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ON THE ORIGIN OF LARGE SCALE STRUCTURES. Piotr Flin. Włodzimierz Godłowski Elena Panko. Instytut Fizyki, Uniwersytet Jana Kochanowskiego, Kielce, Polska Instytut Fizyki, Uniwersytet Opolski, Opole, Polska Kalinenkov Astronomical Observatory, Nikolaev, Ukraine. Outlook.

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Piotr Flin

Włodzimierz Godłowski

Elena Panko

Instytut Fizyki, Uniwersytet Jana Kochanowskiego, Kielce, Polska

Instytut Fizyki, Uniwersytet Opolski, Opole, Polska

Kalinenkov Astronomical Observatory, Nikolaev, Ukraine


  • A fewhistoricalremarks

  • Observations

  • Numericalsimulations

  • Applied observational data:

  • Twosets:

    • LSC: Tully’s group w LSC

    • Strukturescatalogue PF

  • Structureshape

  • Superclusters

  • Binggelieffect

    • PF structures

    • NBG groups

  • 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)


GF ApJ 70,.920 (2010)

Considered model




    Temperature of matter and radiations ~3*103 K:primivalplasmarecombination

    freeelectronsdisappeared, drasticreduction of theradiation and matterinteractions,

  • Independent evolution of radiation and matter.

  • TheUniversebecames transparent

Kind of matter:

Barionic non barionic, what is the distribution of both ?

HOT : lekkie ( ~100 eV) i relatywistyczne aż do rekombinacji cząstki ( neutrino)

WARM (1 – 10 keV) stają się nie- relatywistyczne wcześniej

COLD ciężkie cząstki, która bardzo wcześnie przestają byćrelatywistyczne

Mają bardzo małe prędkości

Gravitinos, photinos, axions (WIMP)

Parameters conected with density perturbations

  • Type of perturbation

  • Amplitude

  • Skale of perturbation(MASS orthescalelenght





    Varioussceneriosstructureoriginpredictsdiferentproerties of structures:

    mainlyshape and theacquitance of angularmomenta of galaxies.

    modele : top – down, bottom – up


Wiele małych eksplozji równocześnie

25 – 50 Mpc

1065 erg


Nadprzewodzące struny kosmiczne

Młode galaktyki, kwazary

do 5 Mpc

1061 erg

  • Turbulences

  • Pancake

  • Hierarchicalclustering (tidaltorquing)

Iye & Sugai, 1991ApJ 374, 12

Observational data

  • FromTully’sCatalogue:

  • 61 galaxygroups

    • 26 groupswith10 - 20 objects

    • 35 >20 objects

  • Positionangle of the group PAg

  • Positionangle of thelinejoining 2 brightestgalaxiesPAl

  • Positionangleof the BCM PAbm

  • DirectiontowardVigo ClustercentrePAV

  • Isotropytested(K-S, c2 )

The distribution of the acuteangle Θ between the position angle of the major axis of a given group (PAg) and direction towards other groups. From top to bottom the distributions for galaxies with D  10 Mpc, 10<D20 Mpc, 10<D20 Mpc and D>20 Mpc are presentedrespectively.

The distribution (from top to bottom) of the differences between position angles (PAg-PAV, PAl-PAV, PAg-PAl).

The distribution (from top to bottom) of the position angle of the major axis of a given group (PAg), the position of the line joining two brightest galaxies in the group (PAl) and direction towards Virgo cluster (PAV).

Twobrightestoriginated on thefilamentdirectedtowardthecentre of of LSC.

Throughthegravitationalinteractiongalaxygroupsareformed on thelineconectedthesetwobrightestgalaxies.

Therefore we observedaligment of structure and lineconnectingtwobrightes

Thisispictureshowingtheorigininthecase of not verymassivesytucture, as LSC. Itisinteresting to lookingreaterscale and in 2D.

Thereare not statisticallycomplete data for such a task. Therefore, we decided to checktheobservedtendency.

We will usethe PF Catalogue .

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 color indicates low galaxy densities, green and yellow high galaxy densities. White spot is the region around the SMC.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 aVoronoi cell in 2D.

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. Ellipticityand major axis position angle are shown in the right corner for each structure.

PJF 2009, AJ 138, 1709

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:



Voronoi considered region within the 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

Struktury pf
Struktury PF considered region within the

6188 struktur

przedział jasności: m3 – m3+3m

PF JAD 2,1 (2006 considered region within the )

Results considered region within the :

veryrichsuperclusters : Superclusters n=8 n>4

Angle P random 0.647 0.750 0.524

Angle deltad: anisotropy 0.150 0.250 0.238 0.250

Angle etah: anisotropy 0.227 0.3000 0.190 0.300

In veryrichclustersanlignmentshould be thegreatest, iforientationioriginatedsimultulanouslywithprotostrcutures..

Anisotropyisincreasingwithstructuresize ( mass).

Theincrease of anizotropii withrichness was observedinthecase of rich ( n>100) structures PF. Herethe same patternisconfirmed.utaj jest potwierdzony.

Conclusions considered region within the :

Galaxygroupsformed first, nexttheymergedue to hierarchicalclustering and formedgreaterstructures.

Theprotomainplane of theprotostructureforms, whichattractsothergroups. Thereforestructuresareflat.

Thistendencyisobservedinthecase of 1D i 2D structur.es Of course, thisispreliminaryresults, whichshould be confirm on much bettterstatisticalsample.

Thank considered region within the you for yourattention

Orientation of the galaxy groups in the local supercluster

Orientation of the galaxy groups in the Local considered region within the Supercluster

Piotr Flin, Włodzimierz Godłowski

Institute of Physics, Jan Kochanowski University, Kielce, Poland

Institute of Physics, Opole University, Opole, Poland

Recent dynamical evolution
Recent dynamical evolution considered region within the

Plionis (2002)

6068 struktur pf
6068 struktur PF considered region within the

The distribution of estimated considered region within the z and the limits of the division into groups

BFJP 2009, ApJ 696, 1689

BFJP 2009, ApJ 696, 1689 considered region within the

BFJP 2009, ApJ 696, 1689 considered region within the

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 four classes with

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. four classes with

(left panel all data, right 457 points)

PJBF 2009, ApJ 700, 1686

The ellipticity-redshift relation for galaxy group samples, four classes with

with the galaxy populations of each structure noted in

the upper right hand corners. The fitted linear relations

together 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

Rozkład eliptyczności dla struktur z N>50 jest identyczny ellipticity evolution rate de/dz ( right panel) versus redshift for four samples of different richness. Error bars correspond to

Mniej spopulowane struktury są bardziej wyciągnięte niż bogate

Małe grupy powstają na filamencie i następnie drogą hierarchicznego grupowania się powstają duże struktury, bardziej sferyczne. Dodatkowy argumentza tym obrazem (średni redshift dla grup jest większy niż dla gromad)

Relacja e-z zależy też od liczebności struktury. Eliptyczność małych grup i tempo ewolucji de/dz różnią się na poziomie 3od tychże dla bogatych struktur

Tylko struktury mające 10-30 członków wykazują silną korelację e –z..

Numeryczne symulacje w ΛCDM dla z <3.0 wskazują, ze eliptyczność rośnie z przesunięciem ku czerwieni, jak też masą gromady. Potwierdzamy pierwszą tendencję, ale bardzo różne z, drugiej nie, ale w symulacjach bardzo masywne gromady21013h-1 Msłońca .

Type ellipticity evolution rate de/dz ( right panel) versus redshift for four samples of different richness. Error bars correspond to



























































The division of ACO clusters

corresponding to

PF structures according

to structure richness

and B-M morphological types.

PJF 2009, AJ 138, 1709

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 θ brightest galaxies PA1 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

Brak orientacji galaktyk w gromadach jest zgodny z CDM brightest galaxies PA

Procesy fizyczne w filamencie:


Anizotropowe zlewanie się struktur (anisotropic merging + infall of matter)

orientacja galaktyk

Oddziaływanie przypływowe ( tidal torque) brak orientacji

Nasz wynik: brak orientacji

Galaktyki uzyskują moment pędu przez oddziaływanie przypływowe sąsiadów we wczesnym wszechświecie. Przepływ materii wzdłuż filamentu powoduje współliniowość najjaśniejszej galaktyki z dużą półosią gromady.

Efekt binggeli ego
Efekt Binggeli’ego brightest galaxies PA

Badanie Lokalnej Supergromady brightest galaxies PA

Kąty pozycyjne : brightest galaxies PA

Pag kat pozycyjny grupy

Pabm kat pozycyjny najjaśniejszej galaktyki

Pal kat pozycyjny linii łączącej dwie najjaśniejsze

galaktyki w grupie najjaśniej

Pav kat pozycyjny na Virgo (kierunek na Virgo )

badano izotropię rozkładów tych 4 kątów

Różnice kątów :

Pag – Pav

Pal – PaV

Pag – Pal

Pabm – Pag

Pabm – Pal

Pabm – Pav

GF ApJ 70,.920 (2010) brightest galaxies PA

Różnice kątów brightest galaxies PA

GF ApJ 70,.920 (2010)

GF ApJ 70,.920 (2010)

Efekt Binggeli’ego dla grup brightest galaxies PA

GF ApJ 70,.920 (2010)

GF ApJ 70,.920 (2010)

Dwie najjaśniejsze galaktyki powstają na filamencie skierowanym do centrum LSC.

Poprzez oddziaływanie grawitacyjne grupy galaktyk powstają wzdłuż tej linii łączącejdwie najjaśniejsze galaktyki.

Dlatego obserwuje się współosiowość kąta pozycyjnego struktury i linii łączącej dwie najjaśniejsze galaktyki.

Dziękuję za uwagę skierowanym do centrum LSC.

Contingency table
Contingency table skierowanym do centrum LSC.

0.05=1, 358 0.01=1.627

Pa distribution
PA Distribution skierowanym do centrum LSC.

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 the angles (coefficients 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: angles (

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:

between the galactic numbers in adjoining angular bins. The correlation function is defined as:2

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.

Wyobraźmy sobie sferę zawierającą masę całkowitą M w epoce rekombinacji (wszechświat jest bardzo jednorodny wtedy) .

Niech < M/M> jest fluktuacją gęstości która wystąpiła wtedy w sferze poruszającej się losowo we wszechświecie. Wielkość < M/M> jest miarą niejednorodności Wszechświata.

 Związek < M/M> z M zwana jest widmem fluktuacji gęstości (density fluctuation spectrum (DFS)). Jest to zależność fundamentalna . Matematyczny kształt tej funkcji opisuje wzrost struktur powstałych drogą grawitacji. Ponieważ po rekombinacji małe fluktuacje rosną liniowo jak (1 + z) -1, kształt DFS w momencie rekombinacji jest zachowany aż do momentu, gdy pierwsze z fluktuacji stają się nieliniowe.

Gęstość wszechświata  zmienia się od miejsca do miejsca, a średnia gęstość to <>.

Aby powstała struktura nadwyżka gęstości w danym miejscu opisana jako

 / <> musi być wystarczająco większa od zera.

NIESTABILNOŚĆ GRAWITACYJNA w epoce rekombinacji (wszechświat jest bardzo jednorodny wtedy) .

 Z tego warunku uzyskuje się dane o parametrach takich jak masa i amplituda.

Są one dane prze index  i współczynniki normalizacji K i M0 widma mas. 

 / <> =k (M/M0)+

Index  jest związany ze wskaźnikiem widma mocy n zdefiniowanym przez (  / <>) 2 ~ l+n poprzez zależność:

 = - ½ + n/6

 Jeżeli jest funkcją czasu to widmo mas też.

 Wydaje się, że  = - 2/3 wtedy perturbacje mają stałą krzywiznę kiedy docierają do horyzontu (n= -1). (Promień wszechświata jest ~ct). Gdy t=1 rok masa wewnątrz

109 – 1011 MO .



Katalog struktur PF 6188 struktur , każda więcej niż 10 0 obiektów

W oparciu o ten katalog utworzono katalog supergromad. Wiadmo, że supergromady są płąskie. Nasze badania to potwierdziły.

Dlatego też porównanie w przypadku 2D robiono na supergromadach.

Niestety nie jest to statystycznie ełna próbka, więc posłuzyła do badań wstępnych.

Mamy 57 supergromad, z k tórych każda zawiera przynajmniej 4 struktury PF.

Dla 257 bardzo bogatych gromad PF ( n>100) znamy rozkład kątów pozycyjnych oraz orietację osi rotacji.

Sprawdzono, jak wygląda rozkład oso rotacji i kątów pozycyjnych bardzo bogatych gromad w supergromadach.

N 0 obiektów


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

Konkluzje 0 obiektów

  • Rozkład eliptyczności struktur zależy od liczebności struktury. Bardziej liczne – bardziej sferyczne.

  • Zależność e(z). W przeszłości silniejsze oddziaływanie.

  • Rozkłady kątów pozycyjnych dla 10 najjaśniejszych galaktyk – losowe.

  • Różnice kątów pozycyjnych struktury i najjaśniejszych galaktyk – losowe.

  • Tylko w przypadku gromad zawierających nadolbrzymią galaktykę cD obserwuje się współosiowość. Specjalna ewolucja tych gromad galaktyk.

  • Struktury powstają na filamencie.

The 0 obiektówdistribution of structureellipticityisidentical forstructureswith N>50 members.

Less populatedstructuresaremoreelongatedthanrichones. 

Thesmallgroupsare forming on thefilament and later on,due to hierarchicalclustering,greater, moresphericalstructuresareformed. Theadditional argument for thispicture: themean group redshiftisgreaterthanclusters.

Theelipticity – redshiftrealtiondepends on thestructurerichness. Thedifferencebetweenellipticity 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.

Simulation: very massive structures were considered (21013h-1 Msun ).