Astronomy & Astrophysics manuscript no. babbage c© ESO 2021
November 8, 2021
Substructures in WINGS clusters ⋆
M. Ramella1, A. Biviano1, A. Pisani2, J. Varela3, D. Bettoni3, W.J. Couch4, M. D’Onofrio5, A. Dressler6, G. Fasano3,
P. Kjærgaard7, M. Moles8, E. Pignatelli3, and B.M. Poggianti3
1 INAF/Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34131, Trieste, Italy
2 Istituto di Istruzione Statale Classico Dante Alighieri, Scientifico Duca degli Abruzzi, Magistrale S. Slataper, viale XX settembre
11, I-34170 Gorizia, Italy
3 INAF/Osservatorio Astronomico di Padova, vicolo Osservatorio 5, I-35122, Padova, Italy
4 School of Physics, University of New South Wales, Sydney 2052, Australia
5 Dipartimento di Astronomia, Università di Padova, vicolo Osservatorio 2, I-35122 Padova, Italy
6 Observatories of the Carnegie Institution of Washington, Pasadena, CA 91101, USA
7 Copenhagen University Observatory. The Niels Bohr Institute for Astronomy Physics and Geophysics, Juliane Maries Vej 30, 2100
Copenhagen, Denmark
8 Instituto de Astrofı́sica de Andalucı́a (C.S.I.C.) Apartado 3004, 18080 Granada, Spain
Received / Accepted
ABSTRACT
Aims. We search for and characterize substructures in the projected distribution of galaxies observed in the wide field CCD images
of the 77 nearby clusters of the WIde-field Nearby Galaxy-cluster Survey (WINGS). This sample is complete in X-ray flux in the
redshift range 0.04 < z < 0.07.
Methods. We search for substructures in WINGS clusters with DEDICA, an adaptive-kernel procedure. We test the procedure on
Monte-Carlo simulations of the observed frames and determine the reliability for the detected structures.
Results. DEDICA identifies at least one reliable structure in the field of 55 clusters. 40 of these clusters have a total of 69 substructures
at the same redshift of the cluster (redshift estimates of substructures are from color-magnitude diagrams). The fraction of clusters
with subclusters (73%) is higher than in most studies. The presence of subclusters affects the relative luminosities of the brightest
cluster galaxies (BCGs). Down to L ∼ 1011.2 L⊙, our observed differential distribution of subcluster luminosities is consistent with the
theoretical prediction of the differential mass function of substructures in cosmological simulations.
Key words. Galaxies: clusters: general – Galaxies: kinematics and dynamics
1. Introduction
According to the current cosmological paradigm, large struc-
tures in the Universe form hierarchically. Clusters of galaxies
are the largest structures that have grown through mergers of
smaller units and have achieved near dynamical equilibrium. In
the hierarchical scenario, clusters are a rather young population,
and we should be able to observe their formation process even at
rather low redshifts. A signature of such process is the presence
of cluster substructures. A cluster is said to contain substruc-
tures (or subclusters) when its surface density is characterized
by multiple, statistically significant peaks on scales larger than
the typical galaxy size, with “surface density” being referred to
the cluster galaxies, the intra-cluster (IC) gas or the dark matter
(DM hereafter; Buote 2002).
Studying cluster substructure therefore allows us to investi-
gate the process by which clusters form, constrain the cosmo-
logical model of structure formation, and ultimately test the hi-
erarchical paradigm itself (e.g. Richstone et al. 1992; Mohr et al.
1995; Thomas et al. 1998). In addition, it also allows us to better
understand the mechanisms affecting galaxy evolution in clus-
ters, which can be accelerated by the perturbative effects of a
cluster-subcluster collision and of the tidal field experienced by
Send offprint requests to: Massimo Ramella, ramella@oats.inaf.it
⋆ Figure 6 is only available in electronic form via
http://www.edpsciences.org
a group accreting onto a cluster (Bekki 1999; Dubinski 1999;
Gnedin 1999). If clusters are to be used as cosmological tools,
it is important to calibrate the effects substructures have on
the estimate of their internal properties (e.g. Schindler & Müller
1993; Pinkney et al. 1996; Roettiger et al. 1998; Biviano et al.
2006; Lopes et al. 2006). Finally, detailed analyses of clus-
ter substructures can be used to constrain the nature of DM
(Markevitch et al. 2004; Clowe et al. 2006).
The analysis of cluster substructures can be performed us-
ing the projected phase-space distribution of cluster galaxies
(e.g. Geller & Beers 1982), the surface-brightness distribution
and temperature of the X-ray emitting IC gas (e.g. Briel et al.
1992), or the shear pattern in the background galaxy distribu-
tion induced by gravitational lensing, that directly samples sub-
structure in the DM component (e.g. Abdelsalam et al. 1998).
None of these tracers of cluster substructure (cluster galaxies, IC
gas, background galaxies) can be considered optimal. The iden-
tification of substructures is in fact subject to different biases
depending on the tracer used. In X-rays projection effects are
less important than in the optical, but the identification of sub-
structures is more subject to a z-dependent bias, arising from the
point spread function of the X-ray telescope and detector (e.g.
Böhringer & Schuecker 2002). Moreover, the different cluster
components respond in a different way to a cluster-subcluster
collision. The subcluster IC gas can be ram-pressure braked and
stripped from the colliding subcluster and lags behind the sub-
cluster galaxies and DM along the direction of collision (e.g.
http://arxiv.org/abs/0704.0579v1
http://www.edpsciences.org
2 M. Ramella et al.: Substructures in the WINGS clusters
Roettiger et al. 1997; Barrena et al. 2002; Clowe et al. 2006).
Hence, it is equally useful to address cluster substructure analy-
sis in the X-ray and in the optical.
Traditionally, the first detections of cluster substructures
were obtained from the projected spatial distributions of galax-
ies (e.g. Shane & Wirtanen 1954; Abell et al. 1964), in com-
bination, when possible, with the distribution of galaxy ve-
locities (e.g. van den Bergh 1960, 1961; de Vaucouleurs 1961).
Increasingly sophisticated techniques for the detection and
characterization of cluster substructures have been developed
over the years (see Moles et al. 1986; Perea et al. 1986a,b;
Buote 2002; Girardi & Biviano 2002, and references therein).
In many of these techniques substructures are identified as de-
viations from symmetry in the spatial and/or velocity distri-
bution of galaxies and in the X-ray surface-brightness (e.g.
West et al. 1988; Fitchett & Merritt 1988; Mohr et al. 1993;
Schuecker et al. 2001). In other techniques substructures are
identified as significant peaks in the surface density distribu-
tion of galaxies or in the X-ray surface brightness, either as
residuals left after the subtraction of a smooth, regular model
representation of the cluster (e.g. Neumann & Böhringer 1997;
Ettori et al. 1998), or in a non-parametric way, e.g. by the tech-
nique of wavelets (e.g. Escalera et al. 1994; Slezak et al. 1994;
Biviano et al. 1996) and by adaptive-kernel techniques (e.g.
Kriessler & Beers 1997; Bardelli et al. 1998a, 2001).
The performances of several different methods have been
evaluated both using numerical simulations (e.g. Mohr et al.
1995; Crone et al. 1996; Pinkney et al. 1996; Buote & Xu
1997; Cen 1997; Valdarnini et al. 1999; Knebe & Müller 2000;
Biviano et al. 2006) and also by applying different methods
to the same cluster data-sets and examine the result differ-
ences (e.g. Escalera et al. 1992, 1994; Mohr et al. 1995, 1996;
Kriessler & Beers 1997; Fadda et al. 1998; Kolokotronis et al.
2001; Schuecker et al. 2001; Lopes et al. 2006). Generally
speaking, the sensitivity of substructure detection increases with
both increasing statistics (e.g. more galaxies or more X-ray pho-
tons) and increasing dimensionality of the test (e.g. using galaxy
velocities in addition to their positions, or using X-ray tempera-
ture in addition to X-ray surface brightness).
Previous investigations have found very different fractions
of clusters with substructure in nearby clusters, depending
on the method and tracer used for substructure detection, on
the cluster sample, and on the size of sampled cluster re-
gions (e.g. Geller & Beers 1982; Dressler & Shectman 1988;
Mohr et al. 1995; Girardi et al. 1997; Kriessler & Beers 1997;
Jones & Forman 1999; Solanes et al. 1999; Kolokotronis et al.
2001; Schuecker et al. 2001; Flin & Krywult 2006; Lopes et al.
2006). Although the distribution of subcluster masses has not
been determined observationally, it is known that subclusters
of ∼ 10% the cluster mass are typical, while more massive
subclusters are less frequent (Escalera et al. 1994; Girardi et al.
1997; Jones & Forman 1999). The situation is probably dif-
ferent for distant clusters which tend to show massive sub-
structures more often than nearby clusters clearly suggesting
hierarchical growth of clusters was more intense in the past
(e.g. Gioia et al. 1999; van Dokkum et al. 2000; Haines et al.
2001; Maughan et al. 2003; Huo et al. 2004; Rosati et al. 2004;
Demarco et al. 2005; Jeltema et al. 2005).
Additional evidence for the hierarchical formation of clus-
ters is provided by the analysis of brightest cluster galaxies
(BCGs hereafter) in substructured clusters. BCGs usually sit
at the bottom of the potential well of their host cluster (e.g.
Adami et al. 1998b). When a BCG is found to be significantly
displaced from its cluster dynamical center, the cluster displays
evidence of substructure (e.g. Beers et al. 1991; Ferrari et al.
2006). From the correlation between cluster and BCG luminosi-
ties, Lin & Mohr (2004) conclude that BCGs grow by merg-
ing as their host clusters grow hierarchically. The related evo-
lution of BCGs and their host clusters is also suggested by the
alignement of the main cluster and BCG axes (e.g. Binggeli
1982; Durret et al. 1998). Both the BCG and the cluster axes
are aligned with the surrounding large scale structure dis-
tribution, where infalling groups come from. These infalling
groups are finally identified as substructures once they enter
the cluster environment (Durret et al. 1998; Arnaud et al. 2000;
West & Blakeslee 2000; Ferrari et al. 2003; Plionis et al. 2003;
Adami et al. 2005). Hence, substructure studies really provide
direct evidence for the hierarchical formation of clusters.
Concerning the impact of subclustering on global cluster
properties, it has been found that subclustering leads to over-
estimating cluster velocity dispersions and virial masses (e.g.
Perea et al. 1990; Bird 1995; Maurogordato et al. 2000), but not
in the general case of small substructures (Escalera et al. 1994;
Girardi et al. 1997; Xu et al. 2000). During the collision of a
subcluster with the main cluster, both the X-ray emitting gas
distribution and its temperature have been found to be signifi-
cantly affected (e.g. Markevitch & Vikhlinin 2001; Clowe et al.
2006). As a consequence, it has been argued that substruc-
ture can explain at least part of the scatter in the scaling rela-
tions of optical-to-X-ray cluster properties (e.g. Fitchett 1988;
Girardi et al. 1996; Barrena et al. 2002; Lopes et al. 2006).
As far as the internal properties of cluster galaxies are
concerned, there is observational evidence that a higher frac-
tion of cluster galaxies with spectral features characteristic
of recent or ongoing starburst episodes is located in sub-
structures or in the regions of cluster-subcluster interactions
(Caldwell et al. 1993; Abraham et al. 1996; Biviano et al. 1997;
Caldwell & Rose 1997; Bardelli et al. 1998b; Moss & Whittle
2000; Miller et al. 2004; Poggianti et al. 2004; Miller 2005;
Giacintucci et al. 2006).
In this paper we search for and characterize substructures
in the sample of 77 nearby clusters of the WIde-field Nearby
Galaxy-cluster Survey (WINGS hereafter, Fasano et al. 2006).
This sample is an almost complete sample in X-ray flux in the
redshift range 0.04 < z < 0.07. We detect substructures from the
spatial, projected distribution of galaxies in the cluster fields, us-
ing the adaptive-kernel based DEDICA algorithm (Pisani 1993,
1996). In Sect. 2 we describe our data-set; in Sect. 3 we de-
scribe the procedure of substructure identification; in Sect. 4 we
use Monte Carlo simulations in order to tweak our procedure;
in Sect. 5 we describe the identification of substructures in our
data-set; in Sect. 6 the catalog of identified substructures is pro-
vided. In Sect. 7 we investigate the properties of the identified
substructures, and in Sect. 8 we consider the relation between
the BCGs and the substructures. We provide a summary of our
work in Sect. 9.
2. The Data
WINGS is an all-sky, photometric (multi-band) and spectro-
scopic survey, whose global goal is the systematic study of the
local cosmic variance of the cluster population and of the prop-
erties of cluster galaxies as a function of cluster properties and
local environment.
The WINGS sample consists of 77 clusters selected from
three X-ray flux limited samples compiled from ROSAT All-
Sky Survey data, with constraints just on the redshift (0.04 < z <
0.07) and distance from the galactic plane (|b| ≥20 deg). The core
M. Ramella et al.: Substructures in the WINGS clusters 3
of the project consists of wide-field optical imaging of the se-
lected clusters in the B and V bands. The imaging data were col-
lected using the WFC@INT (La Palma) and the WFI@MPG (La
Silla) in the northern and southern hemispheres, respectively.
The observation strategy of the survey favors the uniformity
of photometric depth inside the different CCDs, rather than com-
plete coverage of the fields that would require dithering. Thus,
the gaps in the WINGS optical imaging correspond to the phys-
ical gaps between the different CCDs of the mosaics.
During the data reduction process, we give particular care to
sky subtraction (also in presence of crowded fields including big
halo galaxies and/or very bright stars), image cleaning (spikes
and bad pixels) and star/galaxy classification (obtained with both
automatic and interactive tools).
According to Fasano et al. (2006) and Varela et al. (2007),
the overall quality of the data reported in the WINGS photomet-
ric catalogs can be summarized as follows: (i) the astrometric
errors for extended objects have r.m.s. ∼0.2 arcsec; (ii) the av-
erage limiting magnitude is ∼24.0, ranging from 23.0 to 25.0;
(iii) the completeness of the catalogs is achieved (on average) up
to V ∼22.0; (iv) the total (systematic plus random) photometric
r.m.s. errors, derived from both internal and external compar-
isons, vary from ∼0.02 mag, for bright objects, up to ∼0.2 mag,
for objects close to the detection limit.
3. The DEDICA Procedure
We base our search for substructures in WINGS clusters on the
DEDICA procedure (Pisani 1993, 1996). This procedure has the
following advantages:
1. DEDICA gives a total description of the clustering pattern,
in particular the membership probability and significance of
structures besides geometrical properties;
2. DEDICA is scale invariant;
3. DEDICA does not assume any property of the clusters, i.e.
it is completely non-parametric. In particular it does not re-
quire particularly rich samples to run effectively.
The basic nature and properties of DEDICA are described in
Pisani (1993, 1996, and references therein). Here we summarize
the main structure of the algorithm and how we apply it to our
data sample. The core structure of DEDICA is based on the as-
sumption that a structure (or a “cluster” in the algorithm jargon)
corresponds to a local maximum in the density of galaxies.
We proceed as follows. First we need to estimate the proba-
bility density function Ψ(ri) (with i = 1, . . .N) associated with
the set of N galaxies with coordinates ri. Second, we need to
find the local maxima in our estimate of Ψ(ri) in order to iden-
tify clusters and also to evaluate their significance relatively to
the noise. Third and finally, we need to estimate the probability
that a galaxy is a member of the identified clusters.
3.1. The probability density
DEDICA is a non-parametric method in the sense that it does
not require any assumption on the probability density function
that it is aimed to estimate. The only assumptions are that Ψ(ri)
must be continuous and at least twice differentiable.
The function f (ri) is an estimate of Ψ(ri) and it is built by
using an adaptive kernel method given by:
fka(r) =
K(ri, σi; r) (1)
where we use the two dimensional Gaussian kernel K(ri, σi; r)
centered in ri with size σi.
The most valuable feature of DEDICA is the procedure to se-
lect the values of kernel widths σi. It is possible to show that the
optimal choice for σi, i.e. with asymptotically minimum vari-
ance and null bias, is obtained by minimizing the distance be-
tween our estimate f (ri) and Ψ(ri). This distance can be eval-
uated by a particular function called the integrated square error
IS E( f ) given by:
IS E( f ) =
[Ψ(r) − f (r)]2dr (2)
Once the minimum IS E( f ) is reached we have obtained the
DEDICA estimate of the density as in Eq.1.
3.2. Cluster Identification
The second step of DEDICA consists in the identification of the
local maxima in fka(r). The positions of the peaks in the density
function fka(r) are found as the solutions of the iterative equa-
tion:
rm+1 = rm + a ·
∇ fka(rm)
fka(rm)
where a is a scale factor set according to optimal convergence
requirements. The limit R of the sequence rm defined in Eq.3
depends on the starting position rm=1.
rm = R(rm=1) (4)
We run the sequence in Eq.3 at each data position ri. We label
each data point with the limit Ri = R(rm=1 = ri). These limits
Ri are the position of the peak to which the i− th galaxy belong.
In the case that all the galaxies are members of a unique cluster,
all the labels Ri are the same. At the other extreme each galaxy
is a one-member cluster and all Ri have different values. All the
members of a given cluster belong to the same peak in fka(r)
and have the same Ri. We identify cluster members by listing
galaxies having the same values of R. We end up with ν different
clusters each with nµ (µ = 1, . . . , ν) members.
In order to maintain a coherent notation, we identify with
the label µ = 0 the n0 isolated galaxies considered a system of
background galaxies. We have: n0 = N −
µ=1 nµ.
3.3. Cluster Significance and of Membership Probability
The statistical significance S µ (µ = 1, . . . , ν) of each cluster is
based on the assumption that the presence of the µ − th cluster
causes an increase in the local probability density as well as in
the sample likelihood LN = Πi[ fka(ri)] relatively to the value Lµ
that one would have if the members of the µ− th cluster were all
isolated, i.e. belonging to the background.
A large value in the ratio LN/Lµ characterizes the most im-
portant clusters. According to Materne (1979) it is possible to
estimate the significance of each cluster by using the likelihood
ratio test. In other words 2 ln(LN/Lµ) is distributed as a χ
2 vari-
able with ν− 1 degrees of freedom. Therefore, once we compute
the value of χ2 for each cluster (χ2S ), we can also compute the
significance S µ of the cluster.
Here we assume that the contribution to the global density
field fka(ri) of the µ − th cluster is Fµ(ri). The ratio between the
value of Fµ(ri) and the total local density fka(ri) can be used to
estimate the membership probability of each galaxy relatively to
4 M. Ramella et al.: Substructures in the WINGS clusters
the identified clusters. This criterion also allows us to estimate
the probability that a galaxy is isolated.
At the end of the DEDICA procedure we are left with a)
a catalog of galaxies each with information on position, mem-
bership, local density and size of the Gaussian kernel, b) a cat-
alog of structures with information on position, richness, the
χ2S parameter, and peak density. For each cluster we also com-
pute from the coordinate variance matrix the cluster major axis,
ellipticity and position angle.
4. Tweaking the Algorithm with Simulations
In this section we describe our analysis of the performance of
DEDICA and the guidelines we obtain for the interpretation of
the clustering analysis of our observations.
We build simulated fields containing a cluster with and with-
out subclusters. The simulated fields have the same geometry
of the WFC field and are populated with the typical number of
objects we will analyze. For simplicity we consider only WFC
fields. Because DEDICA is scale-free, a different sampling of
the same field of view has no consequence on our analysis.
In the next section we limit our analysis to MV,lim ≤ −16.
At the median redshift of the WINGS cluster, z ≃ 0.05, this
absolute magnitude limit corresponds to an apparent magnitude
Vlim ≃ 21. Within this magnitude limit the representative number
of galaxies in our frames is Ntot= 900.
We then consider Ntot= Nmem+ Nbkg, with Nmemthe number
of cluster members and Nbkgthe number of field – or background
– galaxies. We set Nbkg= 670, close to the average number of
background galaxies we expect in our frame based on typical
observed fields counts, e.g. Berta et al. (2006) or Arnouts et al.
(1997). With this choice, we have Nmem= 230.
We distribute uniformly at random Nbkgobjects. We dis-
tribute at random the remaining Nmem= 230 objects in one or
more overdensities depending on the test we perform. We popu-
late overdensities according to a King profile (King 1962) with
a core radius Rcore = 90 kpc, representative of our clusters. We
then scale Rcore with the number of members of the substructure,
NS . We use
Rcore = 250
NC + NS
where NC is the number of objects in the cluster with Nmem=
NS + NC . This scaling of Rcore with cluster richness is from
Adami et al. (1998a) assuming direct proportionality between
cluster richness and luminosity (e.g. Popesso et al. 2006).
As far as the relative richnesses of the cluster and subcluster
are concerned, we consider the following richness ratios rcs =
NC/NS = 1, 2, 4, 8. With these richness ratios, the number of
objects in the cluster are NC = 115, 153, 184, 204, and those in
subclusters are NS = 115, 77, 46, 26 respectively.
In a first set of simulated fields we place the substructure at
2731 pixels (15 arcmin) from the main cluster so that they do not
overlap. In a second set of simulations, we place main cluster and
substructure at shorter distances, 683 and 1366 pixels, in order to
investigate the ability of DEDICA to resolve structures. At each
of these shorter distances we build simulations with both rcs= 1
and 2.
For each richness ratio and/or distance between cluster and
subcluster we produce 16 simulations with different realizations
of the random positions of the data points representing galaxies.
In order to minimize the effect of the borders on the detection
of structures we add to the simulation a “frame” of 1000 pixel.
5 10 15
simulation
Fig. 1. Fraction of recovered members of each substructure for
different rcs. The solid line connects substructures with rcs = 2
and 4
We fill this frame with a grid of data points at the same density
as the average density of the field.
The first result we obtain from the runs of DEDICA on the
simulations with varying richness ratio is the positive rate at
which we detect real structures. We find that we always recover
both cluster and substructure even when the substructure only
contains NS = 1/8 NC objects, i.e. 26 objects (on top of the uni-
form background). In other words, if there is a real structure
DEDICA finds it.
We also check how many original members the procedure
assigns to structures it recovers. The results are summarized in
Fig. 1. In the diagram, the fraction of recovered members of each
substructure is represented by the values of its rcs. The solid line
connects substructures with rcs = 2 and 4.
From Fig. 1 it is clear that our procedure recovers a large
fraction of members, almost irrespective of the richness of the
original structure. It is also interesting to note that the fluctu-
ations identified as substructures are located very close to the
center of the corresponding simulated substructures. In almost
all cases the distance between original and detected substructure
is significantly shorter than the mean inter-particle distance.
The second important result we obtain from the simulations
is the false positive rate, i.e. the fraction of noise fluctuations
that are as significant as the fluctuations corresponding to real
structures.
First of all we need to define an operative measure of the
reliability of the detected structures. In fact DEDICA provides a
default value S µ (µ = 1, . . . , ν) of the significance (see Sect. 3.3).
However, S µ has a relatively small dynamical range, in particular
for highly significant clusters.
Density or richness both allow a reasonable ”ranking” of
structures. However, both large low-density noise fluctuations
(often built up from more than one noise fluctuation) and very
high density fluctuations produced by few very close data points
could be mistakenly ranked as highly significant structures ac-
cording to, respectively, richness and density criteria.
M. Ramella et al.: Substructures in the WINGS clusters 5
0 20 40 60 80
Fig. 2. χ2S of simulated noise fluctuations (solid line). Labels are
the rcsof simulated structures at the abscissa corresponding to
their χ2S and at arbitrary ordinates.
We therefore prefer to use the parameter χ2S which stands at
the base of the estimate of S µ and which is naturally provided by
DEDICA. The main characteristic of χ2S is that it depends both on
the density of a cluster relative to the background and on its rich-
ness. Using χ2S we classify correctly significantly more structures
than with either density or richness alone.
In Fig. 2 we plot the distribution of χ2S of noise fluctuations
(solid line). In the same plot we also mark the rcsof real struc-
tures as detected by our procedure. We use labels indicating
rcsand place them at the abscissa corresponding to their χ
S and
at arbitrary ordinates.
Fig. 2 shows that the structures detected with rcs= 1, 2 are al-
ways distinguishable from noise fluctuations. Substructures with
rcs= 4 or higher, although correctly detected, have χ
S values that
are close to or lower than the level of noise.
With the second set of simulations, we test the minimum dis-
tance at which cluster and subcluster can still be identified as
separate entities. We place cluster and substructure (rcs= 1, 2) at
distances dcs = 683 and 1366 pixel. These distances are 1/4 and
1/2 respectively of the distance between cluster and substructure
in the first set of simulations. Again we produce 16 simulations
for each of the 4 cases.
We find that at dcs = 1366 pixel cluster and substructure are
always correctly identified. At the shorter distance dcs = 683
pixel, DEDICA merges cluster and substructure in 1 out of 16
cases for rcs= 1 and in 8 out of 16 cases for rcs= 2. With our
density profile, dcs = 683 pixel corresponds to dcs ≃ Rc + Rs
with Rc, Rs the radii of the main cluster and of the subcluster
respectively.
In order to verify the results we obtain for 900 data points
we produce more simulations with Ntot= 450, 600 and 1200. In
all these simulations RC and RS are the same as in the set with
Ntot= 900. We vary Nbkgand Nmemso that Nmem/ Nbkgis the same
as in the case Ntot= 900.
0.5 1 1.5 2 2.5
Fig. 3. Small symbols correspond to χ2S as a function of the num-
ber of members of noise fluctuations. Crosses, circles, dots and
triangles are χ2S for the noise fluctuations of the simulations with
Ntot= 450, 600, 900, and 1200 respectively. Large symbols are
χ2S of simulated clusters and subclusters with rcs= 1. Horizontal
lines mark the levels of χ2S ,threshold.
These simulations confirm the results we obtain in the
case Ntot= 900, and allow us to set a detection threshold,
χ2S ,threshold(Ntot), for significant fluctuations in the analysis of real
clusters.
We summarize the behavior of the noise fluctuations in our
simulations in Fig. 3. In this figure, the small symbols corre-
spond to χ2S as a function of the number of members of noise
fluctuations. In particular, crosses, circles, dots and triangles are
χ2S for the noise fluctuations of the simulations with Ntot= 450,
600, 900, and 1200 respectively.
The larger symbols are the χ2S of the fluctuations correspond-
ing to simulated clusters and subclusters of equal richness (rcs=
The 4 horizontal lines mark the level of χ2S ,threshold, i.e. the
average χ2S of the 3 most significant noise fluctuations in each of
the 4 groups of simulations with Ntot= 450, 600, 900, and 1200.
The expected increase of χ2S ,thresholdwith Ntotis evident.
We note that the only significant difference with these find-
ings we obtain from the simulations with rcs= 2 is that χ
simulated clusters and subclusters is closer to χ2S ,threshold(but still
higher).
We fit χ2S ,thresholdwith Ntotand obtain
log(χ2S ,threshold) = 1/2.55 log(Ntot) + 0.394 (5)
in good agreement with the expected behavior of the poissonian
fluctuations.
As a final test we verify that infra-chip gaps do not have a
dramatic impact on the detection of structures in the cases rcs= 1
and 2. We place a 50 pixel wide gap where it has the maximum
impact, i.e. where the kernel size is shortest. Even if the infra-
6 M. Ramella et al.: Substructures in the WINGS clusters
chip gap cuts through the center of the structures, DEDICA is
able to identify these structures correctly.
We summarize here the main results of our tests on simulated
clusters with substructures:
– DEDICA successfully detects even the poorest structures
above a uniform poissonian noise background.
– DEDICA recovers a large fraction (typically > 3/4) of the
real members of a substructure, almost irrespective of the
richness of the structure.
– DEDICA is able to distinguish between noise fluctuations
and true structures only if these structures are rich enough.
In the case of our simulations, structures have to be richer
than 1/4th of the main structure.
– DEDICA is able to separate neighboring structures provided
they do not overlap.
– infra-chip gaps do not threaten the detection of structures
that are rich enough to be reliably detected.
– the χ2S threshold we use to identify significant structures is
a function of the total number of points and can be scaled
within the whole range of numbers of galaxies observed
within our fields.
In the next section we apply these results to the real WINGS
clusters.
5. Substructure detection in WINGS clusters
We apply our clustering procedure to the 77 clusters of the
WINGS sample. The photometric catalog of each cluster is deep,
reaching a completeness magnitude Vcomplete ≤ 22. The num-
ber of galaxies is correspondingly large, from Ngal ≃ 3, 000 to
Ngal ≃ 10, 000.
The large number of bright background galaxies (faint ap-
parent magnitudes) dilutes the clustering signal of local WINGS
clusters. We perform test runs of the procedure on several clus-
ters with magnitude cuts brighter than Vcomplete. Based on these
tests, we decide to cut galaxy catalogs to the absolute magnitude
threshold MV = −16.0. With this choice a) we maximize the
signal-to-noise ratio of the detected subclusters and b) we still
have enough galaxies for a stable identification of the system. At
the median redshift of WINGS clusters, z ≃ 0.0535, our absolute
magnitude cut corresponds to an apparent magnitude V ≃ 21.2.
This apparent magnitude also approximately corresponds to
the magnitude where the contrast of our typical cluster relative
to the field is maximum (this estimate is based on the average
cluster luminosity function of (Yagi et al. 2002; De Propris et al.
2003) and on the galaxy counts of (Berta et al. 2006)).
The number of galaxies that are brighter than the threshold
MV = −16.0 is in the range 600 < Ntot < 1200 for a large
fraction of clusters observed with either WFC@INT or with
WFI@ESO2.2.
In order to proceed with the identification of significant
structures within WINGS clusters, we need to verify that our
simulations are sufficiently representative of the real cases.
In practice we need to compare the observed distributions of
χ2S values of noise fluctuations with the corresponding simulated
distributions. In the observations it is impossible to identify indi-
vidual fluctuations as noise. In order to have an idea of the distri-
butions of χ2S of noise fluctuations we consider that our fields are
centered on real clusters. As a consequence, on average, fluctua-
tions in the center of the frames are more likely to correspond to
real systems than those at the borders.
0 20 40 60
Fig. 4. χ2S distributions for border (thick solid histogram) and
central (thick dashed histogram) observed fluctuations. The thin
solid line is the normalized distribution of χ2S of the noise fluctu-
ations in our simulations
We therefore consider separately the fluctuations within the
central regions of the frames and all other fluctuations (borders).
We define the central regions as the central 10% of WFC and
WFI areas. We plot in Fig. 4 the two distributions. The thick
solid histogram is for the border and the thick dashed histogram
for the center of the frames. The difference between ”noise” and
”signal” is clear. In the same figure we also plot the normal-
ized distribution of χ2S of the noise fluctuations in our simulations
(thin solid line). The distributions of χ2S of the observed and sim-
ulated fluctuations are in reasonable agreement considering a)
the simple model used for the simulations and that b) in the ob-
servations we can not exclude real low-χ2S structures among noise
fluctuations. We conclude that for our clusters we can adopt the
same reliability threshold χ2S ,thresholdwe determine from our sim-
ulations (Eq. 5).
6. The Catalog of Substructures
We detect at least one significant structure in 55 (71%) clus-
ters. We find that 12 clusters (16%) have no structure above the
threshold (undetected). In the case of another 10 (13%) clusters
we find significant structures only at the border of the field of
view. In absence of a detection in the center of the frame, we con-
sider these border structures unrelated to the target cluster. We
also verify that in the Color-Magnitude Diagram (CMD) these
border structures are redder than expected given the redshift of
the target cluster. We consider also these 10 clusters undetected.
Here we list the 22 undetected clusters: A0133, A0548b,
A0780, A1644, A1668, A1983, A2271, A2382, A2589, A2626,
A2717, A3164, A3395, A3490, A3497, A3528a, A3556, A3560,
A3809, A4059, RX1022, Z1261.
We note that undetected clusters are real physical systems ac-
cording to their x-ray selection. From an operative point of view,
the fact that these clusters are not detected by DEDICA is the
M. Ramella et al.: Substructures in the WINGS clusters 7
Fig. 5. Isodensity contours (logarithmically spaced) of the Abell
85 field. The title lists the coordinates of the center. The orien-
tation is East to the left, North to the top. Galaxies belonging to
the systems detected by DEDICA are shown as dots of different
colors. Black, light green, blue, red, magenta, dark green are for
the main system and the subsequent substructures ordered as in
Table A.1. Large symbols are for galaxies with MV ≤ −17.0 that
lie where local densities are higher than the median local density
of the structure the galaxy belongs to. Open symbols mark the
positions of the first- and second-ranked cluster galaxies, BCG1
and BCG2 respectively. Similar plots for the 55 analysed clusters
are available in the electronic version of this Journal.
result of the division into too many structures of the total avail-
able clustering signal in the field (or of a too large fraction of
the clustering signal going into border structures). Several phys-
ical situations could be at the origin of missed detections. One
possibility is an excess of physical substructures of comparable
richness. Another possibility is that these clusters are embedded
in regions of the large scale structure that are highly clustered.
We do not try to recover these structures because they can
not be prominent enough. Since our analysis is bidimensional,
we can only detect and use confidently the most prominent struc-
tures. Redshifts are needed for a more detailed analysis of cluster
substructures.
We list the 55 clusters with significant structures in Table
A.1. We give, for each substructure: (1) the name of the parent
cluster; (2) the classification of the structure as main (M), sub-
cluster (S), or background (B) together with their order number;
(3) right ascension (J2000), and (4) declination (J2000) in deci-
mal degrees of the DEDICA peak; the parameters of the ellipse
we obtain from the variance matrix of the coordinates of galaxies
in the substructure, i.e. (5) major axis in arcminutes, (6) elliptic-
ity, and (7) position angle in degrees; (8) luminosity (see the next
section); (9) χ2S .
We make available contour plots of the number density fields
of all clusters in Fig. 6 of the electronic version of this Journal.
In Fig. 5 we show an example of these plots. Isodensity contours
are drawn at ten logarithmic intervals. Galaxies belonging to the
systems detected by DEDICA are shown as dots of different col-
ors. We use large symbols for brighter galaxies (MV ≤ −17.0)
that lie where local densities are higher than the median local
density of the structure the galaxy belongs to. We also mark
with open symbols the positions of the first- and second-ranked
cluster galaxies, BCG1 and BCG2 respectively. Color coding is
black, light green, blue, red, magenta, dark green for the main
system and the subsequent substructures ordered as in Table A.1.
We describe and analyze in detail our catalog in the next sec-
tion.
7. Properties of substructures
The first problem we face in order to study the statistical and
physical properties of substructures is to determine their asso-
ciation with the main structure. In fact, the main structure itself
has to be identified among the structures detected by DEDICA
in each frame.
In most cases it is easy to identify the main structure of a
cluster since it is located at the center of the frame and it has
a high χ2S . In two cases (A0168 and A1736) the choice of the
main structure is complicated because there are several similar
structures near the center of the frame. In these cases we select
the main structure for its highest χ2S .
At this point we limit our analysis to members of the struc-
ture that a) have an absolute magnitude MV ≤ −17 (corrected for
Galactic absorption) and that b) are in the upper half of the distri-
bution of DEDICA-defined local galaxy densities of the system
they belong to. The galaxy density threshold we apply allows us
to separate adjacent structures whose definition becomes more
uncertain at lower galaxy density levels. The magnitude cut in-
creases the relative weight of the galaxies we use to evaluate the
nature of structures in the CMD.
After having identified the main structure, we need to deter-
mine which structures in the field of view of a given cluster have
to be considered background structures. We consider a structure
a physical substructure (or subcluster) if its color-magnitude re-
lation (CMR hereafter) is identical, within the errors, to the CMR
of the main structure.
As a first step we define the color-magnitude relation (CMR)
of the “whole cluster”, i.e. of galaxies in the main structure to-
gether with all other galaxies not assigned to any structure by
DEDICA. We compute the (B − V) CMR of the Coma cluster
from published data (Adami et al. 2006). Then we keep fixed
the slope of the linear CMR of Coma and shift it to the mean
redshift of the cluster.
In order to determine that the main structure and a substruc-
ture are at the same redshift, we evaluate the fraction of back-
ground (red) galaxies, fbg, that each structure has in the CMD.
If these fractions are identical within the errors (Gehrels 1986),
we consider the two structures to be at the same redshift.
In practice we determine fbg by assigning to the background
those galaxies of a structure that are redder than a line parallel to
the CMR and vertically shifted (i.e. redwards) by 2.33 times the
root-mean square of the colors of galaxies in the CMR. We note
that the probability that a random variable is greater than 2.33 in
a Gaussian distribution is only 1%.
The result of the selection of main structures and substruc-
tures is the following: 40 clusters have a total of 69 substruc-
tures at the same redshift as the main structure, only 15 clus-
ters are left without substructures. A total of 35 systems are
found in the background. Considering a) the number density of
poor-to-rich clusters (Mazure et al. 1996; Zabludoff et al. 1993),
b) the average luminosity function of clusters (Yagi et al. 2002;
8 M. Ramella et al.: Substructures in the WINGS clusters
Fig. 7. Cumulative distributions of the two different indicators of
subclustering: left panel Nsub, right panel fLsub.
De Propris et al. 2003), c) the total area covered by the 55 clus-
ter fields, and d) the limiting apparent magnitude corresponding
to our absolute magnitude threshold MV = −16.0, we expect to
find ∼ 0.5± 0.2 background systems per cluster field, 28± 11 in
total. This estimate is consistent with the 35 background systems
we find.
The fraction of clusters with subclusters (73%) is higher than
generally found in previous investigations (typically∼ 30%, see,
e.g., Girardi & Biviano 2002; Flin & Krywult 2006; Lopes et al.
2006, and references therein). Even if we count all undetected
clusters as clusters without substructures, this fraction only de-
creases to 52% (40/77). It is however acknowledged that the
fraction of substructured clusters depends, among other factors,
on the algorithm used to detect substructures, on the quality
and depth of the galaxy catalog. For example Kolokotronis et al.
(2001) using optical and X-ray data find that the fraction of clus-
ters with substructures is ≥ 45%, Burgett et al. (2004) using a
battery of tests detect substructures in 84% of the 25 clusters of
their sample.
Having established the “global” fraction of substructured
clusters, we now investigate the degree of subclustering of in-
dividual clusters, i.e. the distribution of the number of substruc-
tures Nsub we find in our sample.
We find 15 (27%) clusters without substructures; 22 (40%)
clusters with Nsub = 1; 10 (18%) clusters with Nsub = 2; 6 (11%)
clusters with Nsub = 3; and 2 (3%) clusters with Nsub = 4. We
plot in the left panel of Fig. 7 the integral distribution of Nsub.
The distribution of the level of subclustering does not change
when we measure it as the fractional luminosity of subclusters,
fLsub, relative to the luminosity of the whole cluster (see Fig. 7,
right panel). The luminosities we estimate are background cor-
rected using the counts of Berta et al. (2006). We use the ellipses
output from DEDICA (see previous section) as a measure of the
area of subclusters.
We find that Nsub and fLsub are clearly correlated according
to the Spearman rank-correlation test.
We now consider the distribution of subcluster luminosities
and plot the corresponding histogram in Fig. 8. In the same fig-
ure we also plot with arbitrary scaling the power-law∝ L−1. This
relation is the prediction for the differential mass function of
substructures in the cosmological simulations of De Lucia et al.
(2004).
Fig. 8. Observed differential distribution of subcluster lumi-
nosities (histogram) and theoretical model (arbitrary scaling;
De Lucia et al. 2004).
Our observations are consistent to within the uncertainties
with the theoretical prediction of De Lucia et al. (2004) down
to L ∼ 1011.2 L⊙. The disagreement at lower luminosity is ex-
pected since: a) below this limit galaxy-sized halos become im-
portant among the simulated substructures, and b) only above
this limit we expect our catalog to be complete. In fact only
subclusters with luminosities brighter than L = 1011.2 L⊙ have
always richnesses that are ≥ 1/3 of the main structure. This
richness limit approximately corresponds to the completeness
limit of DEDICA detections according to our simulations (see
Sect. 4).
8. Brightest Cluster Galaxies
Here we investigate the relation between BCGs and cluster struc-
tures.
We find that, on average, BCG1s are located close to the den-
sity peak of the main structures. In projection on the sky, the bi-
weight average (see Beers et al. 1990) distance of BCG1s from
the peak of the main system is 72 ± 11 kpc. If we only consider
the 44 BCG1s that are on the CMR and are assigned to main
systems by DEDICA, the average distance decreases to 56 ± 8
kpc. The fact that BCG1s are close to the center of the system
is consistent with current theoretical view on the formation of
BCGs (e.g. Dubinski 1998; Nipoti et al. 2004).
BCG2s are more distant than BCG1s from the peak of the
main system: the biweight average distance is 345 ± 47 kpc. If
we only consider the 26 BCG2s that are on the CMR and are
assigned to main systems by DEDICA, the average distance de-
creases to 161 ± 34 kpc.
Projected distances of BCG2s from density peaks remain
larger than those of BCG1s even when we consider the density
peak of the structure or substructure they belong to. In Fig. 9
we plot the cumulative distributions of the distances of BCG1s
(solid line) and BCG2s (dashed line) from the density peak of
their systems. The distributions are different at the > 99.99%
level according to a Kolmogorov-Smirnov test (KS-test).
Now we turn to luminosities and find that the magnitude dif-
ference between BCG1s and BCG2s, ∆M12, is larger in clus-
ters without substructures than in clusters with substructures.
In Fig. 10 we plot the cumulative distributions of ∆M12 for
clusters with (dashed line) and without (solid line) subclusters.
M. Ramella et al.: Substructures in the WINGS clusters 9
Fig. 9. Cumulative distributions of distances of BCG1 (solid
line) and BCG2 (dashed line) from the density peak of their sys-
Fig. 10. Cumulative distributions of the magnitude difference be-
tween BCG1 and BCG2 in clusters with (dashed line) and with-
out subclusters (solid line).
The two distributions are different according to a KS-test at the
99.1% confidence level. We note that Lin & Mohr (2004) find
that ∆M12 is independent of cluster properties. These authors
however do not consider subclustering.
In order to determine whether the higher values of ∆M12 in
clusters without subclusters are due to an increased luminosity
of the BCG1 (L1) or to a decreased luminosity of the BCG2
(L2), we consider the luminosity of the 10
th brightest galaxy
(L10) as a reference. The biweight average luminosity ratios are
< L1/L10 >= 8.6 ± 1.0 and < L2/L10 >= 3.3 ± 0.3 in clus-
ters without substructures, and < L1/L10 >= 7.1 ± 0.4 and
< L2/L10 >= 3.4 ± 0.2 in clusters with substructures. We then
conclude that the ∆M12-effect is caused by a brightening of the
BCG1 relative to the BCG2 in clusters without substructures.
The fact that ∆M12 is higher in clusters without substruc-
tures can be interpreted, at least qualitatively, in the framework
of the hierarchical scenario of structure evolution. Clusters with-
out substructures are likely to be evolved after several merger
phases. Their BCG1s have already had time to accrete many
galaxies, in particular the more massive ones, which slow down
and sink to the cluster center as the result of dynamical friction.
Some of these galaxies may even have been BCGs of the merg-
ing structures. The simulations by De Lucia & Blaizot (2006)
show that the BCG1s continue to increase their mass via can-
nibalism even at recent times, and that there is a large vari-
ance in the mass accretion history of BCG1s from cluster to
cluster. The result of such a cannibalism process is an increase
of the BCG1 luminosity with respect to other cluster galaxies,
and in extreme cases may lead to the formation of fossil groups
(Khosroshahi et al. 2006).
However, according to these simulations, only 15% of all
BCG1s have accreted > 30% of their mass over the last 2 Gyr,
while another 15% have accreted <3% of their mass over the
same period. Our results indicate that about 60% of the BCG1s
are more than 1 magnitude brighter than the corresponding
BCG2s. Given the size and generality of the luminosity dif-
ferences it would seem that cannibalism alone, even if present
along the merging history of a given cluster, cannot account for
it. Most of the BCG1s should have then been assembled in early
times, as pointed out in the downsizing scenario for galaxy for-
mation (Cowie et al. 1996) and entered that merging history al-
ready with luminosity not far form the present one.
9. Summary
In this paper we search for and characterize cluster substructures,
or subclusters, in the sample of 77 nearby clusters of the WINGS
(Fasano et al. 2006). This sample is an almost complete sample
in X-ray flux in the redshift range 0.04 < z < 0.07.
We detect substructures in the spatial projected distribution
of galaxies in the cluster fields using DEDICA (Pisani 1993,
1996) an adaptive-kernel technique. DEDICA has the following
advantages for our study of WINGS clusters:
a) DEDICA gives a total description of the clustering pat-
tern, in particular membership probability and significance of
structures besides geometrical properties.
b) DEDICA is scale invariant
c) DEDICA does not assume any property of the clusters, i.e.
it is completely non-parametric. In particular it does not require
particularly rich samples to run effectively.
In order to test DEDICA and to set guidelines for the in-
terpretation of the results of the application of DEDICA to our
observations we run DEDICA on several sets of simulated fields
containing a cluster with and without subclusters.
We find that: a) DEDICA always identifies both cluster and
subcluster even when the substructure richness ratio cluster-
to-subcluster is rcs= 8, b) DEDICA recovers a large fraction
of members, almost irrespective of the richness of the original
structure (>∼ 70% in most cases), c) structures with richness ra-
tios rcs<∼ 3 are always distinguishable from noise fluctuations of
the poissonian simulated field.
These simulations also allow us to define a threshold that we
use to identify significant structures in the observed fields.
We apply our clustering procedure to the 77 clusters of the
WINGS sample. We cut galaxy catalogs to the absolute magni-
tude threshold MV = −16.0 in order to maximize the signal-to-
noise ratio of the detected subclusters.
We detect at least one significant structure in 55 (71%) clus-
ter fields. We find that 12 clusters (16%) have no structure above
the threshold (undetected). In the remaining 10 (13%) clusters
we find significant structures only at the border of the field of
view. In absence of a detection in the center of the frame, we
consider these border structures unrelated to the target cluster.
We also verify that in the CMD these border structures are redder
10 M. Ramella et al.: Substructures in the WINGS clusters
than expected given the redshift of the target cluster. We consider
also these clusters undetected.
We provide the coordinates of all substructures in the 55
clusters together with their main properties.
Using the CMR of the early-type cluster galaxies we sep-
arate ”true” subclusters from unrelated background structures.
We find that 40 clusters out of 55 (73%) have a total of 69 sub-
structures with 15 clusters left without substructures.
The fraction of clusters with subclusters (73%) we identify is
higher than most previously published values (typically ∼ 30%,
see, e.g., Girardi & Biviano 2002, and references therein). It is
however acknowledged that the fraction of substructured clus-
ters depends, among other factors, on the algorithm used to de-
tect substructures, on the quality and depth of the galaxy catalog
(Kolokotronis et al. 2001; Burgett et al. 2004).
Another important result of our analysis is the distribution of
subcluster luminosities. In the luminosity range where our sub-
structure detection is complete (L ≥ 1011.2 L⊙), we find that the
distribution of subcluster luminosities is in agreement with the
power-law ∝ L−1 predicted for the differential mass function of
substructures in the cosmological simulations of De Lucia et al.
(2004).
Finally, we investigate the relation between BCGs and clus-
ter structures.
We find that, on average, BCG1s are located close to the den-
sity peak of the main structures. In projection on the sky, the bi-
weight average distance of BCG1s from the peak of the main
system is 72±11 kpc. BCG2s are significantly more distant than
BCG1s from the peak of the main system (345 ± 47 kpc).
The fact that BCG1s are close to the center of the system
is consistent with current theoretical view on the formation of
BCGs (Dubinski 1998).
A more surprising result is that the magnitude difference be-
tween BCG1s and BCG2s, ∆M12, is significantly larger in clus-
ters without substructures than in clusters with substructures.
This fact may be interpreted in the framework of the hierarchical
scenario of structure evolution (e.g. De Lucia & Blaizot 2006).
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12 M. Ramella et al.: Substructures in the WINGS clusters
Appendix A: The catalog of substructures
We provide here the catalog of substructures. In Table A.1 we give, for each substructure: (1) the name of the parent cluster; (2) the
classification of the structure as main (M), subcluster (S), or background (B) together with their order number; (3) right ascension
(J2000), and (4) declination (J2000) in decimal degrees of the DEDICA peak; the parameters of the ellipse we obtain from the
variance matrix of the coordinates of galaxies in the substructure, i.e. (5) major axis in arcminutes, (6) ellipticity, and (7) position
angle in degrees; (8) luminosity; (9) χ2S .
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A0085 M 10.4752 -9.3025 2.0 0.23 -17. 0.41536 48.4
A0085 S1 10.4410 -9.4430 1.8 0.35 -39. 0.17649 42.9
A0085 S2 10.3947 -9.3501 2.3 0.40 -72. 0.12337 32.8
A0119 M 14.0625 -1.2630 4.1 0.44 -65. 0.83955 63.4
A0119 S1 14.1183 -1.2106 4.6 0.60 -23. 0.26847 50.8
A0119 S2 14.0267 -1.0441 3.4 0.34 80. 0.03592 32.0
A0119 B1 13.9402 -1.4979 3.1 0.39 46. – 23.5
A0147 M 17.0648 2.2033 3.9 0.45 79. 0.31392 45.2
A0147 S1 16.8673 2.1393 4.1 0.25 -50. 0.05638 24.8
A0147 S2 17.1925 1.9284 4.4 0.38 55. 0.05052 21.4
A0147 B1 17.0753 2.3174 4.4 0.37 75. – 58.0
A0151 M 17.2186 -15.4219 1.7 0.26 -16. 0.47344 39.9
A0151 S1 17.3516 -15.3652 2.1 0.37 -58. 0.13761 42.9
A0151 S2 17.2632 -15.5564 1.6 0.26 -53. 0.19762 40.9
A0151 B1 17.1375 -15.6116 1.5 0.08 -4. – 59.0
A0160 M 18.2344 15.5126 3.6 0.37 82. 0.55525 66.7
A0160 S1 18.2483 15.3138 5.0 0.41 85. 0.03120 38.1
A0160 S2 18.1141 15.7501 3.0 0.16 86. 0.15196 28.3
A0160 S3 17.9981 15.4150 3.9 0.41 0. 0.06315 27.8
A0168 M 18.7755 0.3999 3.1 0.32 -11. 0.24492 30.5
A0168 S1 18.8799 0.2993 2.0 0.33 4. 0.06871 28.6
A0193 M 21.2894 8.6994 2.1 0.08 36. 0.61982 105.7
A0193 B1 20.9945 8.6119 4.9 0.45 -1. – 39.1
A0311 M 32.3793 19.7722 2.3 0.19 43. 0.43320 44.0
A0376 M 41.4276 36.9517 1.7 0.07 -67. 0.13477 40.8
A0376 S1 41.5569 36.9214 4.4 0.49 -22. 0.24350 33.6
A0500 M 69.6476 -22.1308 2.0 0.31 16. 0.41203 45.5
A0500 S1 69.5915 -22.2377 2.3 0.19 36. 0.20520 47.3
A0602 M 118.3638 29.3528 1.8 0.55 -46. 0.20112 55.4
A0602 S1 118.1848 29.4145 2.3 0.52 31. 0.08470 34.8
A0671 M 127.1237 30.4269 1.6 0.24 -51. 0.68582 69.8
A0671 S1 127.2241 30.4342 2.0 0.40 -5. 0.19736 44.3
A0671 S2 127.1617 30.2967 1.9 0.24 -90. 0.13778 43.0
A0754 M 137.1073 -9.6370 2.0 0.25 53. 0.56063 46.8
A0754 S1 137.3707 -9.6760 3.2 0.53 -8. 0.30590 54.9
A0754 S2 137.2619 -9.6367 1.7 0.14 76. 0.23734 51.2
A0957x M 153.4095 -0.9259 2.0 0.09 -83. 0.42106 38.6
A0957x B1 153.5517 -0.7023 2.2 0.44 -63. – 37.9
A0970 M 154.3595 -10.6921 1.5 0.27 -30. 0.46130 62.5
A0970 S1 154.2369 -10.6422 1.7 0.15 15. 0.13660 42.3
A0970 B1 154.1833 -10.6771 1.8 0.23 -76. – 32.2
A1069 M 159.9418 -8.6883 2.8 0.31 52. 0.37270 50.2
A1069 S1 159.9286 -8.5506 2.4 0.23 88. 0.18532 32.7
A1069 B1 159.7678 -8.9262 3.5 0.55 77. – 54.7
A1291 M 173.0467 56.0255 2.5 0.51 -11. 0.25272 32.1
A1291 S1 172.9090 56.1872 1.4 0.48 -82. 0.03530 37.6
A1631a M 193.2410 -15.3413 1.4 0.35 40. 0.20077 33.9
A1736 M 202.0097 -27.3131 3.1 0.35 58. 0.41824 52.1
A1736 S1 201.7305 -27.0170 2.8 0.32 9. 0.24023 42.6
A1736 S2 201.7662 -27.4067 3.4 0.28 7. 0.14528 42.3
A1736 S3 201.5672 -27.4291 2.7 0.44 73. 0.16926 40.4
A1736 S4 201.9057 -27.1600 3.5 0.21 -1. 0.24192 32.9
A1736 S5 201.7036 -27.1236 3.0 0.39 -12. 0.40395 31.7
A1795 M 207.1911 26.5586 0.6 0.17 55. 0.12341 52.4
M. Ramella et al.: Substructures in the WINGS clusters 13
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A1795 S1 207.2329 26.7362 1.3 0.38 82. 0.05123 46.7
A1831 M 209.8120 27.9714 1.9 0.43 9. 1.08418 56.0
A1831 S1 209.7356 28.0636 2.1 0.34 41. 0.36295 59.7
A1831 B1 209.5725 28.0206 1.7 0.25 -10. – 47.7
A1991 M 223.6405 18.6390 2.3 0.54 -78. 0.28195 40.3
A1991 S1 223.7575 18.7812 2.5 0.32 41. 0.11412 49.9
A1991 B1 223.7683 18.7022 1.7 0.31 71. – 36.6
A2107 M 234.9497 21.8075 2.7 0.19 48. 0.50994 61.1
A2107 B1 235.0699 22.0127 4.3 0.48 83. – 32.9
A2107 B2 235.1409 21.8276 2.4 0.10 55. – 20.4
A2124 M 236.2400 36.0990 1.3 0.24 32. 0.41727 43.3
A2124 B1 236.0207 36.1779 1.6 0.22 34. – 59.7
A2149 M 240.3723 53.9406 1.5 0.46 -10. 0.37347 48.7
A2169 M 243.4867 49.1875 0.6 0.22 72. 0.15358 34.2
A2256 M 255.9260 78.6412 1.9 0.29 -86. 1.46563 95.6
A2256 B1 256.3094 78.4886 2.2 0.48 75. – 48.2
A2256 B2 256.6024 78.4283 2.0 0.12 -88. – 46.8
A2399 M 329.3693 -7.7772 3.5 0.64 -26. 0.40505 38.8
A2415 M 331.3829 -5.5444 2.3 0.23 -60. 0.36780 44.8
A2415 S1 331.5610 -5.3960 2.3 0.33 52. 0.05032 33.9
A2415 B1 331.3800 -5.4017 1.9 0.34 32. – 41.4
A2415 B2 331.3295 -5.3890 1.6 0.41 4. – 37.3
A2457 M 338.9462 1.4765 4.3 0.50 -84. 0.88720 107.3
A2457 S1 339.0392 1.6459 4.1 0.65 -50. 0.05960 23.1
A2457 B1 339.0667 1.3266 5.6 0.53 77. – 73.8
A2572a M 349.3192 18.7197 2.9 0.39 23. 0.44749 47.8
A2572a S1 349.1122 18.5320 4.1 0.25 8. 0.07320 34.5
A2572a S2 349.3851 18.5395 2.6 0.31 67. 0.05345 25.1
A2572a S3 349.0037 18.7220 3.2 0.34 86. 0.00884 20.5
A2593 M 351.0766 14.6539 1.1 0.25 58. 0.28333 33.8
A2593 S1 351.0677 14.4048 2.2 0.42 80. 0.09810 27.0
A2622 M 353.7384 27.3856 3.1 0.09 76. 0.48920 68.1
A2622 S1 353.4880 27.2877 4.2 0.35 46. 0.03070 35.1
A2622 B1 353.7837 27.3182 3.0 0.49 -5. – 53.7
A2622 B2 353.8009 27.6217 2.6 0.38 68. – 29.9
A2657 M 356.1725 9.1818 4.5 0.47 22. 0.27061 49.6
A2657 S1 356.2755 9.1799 3.2 0.35 10. 0.20771 34.0
A2657 B1 355.9569 8.9422 2.8 0.06 -10. – 38.6
A2665 M 357.7050 6.1582 3.6 0.26 71. 0.67950 121.8
A2665 S1 357.4003 5.8659 4.9 0.64 84. 0.01780 17.5
A2665 B1 357.8218 6.3522 3.5 0.44 -50. – 32.7
A2734 M 2.8363 -28.8652 3.4 0.33 3. 0.48700 56.3
A2734 S1 2.6950 -28.7728 4.0 0.27 -7. 0.18970 55.0
A2734 S2 2.6987 -29.0394 3.2 0.24 55. 0.03030 43.3
A2734 S3 2.5727 -29.0562 3.4 0.51 84. 0.03100 33.1
A2734 B1 2.7701 -28.6488 3.7 0.39 14. – 28.0
A3128 M 52.4825 -52.5764 2.2 0.17 -36. 0.40452 37.2
A3128 S1 52.7366 -52.7089 4.1 0.44 -9. 0.25240 51.8
A3128 S2 52.6655 -52.4413 2.3 0.32 -65. 0.19646 51.0
A3128 S3 52.3697 -52.7570 3.2 0.47 81. 0.17169 39.0
A3158 M 55.7477 -53.6334 2.6 0.62 2. 0.70205 52.8
A3158 S1 55.8382 -53.6780 3.4 0.58 10. 0.45553 53.4
A3266 M 67.7893 -61.4637 1.1 0.27 -72. 0.42993 63.5
A3376 M 90.1628 -39.9950 2.5 0.14 -43. 0.33708 43.1
A3376 S1 90.4344 -39.9776 2.7 0.20 -4. 0.21279 59.8
A3376 S2 90.4712 -39.7946 2.1 0.39 -88. 0.00904 31.2
A3528b M 193.5928 -29.0136 1.3 0.04 -24. 0.65638 66.4
A3528b S1 193.6030 -29.0721 1.3 0.26 10. 0.16706 59.0
A3530 M 193.9098 -30.3606 1.9 0.26 33. 0.53043 34.9
A3532 M 194.3035 -30.3732 3.6 0.52 -44. 0.76920 51.1
A3532 B1 194.0413 -30.2130 3.8 0.38 66. – 56.3
14 M. Ramella et al.: Substructures in the WINGS clusters
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A3558 M 201.9587 -31.4892 4.9 0.54 49. 1.14860 64.1
A3558 B1 202.2501 -31.6887 2.6 0.49 44. – 37.6
A3562 M 203.4603 -31.6812 2.5 0.18 82. 0.39087 42.4
A3562 S1 203.1622 -31.7742 4.0 0.40 -86. 0.15010 51.1
A3562 S2 203.3137 -31.6953 3.6 0.40 76. 0.11706 41.0
A3562 S3 203.6982 -31.7171 2.5 0.21 -50. 0.07820 36.7
A3562 S4 203.6541 -31.5969 4.0 0.55 -81. 0.06542 30.3
A3667 M 303.1637 -56.8598 2.1 0.14 23. 0.56803 42.0
A3667 S1 303.5297 -56.9660 3.0 0.39 -86. 0.27086 39.2
A3667 S2 302.7241 -56.6674 1.5 0.17 75. 0.28948 34.0
A3667 S3 302.7081 -56.7557 2.3 0.39 12. 0.09961 33.7
A3716 M 312.9910 -52.7677 4.7 0.38 36. 0.76450 77.9
A3716 S1 312.9769 -52.6434 3.5 0.22 -6. 0.49159 56.9
A3716 B1 312.7735 -52.8976 4.1 0.40 28. – 48.4
A3716 B2 313.1888 -52.4785 3.2 0.23 21. – 22.6
A3880 M 336.9796 -30.5474 3.8 0.33 -50. 0.25840 44.1
A3880 B1 336.8684 -30.8171 2.5 0.30 64. – 30.9
A3880 B2 336.7356 -30.7839 2.7 0.35 46. – 28.4
IIZW108 M 318.4443 2.5706 2.6 0.38 42. 0.49940 33.4
IIZW108 S1 318.6247 2.5533 3.2 0.36 -14. 0.08565 42.3
IIZW108 B1 318.3335 2.7751 1.6 0.24 43. – 44.5
IIZW108 B2 318.5190 2.8039 2.5 0.44 22. – 33.6
MKW3s M 230.3916 7.7281 2.3 0.30 -8. 0.37614 48.7
MKW3s S1 230.4576 7.8769 3.3 0.46 -22. 0.04585 39.3
MKW3s B1 230.7349 7.8882 2.0 0.40 16. – 25.5
RX0058 M 14.5875 26.8816 2.4 0.22 -31. 0.31967 44.2
RX0058 S1 14.7652 27.0424 3.8 0.60 64. 0.31661 50.6
RX0058 B1 14.4012 26.7041 3.3 0.08 -12. – 28.9
RX1740 M 265.1398 35.6416 2.8 0.21 -26. 0.17896 42.1
RX1740 S1 265.2600 35.4366 3.3 0.22 38. 0.01946 31.7
RX1740 S2 264.8688 35.6053 3.7 0.52 28. 0.01340 27.9
RX1740 S3 265.0744 35.8116 3.5 0.44 -7. 0.01166 21.8
Z2844 M 150.7281 32.6483 2.9 0.20 -85. 0.10143 48.3
Z2844 S1 150.6524 32.7621 5.2 0.58 63. 0.04930 50.5
Z2844 S2 150.5821 32.8890 2.6 0.39 0. 0.00395 23.1
Z8338 M 272.7447 49.9078 3.0 0.37 -67. 0.45876 43.1
Z8338 S1 272.8606 49.7916 3.2 0.11 62. 0.05549 31.9
Z8338 S2 272.6903 49.9737 3.1 0.67 62. 0.07089 25.7
Z8338 B1 272.4479 49.6815 1.7 0.18 9. – 25.8
Z8852 M 347.6024 7.5824 2.7 0.41 -45. 0.76110 67.9
Z8852 S1 347.5926 7.3999 5.8 0.56 62. 0.12022 32.4
Z8852 S2 347.6986 7.8018 2.3 0.13 81. 0.02493 25.5
Z8852 B1 347.7381 7.6808 2.1 0.25 -73. – 35.9
Z8852 B2 347.4951 7.8165 2.4 0.21 72. – 27.0
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 1
Online Material
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 2
Fig. 6. Isodensity contours (logarithmically spaced) of the 55 clusters with significant structures. The title lists the coordinates of
the center. The orientation is East to the left, North to the top. Galaxies belonging to the systems detected by DEDICA are shown as
dots of different colors. Black, light green, blue, red, magenta, dark green are for the main system and the subsequent substructures
ordered as in Table A.1. Large symbols are for galaxies with MV ≤ −17.0 that lie where local densities are higher than the median
local density of the structure the galaxy belongs to. Open symbols mark the positions of the first- and second-ranked cluster galaxies,
BCG1 and BCG2 respectively.
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 3
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 4
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 5
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 6
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 7
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 8
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 9
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 10
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 11
Fig. 6. (continued)
	Introduction
	The Data
	The DEDICA Procedure
	The probability density
	Cluster Identification
	Cluster Significance and of Membership Probability
	Tweaking the Algorithm with Simulations
	Substructure detection in WINGS clusters
	The Catalog of Substructures
	Properties of substructures
	Brightest Cluster Galaxies
	Summary
	The catalog of substructures

  We search for and characterize substructures in the projected distribution of
galaxies observed in the wide field CCD images of the 77 nearby clusters of the
WIde-field Nearby Galaxy-cluster Survey (WINGS). This sample is complete in
X-ray flux in the redshift range 0.04<z<0.07. We search for substructures in
WINGS clusters with DEDICA, an adaptive-kernel procedure. We test the procedure
on Monte-Carlo simulations of the observed frames and determine the reliability
for the detected structures. DEDICA identifies at least one reliable structure
in the field of 55 clusters. 40 of these clusters have a total of 69
substructures at the same redshift of the cluster (redshift estimates of
substructures are from color-magnitude diagrams). The fraction of clusters with
subclusters (73%) is higher than in most studies. The presence of subclusters
affects the relative luminosities of the brightest cluster galaxies (BCGs).
Down to L ~ 10^11.2 L_Sun, our observed differential distribution of subcluster
luminosities is consistent with the theoretical prediction of the differential
mass function of substructures in cosmological simulations.

Introduction
According to the current cosmological paradigm, large struc-
tures in the Universe form hierarchically. Clusters of galaxies
are the largest structures that have grown through mergers of
smaller units and have achieved near dynamical equilibrium. In
the hierarchical scenario, clusters are a rather young population,
and we should be able to observe their formation process even at
rather low redshifts. A signature of such process is the presence
of cluster substructures. A cluster is said to contain substruc-
tures (or subclusters) when its surface density is characterized
by multiple, statistically significant peaks on scales larger than
the typical galaxy size, with “surface density” being referred to
the cluster galaxies, the intra-cluster (IC) gas or the dark matter
(DM hereafter; Buote 2002).
Studying cluster substructure therefore allows us to investi-
gate the process by which clusters form, constrain the cosmo-
logical model of structure formation, and ultimately test the hi-
erarchical paradigm itself (e.g. Richstone et al. 1992; Mohr et al.
1995; Thomas et al. 1998). In addition, it also allows us to better
understand the mechanisms affecting galaxy evolution in clus-
ters, which can be accelerated by the perturbative effects of a
cluster-subcluster collision and of the tidal field experienced by
Send offprint requests to: Massimo Ramella, ramella@oats.inaf.it
⋆ Figure 6 is only available in electronic form via
http://www.edpsciences.org
a group accreting onto a cluster (Bekki 1999; Dubinski 1999;
Gnedin 1999). If clusters are to be used as cosmological tools,
it is important to calibrate the effects substructures have on
the estimate of their internal properties (e.g. Schindler & Müller
1993; Pinkney et al. 1996; Roettiger et al. 1998; Biviano et al.
2006; Lopes et al. 2006). Finally, detailed analyses of clus-
ter substructures can be used to constrain the nature of DM
(Markevitch et al. 2004; Clowe et al. 2006).
The analysis of cluster substructures can be performed us-
ing the projected phase-space distribution of cluster galaxies
(e.g. Geller & Beers 1982), the surface-brightness distribution
and temperature of the X-ray emitting IC gas (e.g. Briel et al.
1992), or the shear pattern in the background galaxy distribu-
tion induced by gravitational lensing, that directly samples sub-
structure in the DM component (e.g. Abdelsalam et al. 1998).
None of these tracers of cluster substructure (cluster galaxies, IC
gas, background galaxies) can be considered optimal. The iden-
tification of substructures is in fact subject to different biases
depending on the tracer used. In X-rays projection effects are
less important than in the optical, but the identification of sub-
structures is more subject to a z-dependent bias, arising from the
point spread function of the X-ray telescope and detector (e.g.
Böhringer & Schuecker 2002). Moreover, the different cluster
components respond in a different way to a cluster-subcluster
collision. The subcluster IC gas can be ram-pressure braked and
stripped from the colliding subcluster and lags behind the sub-
cluster galaxies and DM along the direction of collision (e.g.
http://arxiv.org/abs/0704.0579v1
http://www.edpsciences.org
2 M. Ramella et al.: Substructures in the WINGS clusters
Roettiger et al. 1997; Barrena et al. 2002; Clowe et al. 2006).
Hence, it is equally useful to address cluster substructure analy-
sis in the X-ray and in the optical.
Traditionally, the first detections of cluster substructures
were obtained from the projected spatial distributions of galax-
ies (e.g. Shane & Wirtanen 1954; Abell et al. 1964), in com-
bination, when possible, with the distribution of galaxy ve-
locities (e.g. van den Bergh 1960, 1961; de Vaucouleurs 1961).
Increasingly sophisticated techniques for the detection and
characterization of cluster substructures have been developed
over the years (see Moles et al. 1986; Perea et al. 1986a,b;
Buote 2002; Girardi & Biviano 2002, and references therein).
In many of these techniques substructures are identified as de-
viations from symmetry in the spatial and/or velocity distri-
bution of galaxies and in the X-ray surface-brightness (e.g.
West et al. 1988; Fitchett & Merritt 1988; Mohr et al. 1993;
Schuecker et al. 2001). In other techniques substructures are
identified as significant peaks in the surface density distribu-
tion of galaxies or in the X-ray surface brightness, either as
residuals left after the subtraction of a smooth, regular model
representation of the cluster (e.g. Neumann & Böhringer 1997;
Ettori et al. 1998), or in a non-parametric way, e.g. by the tech-
nique of wavelets (e.g. Escalera et al. 1994; Slezak et al. 1994;
Biviano et al. 1996) and by adaptive-kernel techniques (e.g.
Kriessler & Beers 1997; Bardelli et al. 1998a, 2001).
The performances of several different methods have been
evaluated both using numerical simulations (e.g. Mohr et al.
1995; Crone et al. 1996; Pinkney et al. 1996; Buote & Xu
1997; Cen 1997; Valdarnini et al. 1999; Knebe & Müller 2000;
Biviano et al. 2006) and also by applying different methods
to the same cluster data-sets and examine the result differ-
ences (e.g. Escalera et al. 1992, 1994; Mohr et al. 1995, 1996;
Kriessler & Beers 1997; Fadda et al. 1998; Kolokotronis et al.
2001; Schuecker et al. 2001; Lopes et al. 2006). Generally
speaking, the sensitivity of substructure detection increases with
both increasing statistics (e.g. more galaxies or more X-ray pho-
tons) and increasing dimensionality of the test (e.g. using galaxy
velocities in addition to their positions, or using X-ray tempera-
ture in addition to X-ray surface brightness).
Previous investigations have found very different fractions
of clusters with substructure in nearby clusters, depending
on the method and tracer used for substructure detection, on
the cluster sample, and on the size of sampled cluster re-
gions (e.g. Geller & Beers 1982; Dressler & Shectman 1988;
Mohr et al. 1995; Girardi et al. 1997; Kriessler & Beers 1997;
Jones & Forman 1999; Solanes et al. 1999; Kolokotronis et al.
2001; Schuecker et al. 2001; Flin & Krywult 2006; Lopes et al.
2006). Although the distribution of subcluster masses has not
been determined observationally, it is known that subclusters
of ∼ 10% the cluster mass are typical, while more massive
subclusters are less frequent (Escalera et al. 1994; Girardi et al.
1997; Jones & Forman 1999). The situation is probably dif-
ferent for distant clusters which tend to show massive sub-
structures more often than nearby clusters clearly suggesting
hierarchical growth of clusters was more intense in the past
(e.g. Gioia et al. 1999; van Dokkum et al. 2000; Haines et al.
2001; Maughan et al. 2003; Huo et al. 2004; Rosati et al. 2004;
Demarco et al. 2005; Jeltema et al. 2005).
Additional evidence for the hierarchical formation of clus-
ters is provided by the analysis of brightest cluster galaxies
(BCGs hereafter) in substructured clusters. BCGs usually sit
at the bottom of the potential well of their host cluster (e.g.
Adami et al. 1998b). When a BCG is found to be significantly
displaced from its cluster dynamical center, the cluster displays
evidence of substructure (e.g. Beers et al. 1991; Ferrari et al.
2006). From the correlation between cluster and BCG luminosi-
ties, Lin & Mohr (2004) conclude that BCGs grow by merg-
ing as their host clusters grow hierarchically. The related evo-
lution of BCGs and their host clusters is also suggested by the
alignement of the main cluster and BCG axes (e.g. Binggeli
1982; Durret et al. 1998). Both the BCG and the cluster axes
are aligned with the surrounding large scale structure dis-
tribution, where infalling groups come from. These infalling
groups are finally identified as substructures once they enter
the cluster environment (Durret et al. 1998; Arnaud et al. 2000;
West & Blakeslee 2000; Ferrari et al. 2003; Plionis et al. 2003;
Adami et al. 2005). Hence, substructure studies really provide
direct evidence for the hierarchical formation of clusters.
Concerning the impact of subclustering on global cluster
properties, it has been found that subclustering leads to over-
estimating cluster velocity dispersions and virial masses (e.g.
Perea et al. 1990; Bird 1995; Maurogordato et al. 2000), but not
in the general case of small substructures (Escalera et al. 1994;
Girardi et al. 1997; Xu et al. 2000). During the collision of a
subcluster with the main cluster, both the X-ray emitting gas
distribution and its temperature have been found to be signifi-
cantly affected (e.g. Markevitch & Vikhlinin 2001; Clowe et al.
2006). As a consequence, it has been argued that substruc-
ture can explain at least part of the scatter in the scaling rela-
tions of optical-to-X-ray cluster properties (e.g. Fitchett 1988;
Girardi et al. 1996; Barrena et al. 2002; Lopes et al. 2006).
As far as the internal properties of cluster galaxies are
concerned, there is observational evidence that a higher frac-
tion of cluster galaxies with spectral features characteristic
of recent or ongoing starburst episodes is located in sub-
structures or in the regions of cluster-subcluster interactions
(Caldwell et al. 1993; Abraham et al. 1996; Biviano et al. 1997;
Caldwell & Rose 1997; Bardelli et al. 1998b; Moss & Whittle
2000; Miller et al. 2004; Poggianti et al. 2004; Miller 2005;
Giacintucci et al. 2006).
In this paper we search for and characterize substructures
in the sample of 77 nearby clusters of the WIde-field Nearby
Galaxy-cluster Survey (WINGS hereafter, Fasano et al. 2006).
This sample is an almost complete sample in X-ray flux in the
redshift range 0.04 < z < 0.07. We detect substructures from the
spatial, projected distribution of galaxies in the cluster fields, us-
ing the adaptive-kernel based DEDICA algorithm (Pisani 1993,
1996). In Sect. 2 we describe our data-set; in Sect. 3 we de-
scribe the procedure of substructure identification; in Sect. 4 we
use Monte Carlo simulations in order to tweak our procedure;
in Sect. 5 we describe the identification of substructures in our
data-set; in Sect. 6 the catalog of identified substructures is pro-
vided. In Sect. 7 we investigate the properties of the identified
substructures, and in Sect. 8 we consider the relation between
the BCGs and the substructures. We provide a summary of our
work in Sect. 9.
2. The Data
WINGS is an all-sky, photometric (multi-band) and spectro-
scopic survey, whose global goal is the systematic study of the
local cosmic variance of the cluster population and of the prop-
erties of cluster galaxies as a function of cluster properties and
local environment.
The WINGS sample consists of 77 clusters selected from
three X-ray flux limited samples compiled from ROSAT All-
Sky Survey data, with constraints just on the redshift (0.04 < z <
0.07) and distance from the galactic plane (|b| ≥20 deg). The core
M. Ramella et al.: Substructures in the WINGS clusters 3
of the project consists of wide-field optical imaging of the se-
lected clusters in the B and V bands. The imaging data were col-
lected using the WFC@INT (La Palma) and the WFI@MPG (La
Silla) in the northern and southern hemispheres, respectively.
The observation strategy of the survey favors the uniformity
of photometric depth inside the different CCDs, rather than com-
plete coverage of the fields that would require dithering. Thus,
the gaps in the WINGS optical imaging correspond to the phys-
ical gaps between the different CCDs of the mosaics.
During the data reduction process, we give particular care to
sky subtraction (also in presence of crowded fields including big
halo galaxies and/or very bright stars), image cleaning (spikes
and bad pixels) and star/galaxy classification (obtained with both
automatic and interactive tools).
According to Fasano et al. (2006) and Varela et al. (2007),
the overall quality of the data reported in the WINGS photomet-
ric catalogs can be summarized as follows: (i) the astrometric
errors for extended objects have r.m.s. ∼0.2 arcsec; (ii) the av-
erage limiting magnitude is ∼24.0, ranging from 23.0 to 25.0;
(iii) the completeness of the catalogs is achieved (on average) up
to V ∼22.0; (iv) the total (systematic plus random) photometric
r.m.s. errors, derived from both internal and external compar-
isons, vary from ∼0.02 mag, for bright objects, up to ∼0.2 mag,
for objects close to the detection limit.
3. The DEDICA Procedure
We base our search for substructures in WINGS clusters on the
DEDICA procedure (Pisani 1993, 1996). This procedure has the
following advantages:
1. DEDICA gives a total description of the clustering pattern,
in particular the membership probability and significance of
structures besides geometrical properties;
2. DEDICA is scale invariant;
3. DEDICA does not assume any property of the clusters, i.e.
it is completely non-parametric. In particular it does not re-
quire particularly rich samples to run effectively.
The basic nature and properties of DEDICA are described in
Pisani (1993, 1996, and references therein). Here we summarize
the main structure of the algorithm and how we apply it to our
data sample. The core structure of DEDICA is based on the as-
sumption that a structure (or a “cluster” in the algorithm jargon)
corresponds to a local maximum in the density of galaxies.
We proceed as follows. First we need to estimate the proba-
bility density function Ψ(ri) (with i = 1, . . .N) associated with
the set of N galaxies with coordinates ri. Second, we need to
find the local maxima in our estimate of Ψ(ri) in order to iden-
tify clusters and also to evaluate their significance relatively to
the noise. Third and finally, we need to estimate the probability
that a galaxy is a member of the identified clusters.
3.1. The probability density
DEDICA is a non-parametric method in the sense that it does
not require any assumption on the probability density function
that it is aimed to estimate. The only assumptions are that Ψ(ri)
must be continuous and at least twice differentiable.
The function f (ri) is an estimate of Ψ(ri) and it is built by
using an adaptive kernel method given by:
fka(r) =
K(ri, σi; r) (1)
where we use the two dimensional Gaussian kernel K(ri, σi; r)
centered in ri with size σi.
The most valuable feature of DEDICA is the procedure to se-
lect the values of kernel widths σi. It is possible to show that the
optimal choice for σi, i.e. with asymptotically minimum vari-
ance and null bias, is obtained by minimizing the distance be-
tween our estimate f (ri) and Ψ(ri). This distance can be eval-
uated by a particular function called the integrated square error
IS E( f ) given by:
IS E( f ) =
[Ψ(r) − f (r)]2dr (2)
Once the minimum IS E( f ) is reached we have obtained the
DEDICA estimate of the density as in Eq.1.
3.2. Cluster Identification
The second step of DEDICA consists in the identification of the
local maxima in fka(r). The positions of the peaks in the density
function fka(r) are found as the solutions of the iterative equa-
tion:
rm+1 = rm + a ·
∇ fka(rm)
fka(rm)
where a is a scale factor set according to optimal convergence
requirements. The limit R of the sequence rm defined in Eq.3
depends on the starting position rm=1.
rm = R(rm=1) (4)
We run the sequence in Eq.3 at each data position ri. We label
each data point with the limit Ri = R(rm=1 = ri). These limits
Ri are the position of the peak to which the i− th galaxy belong.
In the case that all the galaxies are members of a unique cluster,
all the labels Ri are the same. At the other extreme each galaxy
is a one-member cluster and all Ri have different values. All the
members of a given cluster belong to the same peak in fka(r)
and have the same Ri. We identify cluster members by listing
galaxies having the same values of R. We end up with ν different
clusters each with nµ (µ = 1, . . . , ν) members.
In order to maintain a coherent notation, we identify with
the label µ = 0 the n0 isolated galaxies considered a system of
background galaxies. We have: n0 = N −
µ=1 nµ.
3.3. Cluster Significance and of Membership Probability
The statistical significance S µ (µ = 1, . . . , ν) of each cluster is
based on the assumption that the presence of the µ − th cluster
causes an increase in the local probability density as well as in
the sample likelihood LN = Πi[ fka(ri)] relatively to the value Lµ
that one would have if the members of the µ− th cluster were all
isolated, i.e. belonging to the background.
A large value in the ratio LN/Lµ characterizes the most im-
portant clusters. According to Materne (1979) it is possible to
estimate the significance of each cluster by using the likelihood
ratio test. In other words 2 ln(LN/Lµ) is distributed as a χ
2 vari-
able with ν− 1 degrees of freedom. Therefore, once we compute
the value of χ2 for each cluster (χ2S ), we can also compute the
significance S µ of the cluster.
Here we assume that the contribution to the global density
field fka(ri) of the µ − th cluster is Fµ(ri). The ratio between the
value of Fµ(ri) and the total local density fka(ri) can be used to
estimate the membership probability of each galaxy relatively to
4 M. Ramella et al.: Substructures in the WINGS clusters
the identified clusters. This criterion also allows us to estimate
the probability that a galaxy is isolated.
At the end of the DEDICA procedure we are left with a)
a catalog of galaxies each with information on position, mem-
bership, local density and size of the Gaussian kernel, b) a cat-
alog of structures with information on position, richness, the
χ2S parameter, and peak density. For each cluster we also com-
pute from the coordinate variance matrix the cluster major axis,
ellipticity and position angle.
4. Tweaking the Algorithm with Simulations
In this section we describe our analysis of the performance of
DEDICA and the guidelines we obtain for the interpretation of
the clustering analysis of our observations.
We build simulated fields containing a cluster with and with-
out subclusters. The simulated fields have the same geometry
of the WFC field and are populated with the typical number of
objects we will analyze. For simplicity we consider only WFC
fields. Because DEDICA is scale-free, a different sampling of
the same field of view has no consequence on our analysis.
In the next section we limit our analysis to MV,lim ≤ −16.
At the median redshift of the WINGS cluster, z ≃ 0.05, this
absolute magnitude limit corresponds to an apparent magnitude
Vlim ≃ 21. Within this magnitude limit the representative number
of galaxies in our frames is Ntot= 900.
We then consider Ntot= Nmem+ Nbkg, with Nmemthe number
of cluster members and Nbkgthe number of field – or background
– galaxies. We set Nbkg= 670, close to the average number of
background galaxies we expect in our frame based on typical
observed fields counts, e.g. Berta et al. (2006) or Arnouts et al.
(1997). With this choice, we have Nmem= 230.
We distribute uniformly at random Nbkgobjects. We dis-
tribute at random the remaining Nmem= 230 objects in one or
more overdensities depending on the test we perform. We popu-
late overdensities according to a King profile (King 1962) with
a core radius Rcore = 90 kpc, representative of our clusters. We
then scale Rcore with the number of members of the substructure,
NS . We use
Rcore = 250
NC + NS
where NC is the number of objects in the cluster with Nmem=
NS + NC . This scaling of Rcore with cluster richness is from
Adami et al. (1998a) assuming direct proportionality between
cluster richness and luminosity (e.g. Popesso et al. 2006).
As far as the relative richnesses of the cluster and subcluster
are concerned, we consider the following richness ratios rcs =
NC/NS = 1, 2, 4, 8. With these richness ratios, the number of
objects in the cluster are NC = 115, 153, 184, 204, and those in
subclusters are NS = 115, 77, 46, 26 respectively.
In a first set of simulated fields we place the substructure at
2731 pixels (15 arcmin) from the main cluster so that they do not
overlap. In a second set of simulations, we place main cluster and
substructure at shorter distances, 683 and 1366 pixels, in order to
investigate the ability of DEDICA to resolve structures. At each
of these shorter distances we build simulations with both rcs= 1
and 2.
For each richness ratio and/or distance between cluster and
subcluster we produce 16 simulations with different realizations
of the random positions of the data points representing galaxies.
In order to minimize the effect of the borders on the detection
of structures we add to the simulation a “frame” of 1000 pixel.
5 10 15
simulation
Fig. 1. Fraction of recovered members of each substructure for
different rcs. The solid line connects substructures with rcs = 2
and 4
We fill this frame with a grid of data points at the same density
as the average density of the field.
The first result we obtain from the runs of DEDICA on the
simulations with varying richness ratio is the positive rate at
which we detect real structures. We find that we always recover
both cluster and substructure even when the substructure only
contains NS = 1/8 NC objects, i.e. 26 objects (on top of the uni-
form background). In other words, if there is a real structure
DEDICA finds it.
We also check how many original members the procedure
assigns to structures it recovers. The results are summarized in
Fig. 1. In the diagram, the fraction of recovered members of each
substructure is represented by the values of its rcs. The solid line
connects substructures with rcs = 2 and 4.
From Fig. 1 it is clear that our procedure recovers a large
fraction of members, almost irrespective of the richness of the
original structure. It is also interesting to note that the fluctu-
ations identified as substructures are located very close to the
center of the corresponding simulated substructures. In almost
all cases the distance between original and detected substructure
is significantly shorter than the mean inter-particle distance.
The second important result we obtain from the simulations
is the false positive rate, i.e. the fraction of noise fluctuations
that are as significant as the fluctuations corresponding to real
structures.
First of all we need to define an operative measure of the
reliability of the detected structures. In fact DEDICA provides a
default value S µ (µ = 1, . . . , ν) of the significance (see Sect. 3.3).
However, S µ has a relatively small dynamical range, in particular
for highly significant clusters.
Density or richness both allow a reasonable ”ranking” of
structures. However, both large low-density noise fluctuations
(often built up from more than one noise fluctuation) and very
high density fluctuations produced by few very close data points
could be mistakenly ranked as highly significant structures ac-
cording to, respectively, richness and density criteria.
M. Ramella et al.: Substructures in the WINGS clusters 5
0 20 40 60 80
Fig. 2. χ2S of simulated noise fluctuations (solid line). Labels are
the rcsof simulated structures at the abscissa corresponding to
their χ2S and at arbitrary ordinates.
We therefore prefer to use the parameter χ2S which stands at
the base of the estimate of S µ and which is naturally provided by
DEDICA. The main characteristic of χ2S is that it depends both on
the density of a cluster relative to the background and on its rich-
ness. Using χ2S we classify correctly significantly more structures
than with either density or richness alone.
In Fig. 2 we plot the distribution of χ2S of noise fluctuations
(solid line). In the same plot we also mark the rcsof real struc-
tures as detected by our procedure. We use labels indicating
rcsand place them at the abscissa corresponding to their χ
S and
at arbitrary ordinates.
Fig. 2 shows that the structures detected with rcs= 1, 2 are al-
ways distinguishable from noise fluctuations. Substructures with
rcs= 4 or higher, although correctly detected, have χ
S values that
are close to or lower than the level of noise.
With the second set of simulations, we test the minimum dis-
tance at which cluster and subcluster can still be identified as
separate entities. We place cluster and substructure (rcs= 1, 2) at
distances dcs = 683 and 1366 pixel. These distances are 1/4 and
1/2 respectively of the distance between cluster and substructure
in the first set of simulations. Again we produce 16 simulations
for each of the 4 cases.
We find that at dcs = 1366 pixel cluster and substructure are
always correctly identified. At the shorter distance dcs = 683
pixel, DEDICA merges cluster and substructure in 1 out of 16
cases for rcs= 1 and in 8 out of 16 cases for rcs= 2. With our
density profile, dcs = 683 pixel corresponds to dcs ≃ Rc + Rs
with Rc, Rs the radii of the main cluster and of the subcluster
respectively.
In order to verify the results we obtain for 900 data points
we produce more simulations with Ntot= 450, 600 and 1200. In
all these simulations RC and RS are the same as in the set with
Ntot= 900. We vary Nbkgand Nmemso that Nmem/ Nbkgis the same
as in the case Ntot= 900.
0.5 1 1.5 2 2.5
Fig. 3. Small symbols correspond to χ2S as a function of the num-
ber of members of noise fluctuations. Crosses, circles, dots and
triangles are χ2S for the noise fluctuations of the simulations with
Ntot= 450, 600, 900, and 1200 respectively. Large symbols are
χ2S of simulated clusters and subclusters with rcs= 1. Horizontal
lines mark the levels of χ2S ,threshold.
These simulations confirm the results we obtain in the
case Ntot= 900, and allow us to set a detection threshold,
χ2S ,threshold(Ntot), for significant fluctuations in the analysis of real
clusters.
We summarize the behavior of the noise fluctuations in our
simulations in Fig. 3. In this figure, the small symbols corre-
spond to χ2S as a function of the number of members of noise
fluctuations. In particular, crosses, circles, dots and triangles are
χ2S for the noise fluctuations of the simulations with Ntot= 450,
600, 900, and 1200 respectively.
The larger symbols are the χ2S of the fluctuations correspond-
ing to simulated clusters and subclusters of equal richness (rcs=
The 4 horizontal lines mark the level of χ2S ,threshold, i.e. the
average χ2S of the 3 most significant noise fluctuations in each of
the 4 groups of simulations with Ntot= 450, 600, 900, and 1200.
The expected increase of χ2S ,thresholdwith Ntotis evident.
We note that the only significant difference with these find-
ings we obtain from the simulations with rcs= 2 is that χ
simulated clusters and subclusters is closer to χ2S ,threshold(but still
higher).
We fit χ2S ,thresholdwith Ntotand obtain
log(χ2S ,threshold) = 1/2.55 log(Ntot) + 0.394 (5)
in good agreement with the expected behavior of the poissonian
fluctuations.
As a final test we verify that infra-chip gaps do not have a
dramatic impact on the detection of structures in the cases rcs= 1
and 2. We place a 50 pixel wide gap where it has the maximum
impact, i.e. where the kernel size is shortest. Even if the infra-
6 M. Ramella et al.: Substructures in the WINGS clusters
chip gap cuts through the center of the structures, DEDICA is
able to identify these structures correctly.
We summarize here the main results of our tests on simulated
clusters with substructures:
– DEDICA successfully detects even the poorest structures
above a uniform poissonian noise background.
– DEDICA recovers a large fraction (typically > 3/4) of the
real members of a substructure, almost irrespective of the
richness of the structure.
– DEDICA is able to distinguish between noise fluctuations
and true structures only if these structures are rich enough.
In the case of our simulations, structures have to be richer
than 1/4th of the main structure.
– DEDICA is able to separate neighboring structures provided
they do not overlap.
– infra-chip gaps do not threaten the detection of structures
that are rich enough to be reliably detected.
– the χ2S threshold we use to identify significant structures is
a function of the total number of points and can be scaled
within the whole range of numbers of galaxies observed
within our fields.
In the next section we apply these results to the real WINGS
clusters.
5. Substructure detection in WINGS clusters
We apply our clustering procedure to the 77 clusters of the
WINGS sample. The photometric catalog of each cluster is deep,
reaching a completeness magnitude Vcomplete ≤ 22. The num-
ber of galaxies is correspondingly large, from Ngal ≃ 3, 000 to
Ngal ≃ 10, 000.
The large number of bright background galaxies (faint ap-
parent magnitudes) dilutes the clustering signal of local WINGS
clusters. We perform test runs of the procedure on several clus-
ters with magnitude cuts brighter than Vcomplete. Based on these
tests, we decide to cut galaxy catalogs to the absolute magnitude
threshold MV = −16.0. With this choice a) we maximize the
signal-to-noise ratio of the detected subclusters and b) we still
have enough galaxies for a stable identification of the system. At
the median redshift of WINGS clusters, z ≃ 0.0535, our absolute
magnitude cut corresponds to an apparent magnitude V ≃ 21.2.
This apparent magnitude also approximately corresponds to
the magnitude where the contrast of our typical cluster relative
to the field is maximum (this estimate is based on the average
cluster luminosity function of (Yagi et al. 2002; De Propris et al.
2003) and on the galaxy counts of (Berta et al. 2006)).
The number of galaxies that are brighter than the threshold
MV = −16.0 is in the range 600 < Ntot < 1200 for a large
fraction of clusters observed with either WFC@INT or with
WFI@ESO2.2.
In order to proceed with the identification of significant
structures within WINGS clusters, we need to verify that our
simulations are sufficiently representative of the real cases.
In practice we need to compare the observed distributions of
χ2S values of noise fluctuations with the corresponding simulated
distributions. In the observations it is impossible to identify indi-
vidual fluctuations as noise. In order to have an idea of the distri-
butions of χ2S of noise fluctuations we consider that our fields are
centered on real clusters. As a consequence, on average, fluctua-
tions in the center of the frames are more likely to correspond to
real systems than those at the borders.
0 20 40 60
Fig. 4. χ2S distributions for border (thick solid histogram) and
central (thick dashed histogram) observed fluctuations. The thin
solid line is the normalized distribution of χ2S of the noise fluctu-
ations in our simulations
We therefore consider separately the fluctuations within the
central regions of the frames and all other fluctuations (borders).
We define the central regions as the central 10% of WFC and
WFI areas. We plot in Fig. 4 the two distributions. The thick
solid histogram is for the border and the thick dashed histogram
for the center of the frames. The difference between ”noise” and
”signal” is clear. In the same figure we also plot the normal-
ized distribution of χ2S of the noise fluctuations in our simulations
(thin solid line). The distributions of χ2S of the observed and sim-
ulated fluctuations are in reasonable agreement considering a)
the simple model used for the simulations and that b) in the ob-
servations we can not exclude real low-χ2S structures among noise
fluctuations. We conclude that for our clusters we can adopt the
same reliability threshold χ2S ,thresholdwe determine from our sim-
ulations (Eq. 5).
6. The Catalog of Substructures
We detect at least one significant structure in 55 (71%) clus-
ters. We find that 12 clusters (16%) have no structure above the
threshold (undetected). In the case of another 10 (13%) clusters
we find significant structures only at the border of the field of
view. In absence of a detection in the center of the frame, we con-
sider these border structures unrelated to the target cluster. We
also verify that in the Color-Magnitude Diagram (CMD) these
border structures are redder than expected given the redshift of
the target cluster. We consider also these 10 clusters undetected.
Here we list the 22 undetected clusters: A0133, A0548b,
A0780, A1644, A1668, A1983, A2271, A2382, A2589, A2626,
A2717, A3164, A3395, A3490, A3497, A3528a, A3556, A3560,
A3809, A4059, RX1022, Z1261.
We note that undetected clusters are real physical systems ac-
cording to their x-ray selection. From an operative point of view,
the fact that these clusters are not detected by DEDICA is the
M. Ramella et al.: Substructures in the WINGS clusters 7
Fig. 5. Isodensity contours (logarithmically spaced) of the Abell
85 field. The title lists the coordinates of the center. The orien-
tation is East to the left, North to the top. Galaxies belonging to
the systems detected by DEDICA are shown as dots of different
colors. Black, light green, blue, red, magenta, dark green are for
the main system and the subsequent substructures ordered as in
Table A.1. Large symbols are for galaxies with MV ≤ −17.0 that
lie where local densities are higher than the median local density
of the structure the galaxy belongs to. Open symbols mark the
positions of the first- and second-ranked cluster galaxies, BCG1
and BCG2 respectively. Similar plots for the 55 analysed clusters
are available in the electronic version of this Journal.
result of the division into too many structures of the total avail-
able clustering signal in the field (or of a too large fraction of
the clustering signal going into border structures). Several phys-
ical situations could be at the origin of missed detections. One
possibility is an excess of physical substructures of comparable
richness. Another possibility is that these clusters are embedded
in regions of the large scale structure that are highly clustered.
We do not try to recover these structures because they can
not be prominent enough. Since our analysis is bidimensional,
we can only detect and use confidently the most prominent struc-
tures. Redshifts are needed for a more detailed analysis of cluster
substructures.
We list the 55 clusters with significant structures in Table
A.1. We give, for each substructure: (1) the name of the parent
cluster; (2) the classification of the structure as main (M), sub-
cluster (S), or background (B) together with their order number;
(3) right ascension (J2000), and (4) declination (J2000) in deci-
mal degrees of the DEDICA peak; the parameters of the ellipse
we obtain from the variance matrix of the coordinates of galaxies
in the substructure, i.e. (5) major axis in arcminutes, (6) elliptic-
ity, and (7) position angle in degrees; (8) luminosity (see the next
section); (9) χ2S .
We make available contour plots of the number density fields
of all clusters in Fig. 6 of the electronic version of this Journal.
In Fig. 5 we show an example of these plots. Isodensity contours
are drawn at ten logarithmic intervals. Galaxies belonging to the
systems detected by DEDICA are shown as dots of different col-
ors. We use large symbols for brighter galaxies (MV ≤ −17.0)
that lie where local densities are higher than the median local
density of the structure the galaxy belongs to. We also mark
with open symbols the positions of the first- and second-ranked
cluster galaxies, BCG1 and BCG2 respectively. Color coding is
black, light green, blue, red, magenta, dark green for the main
system and the subsequent substructures ordered as in Table A.1.
We describe and analyze in detail our catalog in the next sec-
tion.
7. Properties of substructures
The first problem we face in order to study the statistical and
physical properties of substructures is to determine their asso-
ciation with the main structure. In fact, the main structure itself
has to be identified among the structures detected by DEDICA
in each frame.
In most cases it is easy to identify the main structure of a
cluster since it is located at the center of the frame and it has
a high χ2S . In two cases (A0168 and A1736) the choice of the
main structure is complicated because there are several similar
structures near the center of the frame. In these cases we select
the main structure for its highest χ2S .
At this point we limit our analysis to members of the struc-
ture that a) have an absolute magnitude MV ≤ −17 (corrected for
Galactic absorption) and that b) are in the upper half of the distri-
bution of DEDICA-defined local galaxy densities of the system
they belong to. The galaxy density threshold we apply allows us
to separate adjacent structures whose definition becomes more
uncertain at lower galaxy density levels. The magnitude cut in-
creases the relative weight of the galaxies we use to evaluate the
nature of structures in the CMD.
After having identified the main structure, we need to deter-
mine which structures in the field of view of a given cluster have
to be considered background structures. We consider a structure
a physical substructure (or subcluster) if its color-magnitude re-
lation (CMR hereafter) is identical, within the errors, to the CMR
of the main structure.
As a first step we define the color-magnitude relation (CMR)
of the “whole cluster”, i.e. of galaxies in the main structure to-
gether with all other galaxies not assigned to any structure by
DEDICA. We compute the (B − V) CMR of the Coma cluster
from published data (Adami et al. 2006). Then we keep fixed
the slope of the linear CMR of Coma and shift it to the mean
redshift of the cluster.
In order to determine that the main structure and a substruc-
ture are at the same redshift, we evaluate the fraction of back-
ground (red) galaxies, fbg, that each structure has in the CMD.
If these fractions are identical within the errors (Gehrels 1986),
we consider the two structures to be at the same redshift.
In practice we determine fbg by assigning to the background
those galaxies of a structure that are redder than a line parallel to
the CMR and vertically shifted (i.e. redwards) by 2.33 times the
root-mean square of the colors of galaxies in the CMR. We note
that the probability that a random variable is greater than 2.33 in
a Gaussian distribution is only 1%.
The result of the selection of main structures and substruc-
tures is the following: 40 clusters have a total of 69 substruc-
tures at the same redshift as the main structure, only 15 clus-
ters are left without substructures. A total of 35 systems are
found in the background. Considering a) the number density of
poor-to-rich clusters (Mazure et al. 1996; Zabludoff et al. 1993),
b) the average luminosity function of clusters (Yagi et al. 2002;
8 M. Ramella et al.: Substructures in the WINGS clusters
Fig. 7. Cumulative distributions of the two different indicators of
subclustering: left panel Nsub, right panel fLsub.
De Propris et al. 2003), c) the total area covered by the 55 clus-
ter fields, and d) the limiting apparent magnitude corresponding
to our absolute magnitude threshold MV = −16.0, we expect to
find ∼ 0.5± 0.2 background systems per cluster field, 28± 11 in
total. This estimate is consistent with the 35 background systems
we find.
The fraction of clusters with subclusters (73%) is higher than
generally found in previous investigations (typically∼ 30%, see,
e.g., Girardi & Biviano 2002; Flin & Krywult 2006; Lopes et al.
2006, and references therein). Even if we count all undetected
clusters as clusters without substructures, this fraction only de-
creases to 52% (40/77). It is however acknowledged that the
fraction of substructured clusters depends, among other factors,
on the algorithm used to detect substructures, on the quality
and depth of the galaxy catalog. For example Kolokotronis et al.
(2001) using optical and X-ray data find that the fraction of clus-
ters with substructures is ≥ 45%, Burgett et al. (2004) using a
battery of tests detect substructures in 84% of the 25 clusters of
their sample.
Having established the “global” fraction of substructured
clusters, we now investigate the degree of subclustering of in-
dividual clusters, i.e. the distribution of the number of substruc-
tures Nsub we find in our sample.
We find 15 (27%) clusters without substructures; 22 (40%)
clusters with Nsub = 1; 10 (18%) clusters with Nsub = 2; 6 (11%)
clusters with Nsub = 3; and 2 (3%) clusters with Nsub = 4. We
plot in the left panel of Fig. 7 the integral distribution of Nsub.
The distribution of the level of subclustering does not change
when we measure it as the fractional luminosity of subclusters,
fLsub, relative to the luminosity of the whole cluster (see Fig. 7,
right panel). The luminosities we estimate are background cor-
rected using the counts of Berta et al. (2006). We use the ellipses
output from DEDICA (see previous section) as a measure of the
area of subclusters.
We find that Nsub and fLsub are clearly correlated according
to the Spearman rank-correlation test.
We now consider the distribution of subcluster luminosities
and plot the corresponding histogram in Fig. 8. In the same fig-
ure we also plot with arbitrary scaling the power-law∝ L−1. This
relation is the prediction for the differential mass function of
substructures in the cosmological simulations of De Lucia et al.
(2004).
Fig. 8. Observed differential distribution of subcluster lumi-
nosities (histogram) and theoretical model (arbitrary scaling;
De Lucia et al. 2004).
Our observations are consistent to within the uncertainties
with the theoretical prediction of De Lucia et al. (2004) down
to L ∼ 1011.2 L⊙. The disagreement at lower luminosity is ex-
pected since: a) below this limit galaxy-sized halos become im-
portant among the simulated substructures, and b) only above
this limit we expect our catalog to be complete. In fact only
subclusters with luminosities brighter than L = 1011.2 L⊙ have
always richnesses that are ≥ 1/3 of the main structure. This
richness limit approximately corresponds to the completeness
limit of DEDICA detections according to our simulations (see
Sect. 4).
8. Brightest Cluster Galaxies
Here we investigate the relation between BCGs and cluster struc-
tures.
We find that, on average, BCG1s are located close to the den-
sity peak of the main structures. In projection on the sky, the bi-
weight average (see Beers et al. 1990) distance of BCG1s from
the peak of the main system is 72 ± 11 kpc. If we only consider
the 44 BCG1s that are on the CMR and are assigned to main
systems by DEDICA, the average distance decreases to 56 ± 8
kpc. The fact that BCG1s are close to the center of the system
is consistent with current theoretical view on the formation of
BCGs (e.g. Dubinski 1998; Nipoti et al. 2004).
BCG2s are more distant than BCG1s from the peak of the
main system: the biweight average distance is 345 ± 47 kpc. If
we only consider the 26 BCG2s that are on the CMR and are
assigned to main systems by DEDICA, the average distance de-
creases to 161 ± 34 kpc.
Projected distances of BCG2s from density peaks remain
larger than those of BCG1s even when we consider the density
peak of the structure or substructure they belong to. In Fig. 9
we plot the cumulative distributions of the distances of BCG1s
(solid line) and BCG2s (dashed line) from the density peak of
their systems. The distributions are different at the > 99.99%
level according to a Kolmogorov-Smirnov test (KS-test).
Now we turn to luminosities and find that the magnitude dif-
ference between BCG1s and BCG2s, ∆M12, is larger in clus-
ters without substructures than in clusters with substructures.
In Fig. 10 we plot the cumulative distributions of ∆M12 for
clusters with (dashed line) and without (solid line) subclusters.
M. Ramella et al.: Substructures in the WINGS clusters 9
Fig. 9. Cumulative distributions of distances of BCG1 (solid
line) and BCG2 (dashed line) from the density peak of their sys-
Fig. 10. Cumulative distributions of the magnitude difference be-
tween BCG1 and BCG2 in clusters with (dashed line) and with-
out subclusters (solid line).
The two distributions are different according to a KS-test at the
99.1% confidence level. We note that Lin & Mohr (2004) find
that ∆M12 is independent of cluster properties. These authors
however do not consider subclustering.
In order to determine whether the higher values of ∆M12 in
clusters without subclusters are due to an increased luminosity
of the BCG1 (L1) or to a decreased luminosity of the BCG2
(L2), we consider the luminosity of the 10
th brightest galaxy
(L10) as a reference. The biweight average luminosity ratios are
< L1/L10 >= 8.6 ± 1.0 and < L2/L10 >= 3.3 ± 0.3 in clus-
ters without substructures, and < L1/L10 >= 7.1 ± 0.4 and
< L2/L10 >= 3.4 ± 0.2 in clusters with substructures. We then
conclude that the ∆M12-effect is caused by a brightening of the
BCG1 relative to the BCG2 in clusters without substructures.
The fact that ∆M12 is higher in clusters without substruc-
tures can be interpreted, at least qualitatively, in the framework
of the hierarchical scenario of structure evolution. Clusters with-
out substructures are likely to be evolved after several merger
phases. Their BCG1s have already had time to accrete many
galaxies, in particular the more massive ones, which slow down
and sink to the cluster center as the result of dynamical friction.
Some of these galaxies may even have been BCGs of the merg-
ing structures. The simulations by De Lucia & Blaizot (2006)
show that the BCG1s continue to increase their mass via can-
nibalism even at recent times, and that there is a large vari-
ance in the mass accretion history of BCG1s from cluster to
cluster. The result of such a cannibalism process is an increase
of the BCG1 luminosity with respect to other cluster galaxies,
and in extreme cases may lead to the formation of fossil groups
(Khosroshahi et al. 2006).
However, according to these simulations, only 15% of all
BCG1s have accreted > 30% of their mass over the last 2 Gyr,
while another 15% have accreted <3% of their mass over the
same period. Our results indicate that about 60% of the BCG1s
are more than 1 magnitude brighter than the corresponding
BCG2s. Given the size and generality of the luminosity dif-
ferences it would seem that cannibalism alone, even if present
along the merging history of a given cluster, cannot account for
it. Most of the BCG1s should have then been assembled in early
times, as pointed out in the downsizing scenario for galaxy for-
mation (Cowie et al. 1996) and entered that merging history al-
ready with luminosity not far form the present one.
9. Summary
In this paper we search for and characterize cluster substructures,
or subclusters, in the sample of 77 nearby clusters of the WINGS
(Fasano et al. 2006). This sample is an almost complete sample
in X-ray flux in the redshift range 0.04 < z < 0.07.
We detect substructures in the spatial projected distribution
of galaxies in the cluster fields using DEDICA (Pisani 1993,
1996) an adaptive-kernel technique. DEDICA has the following
advantages for our study of WINGS clusters:
a) DEDICA gives a total description of the clustering pat-
tern, in particular membership probability and significance of
structures besides geometrical properties.
b) DEDICA is scale invariant
c) DEDICA does not assume any property of the clusters, i.e.
it is completely non-parametric. In particular it does not require
particularly rich samples to run effectively.
In order to test DEDICA and to set guidelines for the in-
terpretation of the results of the application of DEDICA to our
observations we run DEDICA on several sets of simulated fields
containing a cluster with and without subclusters.
We find that: a) DEDICA always identifies both cluster and
subcluster even when the substructure richness ratio cluster-
to-subcluster is rcs= 8, b) DEDICA recovers a large fraction
of members, almost irrespective of the richness of the original
structure (>∼ 70% in most cases), c) structures with richness ra-
tios rcs<∼ 3 are always distinguishable from noise fluctuations of
the poissonian simulated field.
These simulations also allow us to define a threshold that we
use to identify significant structures in the observed fields.
We apply our clustering procedure to the 77 clusters of the
WINGS sample. We cut galaxy catalogs to the absolute magni-
tude threshold MV = −16.0 in order to maximize the signal-to-
noise ratio of the detected subclusters.
We detect at least one significant structure in 55 (71%) clus-
ter fields. We find that 12 clusters (16%) have no structure above
the threshold (undetected). In the remaining 10 (13%) clusters
we find significant structures only at the border of the field of
view. In absence of a detection in the center of the frame, we
consider these border structures unrelated to the target cluster.
We also verify that in the CMD these border structures are redder
10 M. Ramella et al.: Substructures in the WINGS clusters
than expected given the redshift of the target cluster. We consider
also these clusters undetected.
We provide the coordinates of all substructures in the 55
clusters together with their main properties.
Using the CMR of the early-type cluster galaxies we sep-
arate ”true” subclusters from unrelated background structures.
We find that 40 clusters out of 55 (73%) have a total of 69 sub-
structures with 15 clusters left without substructures.
The fraction of clusters with subclusters (73%) we identify is
higher than most previously published values (typically ∼ 30%,
see, e.g., Girardi & Biviano 2002, and references therein). It is
however acknowledged that the fraction of substructured clus-
ters depends, among other factors, on the algorithm used to de-
tect substructures, on the quality and depth of the galaxy catalog
(Kolokotronis et al. 2001; Burgett et al. 2004).
Another important result of our analysis is the distribution of
subcluster luminosities. In the luminosity range where our sub-
structure detection is complete (L ≥ 1011.2 L⊙), we find that the
distribution of subcluster luminosities is in agreement with the
power-law ∝ L−1 predicted for the differential mass function of
substructures in the cosmological simulations of De Lucia et al.
(2004).
Finally, we investigate the relation between BCGs and clus-
ter structures.
We find that, on average, BCG1s are located close to the den-
sity peak of the main structures. In projection on the sky, the bi-
weight average distance of BCG1s from the peak of the main
system is 72±11 kpc. BCG2s are significantly more distant than
BCG1s from the peak of the main system (345 ± 47 kpc).
The fact that BCG1s are close to the center of the system
is consistent with current theoretical view on the formation of
BCGs (Dubinski 1998).
A more surprising result is that the magnitude difference be-
tween BCG1s and BCG2s, ∆M12, is significantly larger in clus-
ters without substructures than in clusters with substructures.
This fact may be interpreted in the framework of the hierarchical
scenario of structure evolution (e.g. De Lucia & Blaizot 2006).
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12 M. Ramella et al.: Substructures in the WINGS clusters
Appendix A: The catalog of substructures
We provide here the catalog of substructures. In Table A.1 we give, for each substructure: (1) the name of the parent cluster; (2) the
classification of the structure as main (M), subcluster (S), or background (B) together with their order number; (3) right ascension
(J2000), and (4) declination (J2000) in decimal degrees of the DEDICA peak; the parameters of the ellipse we obtain from the
variance matrix of the coordinates of galaxies in the substructure, i.e. (5) major axis in arcminutes, (6) ellipticity, and (7) position
angle in degrees; (8) luminosity; (9) χ2S .
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A0085 M 10.4752 -9.3025 2.0 0.23 -17. 0.41536 48.4
A0085 S1 10.4410 -9.4430 1.8 0.35 -39. 0.17649 42.9
A0085 S2 10.3947 -9.3501 2.3 0.40 -72. 0.12337 32.8
A0119 M 14.0625 -1.2630 4.1 0.44 -65. 0.83955 63.4
A0119 S1 14.1183 -1.2106 4.6 0.60 -23. 0.26847 50.8
A0119 S2 14.0267 -1.0441 3.4 0.34 80. 0.03592 32.0
A0119 B1 13.9402 -1.4979 3.1 0.39 46. – 23.5
A0147 M 17.0648 2.2033 3.9 0.45 79. 0.31392 45.2
A0147 S1 16.8673 2.1393 4.1 0.25 -50. 0.05638 24.8
A0147 S2 17.1925 1.9284 4.4 0.38 55. 0.05052 21.4
A0147 B1 17.0753 2.3174 4.4 0.37 75. – 58.0
A0151 M 17.2186 -15.4219 1.7 0.26 -16. 0.47344 39.9
A0151 S1 17.3516 -15.3652 2.1 0.37 -58. 0.13761 42.9
A0151 S2 17.2632 -15.5564 1.6 0.26 -53. 0.19762 40.9
A0151 B1 17.1375 -15.6116 1.5 0.08 -4. – 59.0
A0160 M 18.2344 15.5126 3.6 0.37 82. 0.55525 66.7
A0160 S1 18.2483 15.3138 5.0 0.41 85. 0.03120 38.1
A0160 S2 18.1141 15.7501 3.0 0.16 86. 0.15196 28.3
A0160 S3 17.9981 15.4150 3.9 0.41 0. 0.06315 27.8
A0168 M 18.7755 0.3999 3.1 0.32 -11. 0.24492 30.5
A0168 S1 18.8799 0.2993 2.0 0.33 4. 0.06871 28.6
A0193 M 21.2894 8.6994 2.1 0.08 36. 0.61982 105.7
A0193 B1 20.9945 8.6119 4.9 0.45 -1. – 39.1
A0311 M 32.3793 19.7722 2.3 0.19 43. 0.43320 44.0
A0376 M 41.4276 36.9517 1.7 0.07 -67. 0.13477 40.8
A0376 S1 41.5569 36.9214 4.4 0.49 -22. 0.24350 33.6
A0500 M 69.6476 -22.1308 2.0 0.31 16. 0.41203 45.5
A0500 S1 69.5915 -22.2377 2.3 0.19 36. 0.20520 47.3
A0602 M 118.3638 29.3528 1.8 0.55 -46. 0.20112 55.4
A0602 S1 118.1848 29.4145 2.3 0.52 31. 0.08470 34.8
A0671 M 127.1237 30.4269 1.6 0.24 -51. 0.68582 69.8
A0671 S1 127.2241 30.4342 2.0 0.40 -5. 0.19736 44.3
A0671 S2 127.1617 30.2967 1.9 0.24 -90. 0.13778 43.0
A0754 M 137.1073 -9.6370 2.0 0.25 53. 0.56063 46.8
A0754 S1 137.3707 -9.6760 3.2 0.53 -8. 0.30590 54.9
A0754 S2 137.2619 -9.6367 1.7 0.14 76. 0.23734 51.2
A0957x M 153.4095 -0.9259 2.0 0.09 -83. 0.42106 38.6
A0957x B1 153.5517 -0.7023 2.2 0.44 -63. – 37.9
A0970 M 154.3595 -10.6921 1.5 0.27 -30. 0.46130 62.5
A0970 S1 154.2369 -10.6422 1.7 0.15 15. 0.13660 42.3
A0970 B1 154.1833 -10.6771 1.8 0.23 -76. – 32.2
A1069 M 159.9418 -8.6883 2.8 0.31 52. 0.37270 50.2
A1069 S1 159.9286 -8.5506 2.4 0.23 88. 0.18532 32.7
A1069 B1 159.7678 -8.9262 3.5 0.55 77. – 54.7
A1291 M 173.0467 56.0255 2.5 0.51 -11. 0.25272 32.1
A1291 S1 172.9090 56.1872 1.4 0.48 -82. 0.03530 37.6
A1631a M 193.2410 -15.3413 1.4 0.35 40. 0.20077 33.9
A1736 M 202.0097 -27.3131 3.1 0.35 58. 0.41824 52.1
A1736 S1 201.7305 -27.0170 2.8 0.32 9. 0.24023 42.6
A1736 S2 201.7662 -27.4067 3.4 0.28 7. 0.14528 42.3
A1736 S3 201.5672 -27.4291 2.7 0.44 73. 0.16926 40.4
A1736 S4 201.9057 -27.1600 3.5 0.21 -1. 0.24192 32.9
A1736 S5 201.7036 -27.1236 3.0 0.39 -12. 0.40395 31.7
A1795 M 207.1911 26.5586 0.6 0.17 55. 0.12341 52.4
M. Ramella et al.: Substructures in the WINGS clusters 13
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A1795 S1 207.2329 26.7362 1.3 0.38 82. 0.05123 46.7
A1831 M 209.8120 27.9714 1.9 0.43 9. 1.08418 56.0
A1831 S1 209.7356 28.0636 2.1 0.34 41. 0.36295 59.7
A1831 B1 209.5725 28.0206 1.7 0.25 -10. – 47.7
A1991 M 223.6405 18.6390 2.3 0.54 -78. 0.28195 40.3
A1991 S1 223.7575 18.7812 2.5 0.32 41. 0.11412 49.9
A1991 B1 223.7683 18.7022 1.7 0.31 71. – 36.6
A2107 M 234.9497 21.8075 2.7 0.19 48. 0.50994 61.1
A2107 B1 235.0699 22.0127 4.3 0.48 83. – 32.9
A2107 B2 235.1409 21.8276 2.4 0.10 55. – 20.4
A2124 M 236.2400 36.0990 1.3 0.24 32. 0.41727 43.3
A2124 B1 236.0207 36.1779 1.6 0.22 34. – 59.7
A2149 M 240.3723 53.9406 1.5 0.46 -10. 0.37347 48.7
A2169 M 243.4867 49.1875 0.6 0.22 72. 0.15358 34.2
A2256 M 255.9260 78.6412 1.9 0.29 -86. 1.46563 95.6
A2256 B1 256.3094 78.4886 2.2 0.48 75. – 48.2
A2256 B2 256.6024 78.4283 2.0 0.12 -88. – 46.8
A2399 M 329.3693 -7.7772 3.5 0.64 -26. 0.40505 38.8
A2415 M 331.3829 -5.5444 2.3 0.23 -60. 0.36780 44.8
A2415 S1 331.5610 -5.3960 2.3 0.33 52. 0.05032 33.9
A2415 B1 331.3800 -5.4017 1.9 0.34 32. – 41.4
A2415 B2 331.3295 -5.3890 1.6 0.41 4. – 37.3
A2457 M 338.9462 1.4765 4.3 0.50 -84. 0.88720 107.3
A2457 S1 339.0392 1.6459 4.1 0.65 -50. 0.05960 23.1
A2457 B1 339.0667 1.3266 5.6 0.53 77. – 73.8
A2572a M 349.3192 18.7197 2.9 0.39 23. 0.44749 47.8
A2572a S1 349.1122 18.5320 4.1 0.25 8. 0.07320 34.5
A2572a S2 349.3851 18.5395 2.6 0.31 67. 0.05345 25.1
A2572a S3 349.0037 18.7220 3.2 0.34 86. 0.00884 20.5
A2593 M 351.0766 14.6539 1.1 0.25 58. 0.28333 33.8
A2593 S1 351.0677 14.4048 2.2 0.42 80. 0.09810 27.0
A2622 M 353.7384 27.3856 3.1 0.09 76. 0.48920 68.1
A2622 S1 353.4880 27.2877 4.2 0.35 46. 0.03070 35.1
A2622 B1 353.7837 27.3182 3.0 0.49 -5. – 53.7
A2622 B2 353.8009 27.6217 2.6 0.38 68. – 29.9
A2657 M 356.1725 9.1818 4.5 0.47 22. 0.27061 49.6
A2657 S1 356.2755 9.1799 3.2 0.35 10. 0.20771 34.0
A2657 B1 355.9569 8.9422 2.8 0.06 -10. – 38.6
A2665 M 357.7050 6.1582 3.6 0.26 71. 0.67950 121.8
A2665 S1 357.4003 5.8659 4.9 0.64 84. 0.01780 17.5
A2665 B1 357.8218 6.3522 3.5 0.44 -50. – 32.7
A2734 M 2.8363 -28.8652 3.4 0.33 3. 0.48700 56.3
A2734 S1 2.6950 -28.7728 4.0 0.27 -7. 0.18970 55.0
A2734 S2 2.6987 -29.0394 3.2 0.24 55. 0.03030 43.3
A2734 S3 2.5727 -29.0562 3.4 0.51 84. 0.03100 33.1
A2734 B1 2.7701 -28.6488 3.7 0.39 14. – 28.0
A3128 M 52.4825 -52.5764 2.2 0.17 -36. 0.40452 37.2
A3128 S1 52.7366 -52.7089 4.1 0.44 -9. 0.25240 51.8
A3128 S2 52.6655 -52.4413 2.3 0.32 -65. 0.19646 51.0
A3128 S3 52.3697 -52.7570 3.2 0.47 81. 0.17169 39.0
A3158 M 55.7477 -53.6334 2.6 0.62 2. 0.70205 52.8
A3158 S1 55.8382 -53.6780 3.4 0.58 10. 0.45553 53.4
A3266 M 67.7893 -61.4637 1.1 0.27 -72. 0.42993 63.5
A3376 M 90.1628 -39.9950 2.5 0.14 -43. 0.33708 43.1
A3376 S1 90.4344 -39.9776 2.7 0.20 -4. 0.21279 59.8
A3376 S2 90.4712 -39.7946 2.1 0.39 -88. 0.00904 31.2
A3528b M 193.5928 -29.0136 1.3 0.04 -24. 0.65638 66.4
A3528b S1 193.6030 -29.0721 1.3 0.26 10. 0.16706 59.0
A3530 M 193.9098 -30.3606 1.9 0.26 33. 0.53043 34.9
A3532 M 194.3035 -30.3732 3.6 0.52 -44. 0.76920 51.1
A3532 B1 194.0413 -30.2130 3.8 0.38 66. – 56.3
14 M. Ramella et al.: Substructures in the WINGS clusters
ID class αJ2000 δJ2000 a e PA L χ
(deg) (deg) (arcmin) (deg) (1012 L⊙)
A3558 M 201.9587 -31.4892 4.9 0.54 49. 1.14860 64.1
A3558 B1 202.2501 -31.6887 2.6 0.49 44. – 37.6
A3562 M 203.4603 -31.6812 2.5 0.18 82. 0.39087 42.4
A3562 S1 203.1622 -31.7742 4.0 0.40 -86. 0.15010 51.1
A3562 S2 203.3137 -31.6953 3.6 0.40 76. 0.11706 41.0
A3562 S3 203.6982 -31.7171 2.5 0.21 -50. 0.07820 36.7
A3562 S4 203.6541 -31.5969 4.0 0.55 -81. 0.06542 30.3
A3667 M 303.1637 -56.8598 2.1 0.14 23. 0.56803 42.0
A3667 S1 303.5297 -56.9660 3.0 0.39 -86. 0.27086 39.2
A3667 S2 302.7241 -56.6674 1.5 0.17 75. 0.28948 34.0
A3667 S3 302.7081 -56.7557 2.3 0.39 12. 0.09961 33.7
A3716 M 312.9910 -52.7677 4.7 0.38 36. 0.76450 77.9
A3716 S1 312.9769 -52.6434 3.5 0.22 -6. 0.49159 56.9
A3716 B1 312.7735 -52.8976 4.1 0.40 28. – 48.4
A3716 B2 313.1888 -52.4785 3.2 0.23 21. – 22.6
A3880 M 336.9796 -30.5474 3.8 0.33 -50. 0.25840 44.1
A3880 B1 336.8684 -30.8171 2.5 0.30 64. – 30.9
A3880 B2 336.7356 -30.7839 2.7 0.35 46. – 28.4
IIZW108 M 318.4443 2.5706 2.6 0.38 42. 0.49940 33.4
IIZW108 S1 318.6247 2.5533 3.2 0.36 -14. 0.08565 42.3
IIZW108 B1 318.3335 2.7751 1.6 0.24 43. – 44.5
IIZW108 B2 318.5190 2.8039 2.5 0.44 22. – 33.6
MKW3s M 230.3916 7.7281 2.3 0.30 -8. 0.37614 48.7
MKW3s S1 230.4576 7.8769 3.3 0.46 -22. 0.04585 39.3
MKW3s B1 230.7349 7.8882 2.0 0.40 16. – 25.5
RX0058 M 14.5875 26.8816 2.4 0.22 -31. 0.31967 44.2
RX0058 S1 14.7652 27.0424 3.8 0.60 64. 0.31661 50.6
RX0058 B1 14.4012 26.7041 3.3 0.08 -12. – 28.9
RX1740 M 265.1398 35.6416 2.8 0.21 -26. 0.17896 42.1
RX1740 S1 265.2600 35.4366 3.3 0.22 38. 0.01946 31.7
RX1740 S2 264.8688 35.6053 3.7 0.52 28. 0.01340 27.9
RX1740 S3 265.0744 35.8116 3.5 0.44 -7. 0.01166 21.8
Z2844 M 150.7281 32.6483 2.9 0.20 -85. 0.10143 48.3
Z2844 S1 150.6524 32.7621 5.2 0.58 63. 0.04930 50.5
Z2844 S2 150.5821 32.8890 2.6 0.39 0. 0.00395 23.1
Z8338 M 272.7447 49.9078 3.0 0.37 -67. 0.45876 43.1
Z8338 S1 272.8606 49.7916 3.2 0.11 62. 0.05549 31.9
Z8338 S2 272.6903 49.9737 3.1 0.67 62. 0.07089 25.7
Z8338 B1 272.4479 49.6815 1.7 0.18 9. – 25.8
Z8852 M 347.6024 7.5824 2.7 0.41 -45. 0.76110 67.9
Z8852 S1 347.5926 7.3999 5.8 0.56 62. 0.12022 32.4
Z8852 S2 347.6986 7.8018 2.3 0.13 81. 0.02493 25.5
Z8852 B1 347.7381 7.6808 2.1 0.25 -73. – 35.9
Z8852 B2 347.4951 7.8165 2.4 0.21 72. – 27.0
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 1
Online Material
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 2
Fig. 6. Isodensity contours (logarithmically spaced) of the 55 clusters with significant structures. The title lists the coordinates of
the center. The orientation is East to the left, North to the top. Galaxies belonging to the systems detected by DEDICA are shown as
dots of different colors. Black, light green, blue, red, magenta, dark green are for the main system and the subsequent substructures
ordered as in Table A.1. Large symbols are for galaxies with MV ≤ −17.0 that lie where local densities are higher than the median
local density of the structure the galaxy belongs to. Open symbols mark the positions of the first- and second-ranked cluster galaxies,
BCG1 and BCG2 respectively.
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 3
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 4
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 5
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 6
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 7
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 8
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 9
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 10
Fig. 6. (continued)
M. Ramella et al.: Substructures in the WINGS clusters, Online Material p 11
Fig. 6. (continued)
	Introduction
	The Data
	The DEDICA Procedure
	The probability density
	Cluster Identification
	Cluster Significance and of Membership Probability
	Tweaking the Algorithm with Simulations
	Substructure detection in WINGS clusters
	The Catalog of Substructures
	Properties of substructures
	Brightest Cluster Galaxies
	Summary
	The catalog of substructures
