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Some properties of galaxy clusters. Piotr Flin. Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko. The organisation of the talk. Observational data Numerical simulation PF catalogue of structure Shape of structures e-z relation

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Some properties of galaxy clusters

Piotr Flin

Monika Biernacka

Włodzimierz Godłowski

Teresa Juszczyk

Paulina Piwowarska

Elena Panko

the organisation of the talk
The organisation of the talk
  • Observational data
  • Numerical simulation
  • PF catalogue of structure
  • Shape of structures
  • e-z relation
  • Binggeli effect
  • richness vs alignment
  • Tully’s group alignment
  • Conclusions
large scale distribution of matter in the universe cosmic web
Large scale distribution of matter in the Universe(cosmic web)

long structures ( filaments)

flat structures (sheets, walls)

dense, compact regions (galaxy clusters ) surrounded by depopulated regions (voids)

observational data
Observational data
  • The Muenster Red Sky Survey is a large-sky galaxy catalogue covering an area of about 5000 square degrees on the southern hemisphere. The catalogue includes 5.5 millions galaxies and is complete till photo-graphic magnitude rF=18m.3 (Ungruhe 2003).
  • 217 ESO Southern Sky Atlas R Schmidt plates with galactic latitudes b<-45 were digitized with the two PDS microdensitometers of the Astronomisches Institut at Muenster. The classification of objects into stars, galaxies and perturbed objects was done with an automatic procedure with a posterior visual check of the automatic classification. The external calibration of the photographic magnitudes was carried out by means of CCD sequences obtained with three telescopes in Chile and South Africa. The MRSS contains positions, red magnitudes, radii, ellipticities and position angles of about 5.5 million galaxies and it is complete down to rF=18m.3.

Distribution of galaxies of Muenster Red Sky Survey. Blue color indicates low galaxy densities, green and yellow high galaxy densities. White spot is the region around the SMC.

structure finding
Structure finding
  • We selected the Voronoi tessellation technique (VTT hereafter)for cluster detection.
  • This technique is completely non-parametric, and therefore

sensitive to both symmetric and elongated clusters, allowingcorrect studies of non-spherically symmetric structures. For adistribution of seeds, the VTT creates polygonal cellscontainingone seed each and enclosing the whole area closest to the seed.This is the definition of a Voronoi cell in 2D.


Voronoi cells for PF 2243-4774 region (left panel) and the found cluster members as black dots with non-clustered galaxies as open symbols (right panel).

PJF 2009, AJ 138, 1709

structure ellipticity determination
Structure ellipticity determination

Using standard covariance ellipse method for galaxies in the considered region within the magnitude limit m3, m3+3m, we determined the moments of the distribution:

The semiaxes in arcsec for the best-fitting ellipse were calculated from:

Position angle:



Structures PF 0364-3272 and PF 2243-4774 in tangential coordinates, north is up. Open dots represented the structure members, black symbols corresponded to brightest galaxy in cluster, and line notes the direction of fitted ellipse major axe. Ellipticity and major axis position angle are shown in the right corner for each structure.

PJF 2009, AJ 138, 1709




for input data







ACO (0.5r)









ACO (0.3r)









APM (0.5r)









ACO (m10<19m.3)








Table 1. The result of the statistical analysis of m10 - z relation

BFJP, 2009, ApJ 696, 1689


The distribution of estimated z and the limits of the division into groups

BFJP 2009, ApJ 696, 1689


The frequency distributions of structure ellipticities in four classes with

richness identified in the upper right portion of each section

(left panel all data, right panel 457 structures with m3+3m18m.3).

PJBF 2009, ApJ 700, 1686


The frequency distribution of structure redshifts for samples containing different number of galaxies in the structure (left panel all data, right panel 457 points)

PJBF 2009, ApJ 700, 1686


The dependence of group richness on redshift z.(left panel all data, right 457points)

PJBF 2009, ApJ 700, 1686


The ellipticity-redshift relation for galaxy group samples,with the galaxy populations of each structure noted in the upper right hand corners. The fitted linear relationstogether with their = 0.95 confidence intervals are also plotted.

PJBF 2009, ApJ 700, 1686


The cluster ellipticity e (left panel) and cluster ellipticity evolution rate de/dz (right panel) versus redshift for four samples of different richness. Error bars correspond to  = 0.95 confidence intervals. (upper panel all data, lower 457 points)

PJBF 2009, ApJ 700, 1686


The distribution of structure ellipticity is identical for structures with N>50 members

  • Less populated structures are more elongated than rich ones. 
  • The small groups are forming on the filament and later on, due to hierarchical clustering, greater, more spherical structures are formed. The additional argument for this picture: the mean group redshift is greater than clusters.
  • The elipticity – redshift realtion depends on the structure richness. The difference between ellipticity and evolution rate de/dz for small groups are at the 3level different from rich ones.
  • Only groups with 10-30 member galaxies exhibit the strong e-z correlation.
  • Numerical simulations show that in ΛCDM for z <3.0 ellipticity increases with z, as well as the structure mass. We support the first point, but our redshits are small. In simulations: very massive structures were considered (21013h-1 Msun ).

The frequency distribution of position angles for the two brightest galaxies PA1 and PA2 in the structure and structure position angle PAs. Dotted lines refer to an isotropic distribution, and a 1 error bar is also shown.

PJF 2009, AJ 138, 1709


The frequency distribution of the angle θ1 between the brightest galaxy and parent cluster for groups of BM type I and I-II. Dotted lines show the isotropic distribution, together with a 1 error bar.

PJF 2009, AJ 138, 1709


The lack of galaxy orientation is in agreement with CDM

The physical processes in the filament:


(anisotropic merging of structures + infall of matter) orientation of galaxies


(tidal torque) lack of orientation

Our result: lack of orientation

Angular momenta of galaxies are due to tidal interaction of neighbours in the early Universe. The flow of matter along the filament causes the co-linearity of the brightest galaxy with the structure great semi-axis.


The orientation of galaxies in clusters

  • rich clusters having at least 100 members each. The relation between
  • parameters describing galaxy orientation (position angle p, the angles: δDand η)
  • and value of statistics, used for anisotropy calculation

Value of statistics increase with the amount of the galaxy members, which is equivalent tothe existance of a relation between anisotropy and the number of galaxies in a cluster.

GPPF 2010, ApJ 723. 985


Local Supercluster

Investigation of Tully’s group (NGC) alignment



GF ApJ 708,.920 (2010)


Position angles:

Pag group position angle

Pabm PA of the brightest galaxy

Pal PA of the line joining two brightest galaxies in group

Pav Virgo PA (direction toward Virgo )

The distribution of the four PA were checked as well the differences between:

Pag – Pav

Pal – PaV

Pag – Pal

Pabm – Pag

Pabm – Pal

Pabm – Pav


Angle difference

GF ApJ 708,.920 (2010)


Binggeli effect

for Tully’s group

GF ApJ 708,.920 (2010)



Two brightest galaxies are formed on the filament

directed toward LSC centre.

The gravitational interaction of groups originates on the line joining these two brightest galaxies.

Therfore we observed the alignment of the structure position angle and line joining two brightest galaxies

  • The distribution of structure ellipticities depends on the structure richness. Richer are more spherical.
  • The e – z dependence shows that in the past the interactions were stronger.
  • The distribution of the position angles of the 10 brightest galaxies are random ones.
  • The differences between structure position angle and brightest galaxies are random.
  • Only in the case of cD galaxies the alignment is observed; the special evolution of such clusters.
  • Structures are formed on the filament
  • Richer groups exhibit bigger alignment
struktury pf
Struktury PF

6068 struktur

przedział jasności: m3 – m3+3m

contingency table
Contingency table

0.05=1, 358 0.01=1.627

pa distribution
PA Distribution

The division of ACO clusters corresponding to PF structures according to structure

richness and B-M morphological types


In order to check the distribution of galaxy orientation angles (, ) and position angles p, we tested whether the respective distribution of the ,  or p angles is isotropic. Below, a short summary is presented of the tests

considered here (not always explicitly): the 2-test, the Fourier test and the auto-correlation test.

In all of these tests, the entire range of the  angle (where for  one can put +/2,  or p respectively)

is divided into n bins, which in the 2 test gives n-1degrees of freedom. During the analysis, we used n = 18 bins of equal width.

Let N denote the total number of galaxies in the considered cluster, and Nk - the number of galaxies with orientations within the k-th angular bin. Moreover, N0 - denotes the average number of galaxies per

bin and, finally, N0,k - the expected number of galaxies in the k-th bin. The 2-test of the distribution yields the critical value 27.6 (at the siginificance level  =0.05) for 17 degrees of freedom:

However, when we consider individual clusters the number of galaxies involved may be small in some cases, and the 2 test will not necessarily work well (e.g. the 2 test requires the expected number of data per bin to equal at least 7.As a check, in a few cases we repeated the derivations for different values of n, but no significant differences appeared. However, the main statistical test used in the present paper is the Fourier test. In the Fourier test the actual distribution Nk is approximated as:

(we take into account only the first Fourier mode).


We obtain the following expression for thecoefficients ij (i,j = 1, 2):

with the standard deviation

where N0 is the average of all N0,k. However, we should note that we could formally replace the symbol  with = only in the cases where all N0,k are equal (for example, in the cases when we tested the isotropy of the distribution of the position angle).


The probability that the amplitude:

is greater than a certain chosen value is given by the formula:

while the standard deviation of this amplitude is

From the value of 11 one can deduce the direction of the departure from isotropy. If 11 < 0, then, for

2, an excess of galaxies with rotation axes parallel to the LSC plane is present. For 11 > 0 the rotation axes tend to be perpendicular to the LSC plane.

Similarly, while analysing the distribution of the position angles of galaxies (p), if 11 < 0, an excess of galaxies with position angles parallel to the plane of the coordinate system (i.e. normal to the galaxy plane is perpendicular to the plane of the coordinate system) is present. For 11 > 0, the position angles of galaxy are perpendicular to the plane of the coordinate system.


The auto-correlation test quantifies the correlations between the galactic numbers in adjoining angular bins. The correlation function is defined as:

In the case of an isotropic distribution we expected C = 0 with the standard deviation:


Statistical analysis indicates that structures containing more than 50 member galaxies appear to originate from the same parent population, in other words their structure ellipticity distributions are essentially identical. In agreement with earlier works (Struble & Ftaclas 1994, Plionis et al. 2004), it is found that the more poorly populated structures are more elongated than richly populated ones. It is suggested that such a result may reflect variations in the initial conditions during structure formation (Biernacka et al. 2008). Small elongated groups appear to have formed along pre-existing filaments, and later become more spherical in shape as a result of hierarchical clustering. Such a conclusion is supported by the discovery that, in the sample of 6188 structures investigated here, the mean redshifts for galaxy groups are larger than the mean redshifts for richer clusters.

The e-z relation depends upon richness as well, with the dependence being similar to the rate of evolution of ellipticity de/dz as a function of redshift z. For poorly populated groups both the ellipticity and the ellipticity evolution rate de/dz differ at a 3 level from results found for other, more richly populated, samples. A redshift of z = 0.12 appears to divide the two samples. The sample containing galaxy aggregations containing between 10 and 30 members displays a significant correlation with redshift, while the three remaining samples for richer groups exhibit either a weak correlation or an anti-correlation.

Recently, Plionis et al. (2009) investigated a sample of 150 ACO clusters with z < 0.14 containing at least 20 members. Their sample does not contain merging and interacting clusters, or clusters with dynamical substructures. They found that the direction of evolution is different for clusters of different richness. While their values of de/dz differ from the present results, the directions of the trends are identical. The differences that do exist can be attributed to the analysis of totally different samples, with different richness classes for the subsamples and different redshift limits.

It has proven to be difficult to compare the present results with numerical simulations. A very extensive numerical study (Hopkins et al. 2005) in the framework of CDM cosmology examines cluster ellipticities to redshift z =3. The present study investigates low- edshift clusters, making a simple comparison impossible. The numerical simulations indicate that cluster mean ellipticity should increase with redshift as well as cluster mass. The present results agree with the first prediction, but conflict with the second. As pointed out above, however, the redshift coverage of our galaxy samples is very small in comparison with that of existing numerical simulations, and the simulations considered cluster masses of clusters greater than 21013h-1M, which corresponds only to the richest of our samples.


The absence of alignment for brighter cluster galaxies is consistent with the CDM scenario of galaxy formation. There are two different, but not exclusive, points of view about the physical processes in filaments. One stresses the importance of anisotropic merging, the other tidal interaction (see e.g. Lee & Evrard 2007). In the naive prediction one can expect that the anisotropic merging and infall of matter along filaments will result in galaxies oriented non-randomly, while the action of tidal torques will produce a random orientation of galaxies. Our result supports the idea that galaxies formed in long filamentary structures. The lack of alignment of brighter galaxies points toward a process in which galaxies acquire angular momentum from tides exerted by their neighbours in the early Universe. On the other hand, the flow of matter along filaments causes the alignment of BCM galaxies with cluster long axes.


From the presented analysis of the orientation of galaxy groups in the Local Supercluster the

following picture of the structure formation appears. The two brightest

galaxies were formed first. They originated in the filamentary structure

directed towards the centre of the protocluster. This is the place where

the Virgo cluster centre is located now.

Due to gravitational clustering, the groups are formed in such a manner

that galaxies follow the line determined by the two brightest objects.

Therefore, the alignment of structure position angle and line joining two

brightest galaxies is observed. The other groups are forming on the

same or nearby filament. The flatness of the LSC additionally contributes

to the observed alignment of galaxy groups. The majority of the groups lie

close to us. Due to completeness of the Catalog, the lack of groups

further than the Virgo Cluster centre is observed, but nearby groups are

very well selected and they contain only more massive galaxies.

This picture is in agreement with predictions of several CDM models,

in which structure formation is due to hierarchical clustering. Moreover, the

formation is occurring on the filamentary structure.



  • Pancake (naleśnik)
  • Hierarchiczne grupowanie się (momenty skręcające)

Iye & Sugai, 1991ApJ 374, 12





























































The division of ACO clusters

corresponding to

PF structures according

to structure richness

and B-M morphological types.

PJF 2009, AJ 138, 1709