv

for such a starburst is a recent interaction with the clus

icantly skewed and therefore nongaussian see Table

ter environment These galaxies share a similar veloc

This was recently p ointed out by CD who were able

ity distribution as that of the blue galaxies see Fig

to split the group and the cluster comp onents using the

1

Their average velocity km s and velocity dis

KMM algorithm see eg Bird they obtained an

1

1

p ersion km s are also quite similar to those

average velocity of km s and a velocity disp ersion

1

of the NGC group although their spatial distribution

of km s for the group The average velocity is in p er

is not restricted to the region of NGC Note that the

fect agreement with the velocity of NGC

1

values of the average velocity and disp ersion are dierent

km s

from those given in Caldwell et al and in CD

However CD did not address the p ossible problem

b ecause here we have used the biweight estimator which

of the incompleteness of their sample in order to check

is more reliable than the classical disp ersion in the case of

the robustness of their result we have considered only the

p o or datasets Beers et al While the average ve

galaxies of sample C with magnitudes b the com

allv

lo city is roughly two standard deviations oset from the

pleteness of this sample is see Table By p erform

average velocity of the NGC group and the velocity

ing a maximum likelihoo d t with two gaussians to the ve

disp ersion is aected by an enormous error this result is

lo city distribution of this sample we recover within the

intriguing

errors the average velocity and velocity disp ersion found

by CD for the group p opulation The nice agreement

Discussion

with the values found by CD suggests that their result

is robust despite incompleteness Using the ratio b etween

The main cluster body

the numbers of galaxies b elonging to the two gaussians

and assuming that all the likely cluster members with As shown in the previous sections the bright and faint

out available velocities b elong to the cluster and not to galaxies have markedly dierent distributions and kine

the group we can set a lower limit of to the ratio matics Bright galaxies tend to b e lo cated in groups domi

b etween the number of galaxies in the group and in the nated by their very brightest members while faint galaxies

cluster delineate a much smo other singlep eaked structure This is

A Biviano et al Unveiling hidden structures in the Coma cluster

velocities are dierent from the average cluster velocity

they are more likely to b e lo cated in sub clusters still in the pro cess of merging with the cluster Indeed the den

-4

sity and Xray maxima around the two central dominant

galaxies indicate the presence of groups linked to these

-4.5 two galaxies this is supp orted by the kinematical analysis

see Fig and by previous investigations Fitchett

Webster White et al Vikhlinin et al

-5 CD claimed that the two central dominant galaxies do

not lie at the mean velocity of their own groups but they

did not realize that the bright galaxies do cluster around two central galaxies while only the faint galaxies do -5.5 the

2.5 3 3.5 not indeed their velocity gradient is opp osite to the mean

velocity gradient of these two groups see x and x

The Xray secondary maximum feature A in Fig

has already b een noted by White et al who pro

to identify it with a remnant of gas stripp ed from

0.3 p osed

NGC The fact that this p eak is also seen in the

faint galaxy distribution suggests an alternative expla this could be the Xray maximum of the main body

0.2 nation

of the Coma cluster The A feature indeed p ossesses

another prop erty typical of clusters it is visible on small

0.1 or medium scales while it is blurred on the largest scale

indicating that its intrinsic characteristic scale is small

1

ie corresp onding to h kp c Indeed in two 0 pap ers devoted to the analysis of Xray clusters with

4000 6000 8000

improved techniques Gerbal et al and Durret et

al have shown that Xray core radii are very small

1

h kp c in opp osition to what is often claimed

in the literature but in agreement with results derived

Fig Upp er panel the adaptive kernel number density pro

from the gravitational lensing analysis of the unseen mat

les of blue thick line and red thin line cluster members

ter distribution The central p eak of the Xray brightness

The dashed lines indicate the condence bands on the

must then have a medium typical scale and this is why

two proles obtained with b o otstrap resamplings Lower

it is visible on the medium scale image and not on the

panel the velocity distributio n of the blue thick histogram

larger one

and red thin histogram galaxy p opulation s and of the

Our interpretation naturally accounts for the fact that

galaxies with abnormal sp ectra dashed histogram detected

b oth NGC and NGC have velocities signi

by Caldwell et al

cantly dierent from the cluster mean see x since

b oth galaxies are lo cated within their own groups even

true not only for the groups around the two core dominant

tually falling on to the main b o dy of Coma These groups

galaxies but also for other groups even in the external re

would then only b e two of the groups merging with or

gions This is reminiscent of the luminosity segregation

falling onto the main cluster b o dy In this case Coma

already observed by Ro o d The dichotomy is nat

would still b e undergoing a formation pro cess with the

urally not p erfect and there probably are faint galaxies

main b o dy continuously accreting matter ie more or less

lo cated in groups as well as suggested by the Western ex

large groups of galaxies The main b o dy would in fact b e

tension towards NGC of the maximum in the faint

formed by the mixing of such groups and clusters arrived

galaxy density map Fig The Xray maps show sev

in the past suggesting the continuous existence of violent

eral maxima in particular two are centered on NGC

relaxation pro cesses Notice that such pro cesses are noth

and and one is coincident with the faint galaxy dis

ing but secondary infal l adapted to a more realistic view

tribution density p eak The coincidence of the optical and

of the universe than the simple case of spherical symmetry

Xray emitting gas distributions strongly suggests that the

In particular we suggest that the infall of the

detected features are real

NGC group onto the high density cluster core region

It is usually assumed that the main cluster structure A in Fig is pro ducing a compression wave that has

coincides with the overdensity around NGC How increased the pressure and as a consequence the Xray

ever neither this galaxy nor the brightest cluster member luminosity of the gas along the east edge of this group the

NGC are at rest in the cluster p otential since their Xray emission of this compressed gas would corresp ond

A Biviano et al Unveiling hidden structures in the Coma cluster

to the extended lament B in Fig Such an interpre Ab ell Note however that the NGC group av

1

tation nds supp ort in hydrodynamical simulations see erage velocity km s is opp osite to what ex

eg Evrard showing that the Xray emission is not p ected from an extrap olation of the central gradient to

only asso ciated with a smo oth gas distribution but can the group p osition

also arise from sho cks induced by the arrival of groups

This gradient is an intrinsic prop erty of the main clus

into the cluster

ter b o dy In fact it cannot simply reect the presence of

Finally the fact that we detect the main b o dy in sub clustering around the two central dominant galaxies

the faint galaxy p opulation while the bright galaxies are b ecause it go es in the opp osite sense On the other hand

mainly lo cated in sub clusters can b e explained as the ef the lo cation of the Coma cluster at the intersection of

fect of dynamical evolution in the groups b efore their infall several sheets may suggest that the velocity gradient re

onto the cluster The very existence of such large galaxies ects the largescalestructure galaxy distribution In par

like NGC and NGC argues in favour of this hy ticular Coma is within the Great Wal l Geller Huchra

p othesis In fact brightest cluster members are exp ected Ramella et al which is inclined with resp ect

to form in groups b efore violent relaxation o ccurs Mer to the line of sight However while in the same direction

ritt probably through mergers which imply small the intensity of the gradient found here is much higher

velocity encounters Such small velocities may b e attained than that of the Great Wall which is indeed roughly sim

among bright massive galaxies by the loss of their kinetic ilar to the one previously detected by Gregory Tit

1 1 1 1

energy through the pro cess of dynamical friction see eg km s arcsec ie km s h Mp c

Biviano et al Yepes DomnguezTenreiro Morevoer we only detect a gradient in the inner circle of

The groups could then evolve to a corehalo structure radius

with bright galaxies in their core and faint galaxies in

What is the physical meaning of this gradient The

their halo When the infall onto the cluster o ccurs the

velocity map see Fig is complex and not as ex

less b ound halo p opulation would b e more easily tidally

p ected from simple rotation Moreover if we interpret the

stripp ed o the group and b ecome part of the cluster

gradient as arising from rotation the rotational velocity

p opulation at variance with the core p opulation which

would b e to o low to account for the attening of the main

could resist longer to tidal disruption Of course there are

b o dy as one can estimate using the anisotropy parameter

probably unevolved groups as well infalling onto the clus

v dened in eg Ferguson Binggeli eq

ter but these would lo ose their identity very so on b ecause

The fact that the gradient is principally oriented towards

of tidal disruption and escap e detection the dense cores

NGC may suggest a transient tidal eect Among

of evolved groups would survive longer as indicated by

the numerous consequences of such a transient tidal ef

numerical simulations GonzalezCasadoet al

fect are the deformation of the matter distribution and

a mean velocity eld which is no longer constant The ef

fects of tides on spheroidal galaxies infalling onto our own

Does the main body rotate

Galaxy are describ ed in a pap er by Piatek Pryor

They nd that tides deform the spheroidal galaxies and

As shown in x the sample C has kinematical

f aintv

induce apparent rotation tides pro duce large ordered mo

prop erties on its own this lends further supp ort to the

tions rather than large random motions We think that hypothesis that the density p eak of this sample is inde

something similar may b e happ ening in the Coma cluster

p endent from the density p eaks asso ciated with the two

with the central part of the main b o dy suering from the

central dominant galaxies In particular we have shown

tidal inuence of the infalling groups like those around

that the faint galaxy velocity distribution has a signicant

NGC and NGC The search for this kind of ef

gradient see Fig and This gradient was also noted

fect with realistic numerical simulations of clusters could by CD but they did not recognize that it is restricted

give constraints on the relative masses of the satellite and to the faint galaxy p opulation no signicant gradient is

main b o dy as well as on the history of encounters

found in the velocity distribution of the bright galaxy p op

ulation if anything the gradient is in the opp osite sense

see Fig

Ongoing infal l

It is quite remarkable that this velocity gradient is

The groups around NGC and NGC are likely globally oriented from the NorthEast to the SouthWest

 

to b e orbiting within the Coma cluster and they are not in rough coincidence with several main direc

at rest at the b ottom of the cluster p otential There are tions in Coma These privileged directions have recently

at least two more groups one centered on the galaxy b een p ointed out by West who explains them as

NGC and the other less conspicuous on the galaxy a consequence of the infall of structures onto the cluster

NGC and other groups may b e present around other from the large scale structure laments surrounding it In

bright galaxies Mellier et al The average velocities particular the direction of the velocity gradient is closer to

of these galaxies and their groups are also quite dierent the direction b etween the centre of Coma and NGC

from the cluster mean velocity Altogether this suggests rather than to the direction to the neighboring cluster

A Biviano et al Unveiling hidden structures in the Coma cluster

that the Coma cluster is still in the pro cess of accreting ulations in which the eects of dynamical friction are in

groups from the surrounding large scale structure cluded see eg Chan et al and references therein

Not only is Coma accreting groups but also individual

galaxies The atness of the density prole of the blue

Conclusions

galaxy p opulation near the center indicates that these

The analysis of Coma simultaneously in Xrays and at

galaxies tend to avoid the center yet the similarity of their

optical wavelengths allows us to draw a coherent picture

density prole to that of red galaxies see Fig at large

of this cluster

radii suggests that these blue galaxies are cluster mem

b ers It is then p ossible that these galaxies sp end only a

A main b o dy centered on the p eak of the distribution

little time in the central region of the cluster b ecause they

of faint galaxies which coincides with a secondary X

have very elongated orbits This is also indicated by the

ray p eak is unveiled groups are falling on to this main

double p eaked velocity histogram of the blue galaxy p op

b o dy

ulation typical of galaxies on strongly radial orbits see

Faint galaxies are b etter tracers of the cluster struc

eg Merritt This situation is not at all unusual in

ture than bright galaxies since many of the latter are

galaxy clusters Moss Dickens So dreet al

sub clustered around the very brightest galaxies

Zabludo Franx Biviano et al c Supp orting

We detect a gradient in the velocities of the faint galax

this interpretation is the similarity of the blue galaxy ve

ies tracing the main cluster b o dy we suggest that

lo city distribution to those of the HIdecient galaxies see

this gradient arises from tidal interactions of the main

Fig in Gavazzi and of the abnormalsp ectrum

cluster b o dy with infalling groups in particular with

earlytype galaxies see Fig detected by Caldwell et al

NGC

Both the HIdecient galaxies and the abnormal

The infall of the group surrounding NGC may

sp ectrum earlytype galaxies are likely to have interacted

have induced a pressure wave in the Xray emitting

with the cluster environment and are therefore probable

gas

cluster members so that this may also b e true of the gen

Groups are still visible mainly b ecause of a b ound p op

eral blue galaxy p opulation

ulation of bright galaxies which has probably evolved

to a dense core structure b efore the infall of their own

The group around NGC has an average veloc

group and is thus less prone to tidal stripping

ity close to the p eak in the velocity distribution of the

The cluster is still accreting these groups and also indi

abnormalsp ectrum galaxies This fact led CD to con

vidual galaxies from the surrounding large scale struc

clude that b oth the group and these galaxies are falling

ture

onto the cluster coming from the same galaxy lament

While this is certainly a p ossibility supp orted by the

Acknowledgements We deeply thank JG Go dwin N Met

similarity of the velocity distributions of the abnormal

calfe JV Peach for providing us with their unpublished

sp ectrum and blue galaxies the abnormalsp ectrum galax

catalogue of stellar ob jects in the Coma eld M Colless for

ies also have a similar velocity disp ersion as the NGC

providing us with his catalogue of redshifts in advance of publi

group and most of them are lo cated near this group The

cation and C Clemens for sending us an electronic copy of the

p ossibility then remains that these galaxies are or have

ZCAT catalogue We are also grateful to S White for providing

b een members of the NGC group In this case if

us with the ROSAT images of Coma b efore their release in the

Garching public archive We acknowledge the help of D Fadda

they have already interacted with the cluster this would

in the software implementation of the adaptive kernel tech

b e true of the NGC group as well

nique at an early stage of this pro ject We thank D Merritt

Burns et al suggested that the NGC group

and A Pisani for useful discussions We acknowledge nancial

has passed through the core of Coma following a straight

supp ort from GDR Cosmologie CNRS and from the Euro

tra jectory As shown by GonzalezCasado et al

p ean Cosmology Network a EU HCM program C Lob o

this would cause the group structure to b e severely af

is fully supp orted by the BDRM grant attributed by

JNICT Portugal

fected by tidal forces However the NGC group has

a richness velocity disp ersion and Xray luminosity that

ts very well the relations b etween these quantities as

App endix A Adaptive kernel maps

derived for clusters of galaxies Edge Stewart Gi

A thorough description of the adaptive kernel techniques is

rardi et al this argues against the p ossibility that

given in Pisani Here we only address the issues

the group has suered strong tidal eects A p ossible al

that are not rep orted in those pap ers

ternative scenario is a nonradial infall of the NGC

group onto the cluster one or several passages through

A Statistical signicance

the outer parts of the cluster may already have o ccurred

which would leave the group intact except for some galax

In order to assign the statistical signicance to a given fea

ies that may have b een lost in its trail Such a scenario

ture we have run b o otstrap resamplings on each map In

agrees with predictions derived from recent numerical sim practice this consists in evaluating an adaptive kernel map of

A Biviano et al Unveiling hidden structures in the Coma cluster

for restoring an image where some comp onents have b een sub the quantity of interest typically the density for each b o ot

tracted We have already applied these concepts to design a strap sample we then compute the standard deviation of the

hierarchical lter which allows to remove the smallscale noise b o otstrap values for each pixel in the map This provides an

while keeping the relevant details asso ciated to the ob jects estimate of the error in the observed quantity in each pixel

Slezak et al Both improvements and generalization of We then subtract to the observed value in each pixel a given

this metho d are explained here in a concise way since a full number say of standard deviations and obtain a new map

description of the mo del we use and numerical simulations and which we compare to the original one to see if the observed

tests will b e given in Rue Bijaoui features are still visible Features aected by large errors will

not b e visible in the density map at condence level

B The multiscale vision model

A Velocity maps

Using an isotropic analyzing wavelet without any decimation

i

from one scale a to another a D image is transformed

We dene an adaptive kernel map of the average velocities

i

into a set of wavelet images fW g exhibiting details related to by multiplying the dimensional gaussian adaptive kernel

i

D

dierent spatial frequencies so that a complex ob ject showing

x

K of each galaxy j by its velocity when available

j

features of dierent sizes is asso ciated to non zero co ecients

v

j

at successive scales An ob ject now has to b e describ ed in this

N N

v v

wavelet space and by consequence the connectivity prop erty

X X

D D

x x

v K v K A

which denes it in the direct space needs to b e enlarged to the j

j j

j j

D set of wavelet co ecients W k l To do so one must dene

i

an interscale connectivity relation linking the various comp o

nents corresp onding to the connected regions D n detected

x

where is the p osition vector of a given pixel of the image

i

at each scale a by the eld lab elli ng L k l n This image

and N is the number of galaxies with available velocity

i i

v

segmentation p ermits to select signicant wavelet co ecients

In order to increase the signaltonoise in these maps we

from noisy data Rue Bijaoui decided to base this

adopt a larger initial kernel size than in the density maps

relationship R on the lo cation k l of the maximum

max max

value inside D n and we have adopted the same rule

i

A Substructure maps

Before dening a map let us remind the denition of the

D n R D m if L k l m B

i i i max max

parameter

Starting from the largest scale to the smallest one the iden

tication of the elds which app ear to b e connected in this

v v A

j j v j v

manner results in a connection tree So any complex ob ject

v is the average velocity and is the velocity disp er where

is viewed as an arb orescent structure V in the wavelet space

j v j

p

N nearest neigh sion of the galaxy group dened by the

the whole information of which is required to characterize cor

v

b ours to the j th galaxy and v and are the average velocity

rectly the ob ject with all its comp onents A key issue in this

v

and velocity disp ersion of all the N galaxies with available

approach is thus the p ossibil ity to extract easily these comp o

v

velocities

nents by considering their related subtrees ie the regions of

x

v We then dene a lo cal average velocity as in eq A

the wavelet structure connected to the eld identied as the

largest structural element of the comp onent One can there

x

and a lo cal velocity disp ersion as follows

v

fore either study these welldened comp onents in a separate

N N

v v

way or analyze an ob ject where undesirable features like su

X X

D D

x x x

v K A K v

p erimp osed smaller ob jects have b een quite p erfectly removed j

v

j j

j j

by eliminating their subtrees Note that the partition related

to such somewhat bright subob jects can b e distinguished from

Then as a straightforward extension of the Dressler

genuine comp onents b elonging to a complex ob ject by the max

Shectman test we compute the lo cal values of

imum wavelet value inside their ro ot domain It must b e higher

than the values of the maxima for the connected elds at the

x x x

v v A

v v

previous larger and next smaller scales since wavelet values in

deed increase or decrease according to the match b etween the

x

The isopleths of give the map

wavelet scale and the typical size and amplitude of the signal

The most ecient way to characterize each source detected in

the wavelet space is to analyze an image I of this source in the

App endix B Wavelet maps

direct space Let us now address this issue

Images which exhibit features of dierent characteristic sizes

at various lo cations are much more accurately analyzed using

B The image reconstruction

spacescale techniques than monoscale informations In Slezak

Assuming a Gaussian noise and providing that the standard de et al we discussed the ability of the wavelet transform

viation parameters of the Gaussian density probabili ty dis to lo cate these structures according to their typical scales and

i

tributions for the noise pro cess P W k l are obtained from presented quite extensively the basic mathematical formulae

i

the clipp ed histogram of the oversampled and noisedominated as well as a fast computation algorithm Therefore we fo cus

co ecient map W see Slezak et al the elds D n are esp ecially this app endix on the use of a multiscale vision mo del

i

A Biviano et al Unveiling hidden structures in the Coma cluster

the ob ject is missing and the discrepancy b etween its original lab elled by p erforming an image segmentation at a level

i

and restored images may b e large on each wavelet map W The connection trees are then con

i

structed following the rule describ ed in x B They are pruned

Thanks to the unfolding of the data in the wavelet space

in order to remove isolated domains and the existing ob jects

and by considering whole hierarchical connection trees or part

and comp onents are identied from the maximum value of their

of them this iterative pro cess enables one to restore either

ro ot elds

images of ob jects where the noise and sup erimp osed features

We now have to compute for each ob ject an image I from the

have b een accurately subtracted without loss of any smallscale

set V of the wavelet co ecients asso ciated to its tree by solving

information or images of these features where the extended

the equation

underlying main ob jects have b een removed

V O I P WT I W B

D D

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