SOME PROPERTIES OF NEARBY GALAXY CLUSTERS

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ON THE ORIGIN OF LARGE SCALE STRUCTURES
Piotr Flin
Wlodzimierz Godlowski Elena Panko
Instytut Fizyki, Uniwersytet Jana Kochanowskiego,
Kielce, Polska Instytut Fizyki, Uniwersytet
Opolski, Opole, Polska Kalinenkov Astronomical
Observatory, Nikolaev, Ukraine
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Piotr Flin Wlodzimierz Godlowski Elena Panko
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Plan

• Kilka uwag historycznych
• Obserwacje
• Symulacje numeryczne
• Uzywane obserwacje
• Dwa zestawy danych
• Grupy Tullyego w LSC
• Katalog struktur PF
• Ksztalt struktur
• Supergromady
• Efekt Binggeliego
• obiekty katalogu PF
• obiekty NBG
• Konkluzje

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Outlook

• A few historical remarks
• Observations
• Numerical simulations
• Applied observational data
• Two sets
• LSC Tullys group w LSC
• Struktures catalogue PF
• Structure shape
• Superclusters
• Binggeli effect
• PF structures
• NBG groups
• Conclusions

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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)
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Cosmic web structures and voidskosmiczna siec
strucures and voids
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Cen Ostriker (2006)
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Motivation
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LSC
GF ApJ 70,.920 (2010)
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Considered model

• HOT BIG BANG
• EKSPANSION OF THE UNIVERSE
• 106 YAERS AFTER THE BIG bANG
• Temperature of matter and radiations 3103 K
  primival plasma recombination
• free electrons disappeared, drastic
  reduction of the radiation and matter
  interactions,
• Independent evolution of radiation and matter.
• The Universe becames transparent

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Kind of matter Barionic non barionic, what
is the distribution of both ?     HOT
lekkie ( 100 eV) i relatywistyczne az do
rekombinacji czastki (
neutrino) WARM (1 10 keV) staja
sie nie- relatywistyczne wczesniej COLD
ciezkie czastki, która bardzo wczesnie
przestaja byc relatywistyczne
Maja bardzo male predkosci
Gravitinos, photinos, axions
(WIMP)
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Parameters conected with density perturbations

• Type of perturbation
• Amplitude
• Skale of perturbation (MASS or the scale lenght
  
• TREE MAIN TYPES OF FLUKTUATIONS
• ADIABATIC (RADIATION AND MATTER ARE PERTURBED ),
  (ENTROPIA PER BARION IS CONSTANT)
• ISOTERMIC PERTURBACJE (TEMPERATURE AND
  RADIATION DENSITY CONST, ONLY MATTER FORMS
  AGGREGATIONS)
• 3. TURBULENCES (EDGGES) - (BOTH MATTER AND
  RADIATION)
• Various scenerios structure origin predicts
  diferent proerties of structures
• mainly shape and the acquitance of angular
  momenta of galaxies.
• modele top down, bottom up

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Explosive scenario
Wiele malych eksplozji równoczesnie
25 50 Mpc
1065 erg
lub
Nadprzewodzace struny kosmiczne
Mlode galaktyki, kwazary
do 5 Mpc 1061 erg
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1. Turbulences
2. Pancake
3. Hierarchical clustering (tidal torquing)

Iye Sugai, 1991ApJ 374, 12
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Observational data

• From Tullys Catalogue
• 61 galaxy groups
• 26 groups with 10 - 20 objects
• 35 gt20 objects
• Position angle of the group
  PAg
• Position angle of the line joining 2 brightest
  galaxies PAl
• Position angle of the BCM
  PAbm
• Direction toward Vigo Cluster centre
  PAV
• Isotropy tested (K-S, c2 )

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• The distribution of the acute angle T 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, 10ltD? 20 Mpc, 10ltD? 20 Mpc and
  Dgt20 Mpc are presented respectively.

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

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• 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).

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Two brightest originated on the filament
directed toward the centre of of LSC. Through
the gravitational interaction galaxy groups are
formed on the line conected these two brightest
galaxies. Therefore we observed aligment of
structure and line connecting two brightes
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This is picture showing the origin in the case of
not very massive sytucture, as LSC. It is
interesting to look in greater scale and in
2D. There are not statistically complete data
for such a task. Therefore, we decided to check
the observed tendency. We will use the PF
Catalogue .
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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 rF18m.3
  (Ungruhe 2003).
• 217 ESO Southern Sky Atlas R Schmidt plates with
  galactic latitudes blt-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 rF18m.3.

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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.
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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, allowing correct studies of
  non-spherically symmetric structures. For a
  distribution of seeds, the VTT creates polygonal
  cells containing one seed each and enclosing the
  whole area closest to the seed. This is the
  definition of a Voronoi cell in 2D.

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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
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Using standard covariance ellipse method for
galaxies in the considered region within the
magnitude limit m3, m33m, we determined the
moments of the distribution
The semiaxes in arcsec for the best-fitting
ellipse were calculated from
Ellipticity
Position angle
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PJF 2009, AJ 138, 1709
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Struktury PF
6188 struktur przedzial jasnosci m3 m33m
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PF JAD 2,1 (2006)
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Results
very rich superclusters
Superclusters n8 ngt4 Angle P
random 0.647 0.750
0.524 Angle delta d anisotropy 0.150
0.250 0.238
0.250 Angle eta h anisotropy 0.227
0.3000 0.190
0.300
In very rich clusters anlignment should be the
greatest, if orientation ioriginated
simultulanously with protostrcutures..
Anisotropy is increasing with structure size (
mass). The increase of anizotropii with
richness was observed in the case of rich (
ngt100) structures PF. Here the same pattern
is confirmed.utaj jest potwierdzony.
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Conclusions
Galaxy groups formed first, next they merge
due to hierarchical clustering and formed
greater structures. The protomain plane of the
protostructure forms, which attracts other
groups. Therefore structures are flat. This
tendency is observed in the case of 1D i 2D
structur.es Of course, this is preliminary
results, which should be confirm on much bettter
statistical sample.
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Thank you for your attention
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Orientation of the galaxy groups in the Local
Supercluster

• Piotr Flin, Wlodzimierz Godlowski
• Institute of Physics, Jan Kochanowski University,
  Kielce, Poland
• Institute of Physics, Opole University, Opole,
  Poland

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Recent dynamical evolution
Plionis (2002)
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6068 struktur PF
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The distribution of estimated z and the limits of
the division into groups
BFJP 2009, ApJ 696, 1689
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BFJP 2009, ApJ 696, 1689
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BFJP 2009, ApJ 696, 1689
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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 m33m?18m.3).
PJBF 2009, ApJ 700, 1686
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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
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The dependence of group richness on redshift z.
(left panel all data, right 457 points)
PJBF 2009, ApJ 700, 1686
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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 relations together
with their ? 0.95 confidence intervals are also
plotted.
PJBF 2009, ApJ 700, 1686
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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
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Rozklad eliptycznosci dla struktur z Ngt50 jest
identyczny   Mniej spopulowane struktury sa
bardziej wyciagniete niz bogate   Male grupy
powstaja na filamencie i nastepnie droga
hierarchicznego grupowania sie powstaja duze
struktury, bardziej sferyczne. Dodatkowy
argument za tym obrazem (sredni redshift dla
grup jest wiekszy niz dla gromad)     Relacja
e-z zalezy tez od liczebnosci struktury.
Eliptycznosc malych grup i tempo ewolucji de/dz
róznia sie na poziomie 3? od tychze dla
bogatych struktur   Tylko struktury majace 10-30
czlonków wykazuja silna korelacje e
z..     Numeryczne symulacje w ?CDM dla z
lt3.0 wskazuja, ze eliptycznosc rosnie z
przesunieciem ku czerwieni, jak tez masa
gromady. Potwierdzamy pierwsza tendencje, ale
bardzo rózne z, drugiej nie, ale w symulacjach
bardzo masywne gromady 2?1013 h-1 Mslonca .
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The division of ACO clusters corresponding to
PF structures according to structure richness
and B-M morphological types.
PJF 2009, AJ 138, 1709
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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
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The frequency distribution of the angle ?1
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
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Brak orientacji galaktyk w gromadach jest zgodny
z CDM   Procesy fizyczne w filamencie
  albo Anizotropowe zlewanie sie struktur
(anisotropic merging infall of matter)

orientacja galaktyk
  Oddzialywanie przyplywowe ( tidal torque)
brak orientacji  
  Nasz
wynik brak orientacji   Galaktyki uzyskuja
moment pedu przez oddzialywanie przyplywowe
sasiadów we wczesnym wszechswiecie. Przeplyw
materii wzdluz filamentu powoduje
wspólliniowosc najjasniejszej galaktyki z duza
pólosia gromady.  
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Efekt Binggeliego
 
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Badanie Lokalnej Supergromady
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Katy pozycyjne Pag kat pozycyjny grupy Pabm
kat pozycyjny najjasniejszej galaktyki Pal kat
pozycyjny linii laczacej dwie najjasniejsze
galaktyki w grupie najjasniej Pav kat
pozycyjny na Virgo (kierunek na Virgo )
badano izotropie rozkladów tych 4 katów Róznice
katów Pag Pav Pal PaV Pag Pal Pabm
Pag Pabm Pal Pabm Pav
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GF ApJ 70,.920 (2010)
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Róznice katów
GF ApJ 70,.920 (2010)
GF ApJ 70,.920 (2010)
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Efekt Binggeliego dla grup
GF ApJ 70,.920 (2010)
GF ApJ 70,.920 (2010)
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Dwie najjasniejsze galaktyki powstaja na
filamencie skierowanym do centrum LSC. Poprzez
oddzialywanie grawitacyjne grupy galaktyk
powstaja wzdluz tej linii laczacej dwie
najjasniejsze galaktyki. Dlatego obserwuje sie
wspólosiowosc kata pozycyjnego struktury i linii
laczacej dwie najjasniejsze galaktyki.  
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• Dziekuje za uwage

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Contingency table
21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 gt100
10-20 3,7354 6,2565 7,2929 6,6493 6,1754 5,7794 4,5407 4,4379 7,4503
21-30 3,1015 4,5013 4,6979 4,5504 4,9033 3,0930 3,8179 6,3343
31-40 1,6189 2,4571 2,5490 3,1751 1,6852 2,6718 3,8782
41-50 1,3196 1,5201 2,2652 0,9619 2,0691 2,5903
51-60 0,6179 1,1031 0,1750 1,2746 1,0271
61-70 0,8063 0,2955 1,0595 0,8441
71-80 0,8065 0,4377 0,2852
81-90 1,0573 0,6658
90-100 0,6831
?0.051, 358 ?0.011.627
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PA Distribution
The division of ACO clusters corresponding to
PF structures according to structure
richness and B-M
morphological types
Type All ?100 50-99 30-49 10-29
I 105 34 38 22 11
I-II 223 50 82 63 28
I-II 8 4 1 2 1
II 223 55 72 59 37
II 34 5 13 7 9
II-III 229 50 59 65 55
III 220 48 62 76 34
III 14 2 4 5 3
1056 248 331 299 178
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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).
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We obtain the following expression for the
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).
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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
lt 0, then, for ??????2, an excess of galaxies
with rotation axes parallel to the LSC plane is
present. For ?11 gt 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 lt 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 gt
0, the position angles of galaxy are
perpendicular to the plane of the coordinate
system.
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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
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?2
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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 lt 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?1013 h-1M?, which corresponds only to the
richest of our samples.
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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.
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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.
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Wyobrazmy sobie sfere zawierajaca mase
calkowita M w epoce rekombinacji (wszechswiat
jest bardzo jednorodny wtedy) . Niech lt ?M/Mgt
jest fluktuacja gestosci która wystapila wtedy
w sferze poruszajacej sie losowo we
wszechswiecie. Wielkosc lt ?M/Mgt jest miara
niejednorodnosci Wszechswiata.  Zwiazek lt ?M/Mgt
z M zwana jest widmem fluktuacji gestosci
(density fluctuation spectrum (DFS)). Jest to
zaleznosc fundamentalna . Matematyczny ksztalt
tej funkcji opisuje wzrost struktur powstalych
droga grawitacji. Poniewaz po rekombinacji
male fluktuacje rosna liniowo jak (1 z)
-1, ksztalt DFS w momencie rekombinacji jest
zachowany az do momentu, gdy pierwsze z
fluktuacji staja sie nieliniowe. Gestosc
wszechswiata ? zmienia sie od miejsca do miejsca,
a srednia gestosc to lt?gt. Aby powstala struktura
nadwyzka gestosci w danym miejscu opisana jako
?? / lt?gt musi byc
wystarczajaco wieksza od zera.
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NIESTABILNOSC GRAWITACYJNA  Z tego warunku
uzyskuje sie dane o parametrach takich jak masa
i amplituda. Sa one dane prze index ? i
wspólczynniki normalizacji K i M0 widma mas. 
?? / lt?gt k
(M/M0)?  Index ? jest zwiazany ze wskaznikiem
widma mocy n zdefiniowanym przez
( ?? / lt?gt) 2 ln poprzez
zaleznosc  ? - ½ n/6  Jezeli jest
funkcja czasu to widmo mas tez.  Wydaje sie, ze
? - 2/3 wtedy perturbacje maja stala krzywizne
kiedy docieraja do horyzontu (n -1). (Promien
wszechswiata jest ct). Gdy t 1 rok masa
wewnatrz 109 1011 MO .  ASTROPARTICLE
PHYSICS EARLY UNIVERSE, GUT BOTH VALUE OF ?
AS WELL TYPE OF PERTURBATIONS GENERATED IN THE
EARLY UNIVERSE
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Katalog struktur PF 6188 struktur , kazda wiecej
niz 10 0 obiektów W oparciu o ten katalog
utworzono katalog supergromad. Wiadmo, ze
supergromady sa plaskie. Nasze badania to
potwierdzily. Dlatego tez porównanie w
przypadku 2D robiono na supergromadach. Niestety
nie jest to statystycznie elna próbka, wiec
posluzyla do badan wstepnych. Mamy 57
supergromad, z k tórych kazda zawiera
przynajmniej 4 struktury PF. Dla 257 bardzo
bogatych gromad PF ( ngt100) znamy rozklad
katów pozycyjnych oraz orietacje osi
rotacji. Sprawdzono, jak wyglada rozklad oso
rotacji i katów pozycyjnych bardzo bogatych
gromad w supergromadach.
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Nie ma mozliwosci bezposredniego obserwowania
poczatkowego widma mas, ewentualnie z wyjatkiem
tylko duzych mas. Jest to wynikiem tego, iz wiele
fizycznych procesów wplywalo na perturbacje we
wczesnym Wszechswiecie. Niektóre z tych procesów
sa zalezne od masy, inne nie. W epoce
promieniowania amplituda fluktuacji gestosci o
dlugosciach fali mniejszych niz horyzont
kosmologiczny pozostaje niezmieniona.
Fluktuacje o wiekszej dlugosci fali niz horyzont
rosna proporcjonalnie do czasu. Fluktuacje o
coraz to wiekszych dlugosciach fali wchodza w
horyzont i ulegaja zamrozeniu. Kiedy gestosci
energii promieniowania i materii staja sie
równe (zeq ? 2.5 x 104 ? h2 ) wszystkie
perturbacje gestosci moga rosnac. Widmo mocy dla
malych liczb falowych (czyli duzych dlugosci fal)
pozostaje niezmienione, dla malych dlugosci fal
szybko maleje do zera. Rozwazmy perturbacje
1011, 1015, 1019 MO . (masa galaktyki, masa
najwiekszego skupiska gdzie ?? / lt?gt gt1 ,
oceniona przyblizonej masy Wszechswiata w
momencie oddzielenia (decoupling)) materii i
promieniowania.
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112
Table 1. The result of the statistical analysis
of m10 - z relation
 
BFJP, 2009, ApJ 696, 1689
113
Konkluzje

• Rozklad eliptycznosci struktur zalezy od
  liczebnosci struktury. Bardziej liczne bardziej
  sferyczne.
• Zaleznosc e(z). W przeszlosci silniejsze
  oddzialywanie.
• Rozklady katów pozycyjnych dla 10 najjasniejszych
  galaktyk losowe.
• Róznice katów pozycyjnych struktury i
  najjasniejszych galaktyk losowe.
• Tylko w przypadku gromad zawierajacych
  nadolbrzymia galaktyke cD obserwuje sie
  wspólosiowosc. Specjalna ewolucja tych gromad
  galaktyk.
• Struktury powstaja na filamencie.

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The distribution of structure ellipticity is
identical for structures with Ngt50
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
?CDM for z lt3.0 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?1013
h-1 Msun ).
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Rozklad materii we Wszechswiecie (
wielkoskalowa struktura)   Kosmiczna siec (
pajeczyna)   bardzo wydluzone struktury wlókniste
( filaments) plaskie struktury ( sciany)
(sheets, walls) geste zwarte
gromady galaktyk otoczone przez
prawie puste obszary (pustki,
voids)   Topologia tych obszarów Filaments
(1D) Sheets (2D)   Przechodzenie od
obszarów pustych do pustych przekraczanie
scian, czy jak w gabce