monika biernacka włodzimierz godłowski teresa juszczyk paulina piwowarska elena panko
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/1.jpg)
Monika BiernackaWłodzimierz Godłowski
Teresa JuszczykPaulina Piwowarska
Elena Panko
Some properties of galaxy clusters
Piotr Flin
![Page 2: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/2.jpg)
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
![Page 3: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/3.jpg)
Motivation of studyMotivation of study
![Page 4: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/4.jpg)
![Page 5: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/5.jpg)
Large scale distribution of matter in the Large scale distribution of matter in the UniverseUniverse (cosmic web)(cosmic web)
long structures ( filaments)flat structures (sheets, walls) dense, compact regions (galaxy clusters ) surrounded by depopulated regions (voids)
![Page 6: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/6.jpg)
![Page 7: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/7.jpg)
![Page 8: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/8.jpg)
Observational dataObservational 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.
![Page 9: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/9.jpg)
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.
![Page 10: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/10.jpg)
Structure findingStructure finding
• We selected the Voronoi tessellation technique (VTT hereafter) for cluster detection.
• This technique is completely non-parametric, and thereforesensitive 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.
![Page 11: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/11.jpg)
-2000 -1000 0 1000 2000
-1000
0
1000
2000
y
x
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
![Page 12: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/12.jpg)
Structure ellipticity determinationStructure 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:
mN
xx
mN
yy
mN
xxx
2
2
mN
yyy
2
2
mN
yyxxyx
The semiaxes in arcsec for the best-fitting ellipse were calculated from:
2
222222
22yx
yxyxa
2
222222
22yx
yxyxb
Ellipticity:a
bE 1 Position angle:
2222tan
yx
yx
![Page 13: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/13.jpg)
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
![Page 14: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/14.jpg)
![Page 15: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/15.jpg)
Table 1. The result of the statistical analysis of m10 - z relation
N Identification for input data
a b Number SD R
1 ACO (0.5r) -3.895 (±0.210)
0.1737 (±0.012)
455 0.17 0.56
2 ACO (0.3r) -3.771(±0.242)
0.1660(±0.015)
290 0.17 0.55
3 APM (0.5r) -3.813(±0.148)
0.1684(±0.009)
372 0.11 0.65
4 ACO (m10<19m.3) -3.767(±0.195)
0.1641(±0.0116)
519 0.18 0.28
BFJP, 2009, ApJ 696, 1689
![Page 16: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/16.jpg)
Recent dynamical evolutionRecent dynamical evolution
Plionis (2002)
![Page 17: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/17.jpg)
6068 struktur PF 6068 struktur PF
![Page 18: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/18.jpg)
The distribution of estimated z and the limits of the division into groups
BFJP 2009, ApJ 696, 1689
![Page 19: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/19.jpg)
BFJP 2009, ApJ 696, 1689
![Page 20: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/20.jpg)
BFJP 2009, ApJ 696, 1689
![Page 21: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/21.jpg)
The frequency distributions of structure ellipticities in four classes withrichness identified in the upper right portion of each section (left panel all data, right panel 457 structures with m3+3m18m.3). PJBF 2009, ApJ 700, 1686
![Page 22: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/22.jpg)
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
![Page 23: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/23.jpg)
The dependence of group richness on redshift z. (left panel all data, right 457 points)
PJBF 2009, ApJ 700, 1686
![Page 24: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/24.jpg)
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
![Page 25: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/25.jpg)
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
![Page 26: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/26.jpg)
• 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 (21013 h-1 Msun ).
![Page 27: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/27.jpg)
![Page 28: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/28.jpg)
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
![Page 29: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/29.jpg)
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
![Page 30: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/30.jpg)
The lack of galaxy orientation is in agreement with CDM
The physical processes in the filament:
Either:(anisotropic merging of structures + infall of matter) orientation of
galaxies
or: (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.
![Page 31: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/31.jpg)
BinBinggeli efggeli effefecct t structure is pointing toward neighboursstructure is pointing toward neighbours
![Page 32: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/32.jpg)
![Page 33: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/33.jpg)
Only in the case of BM I type clusters the effect is observed, and also BM II-III
![Page 34: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/34.jpg)
![Page 35: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/35.jpg)
The orientation of galaxies in clusters 247rich clusters having at least 100 members each. The relation betweenparameters describing galaxy orientation (position angle p, the angles: δD and η)and value of statistics, used for anisotropy calculation
Value of statistics increase with the amount of the galaxy members, which is equivalent to the existance of a relation between anisotropy and the number of galaxies in a cluster.
GPPF 2010, ApJ 723. 985
![Page 36: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/36.jpg)
Local Supercluster
Investigation of Tully’s group (NGC) alignment
![Page 37: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/37.jpg)
GF ApJ 708,.920 (2010)
LSC
![Page 38: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/38.jpg)
Position angles:
Pag group position anglePabm PA of the brightest galaxyPal 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
![Page 39: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/39.jpg)
GF ApJ 708,.920 (2010)
![Page 40: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/40.jpg)
GF ApJ 708,.920 (2010)
Angle difference
![Page 41: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/41.jpg)
GF ApJ 708,.920 (2010)
Binggeli effect
for Tully’s group
![Page 42: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/42.jpg)
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
Conclusions
![Page 43: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/43.jpg)
ConclusionsConclusions
• 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
![Page 44: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/44.jpg)
Thank you
![Page 45: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/45.jpg)
![Page 46: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/46.jpg)
Struktury PFStruktury PF
6068 struktur
przedział jasności: m3 – m3+3m
![Page 47: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/47.jpg)
Contingency tableContingency table
21-3021-30 31-4031-40 41-5041-50 51-6051-60 61-7061-70 71-8071-80 81-9081-90 91-10091-100 >100>100
10-2010-20 3,7354 6,2565 7,2929 6,6493 6,1754 5,7794 4,5407 4,4379 7,4503
21-3021-30 3,1015 4,5013 4,6979 4,5504 4,9033 3,0930 3,8179 6,3343
31-4031-40 1,6189 2,4571 2,5490 3,1751 1,6852 2,6718 3,8782
41-5041-50 1,3196 1,5201 2,2652 0,9619 2,0691 2,5903
51-6051-60 0,6179 1,1031 0,1750 1,2746 1,0271
61-7061-70 0,8063 0,2955 1,0595 0,8441
71-8071-80 0,8065 0,4377 0,2852
81-9081-90 1,0573 0,6658
90-10090-100 0,6831
0.05=1, 358 0.01=1.627
![Page 48: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/48.jpg)
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
PA DistributionPA Distribution
![Page 49: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/49.jpg)
![Page 50: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/50.jpg)
![Page 51: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/51.jpg)
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:
n
k k
kk
N
NN
1 ,0
2,02
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:
kkkk NN 2sin2cos1 2111,0
(we take into account only the first Fourier mode).
![Page 52: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/52.jpg)
We obtain the following expression for the coefficients ij (i,j = 1, 2):
n
kkk
n
kkkk
j
n
kkk
n
kkkk
j
JN
JNN
JN
JNN
1
2,0
1,0
2
1
2,0
1,0
1
2sin
2sin
2cos
2cos
with the standard deviation
2
1
0
21
1
2,021
21
0
21
1
2,011
22sin
22cos
nNN
nNN
n
kkk
n
kkk
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).
![Page 53: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/53.jpg)
The probability that the amplitude:
21
221
2111
is greater than a certain chosen value is given by the formula:
2
101 4exp N
nP
while the standard deviation of this amplitude is
2
1
01
2
nN
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.
![Page 54: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/54.jpg)
The auto-correlation test quantifies the correlations between the galactic numbers in adjoining angular bins. The correlation function is defined as:
n
k kk
kkkk
NN
NNNNC
1 21
1,0,0
1,01,0
In the case of an isotropic distribution we expected C = 0 with the standard deviation:
21nC
![Page 55: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/55.jpg)
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 21013 h-1M, which corresponds only to the richest of our samples.
![Page 56: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/56.jpg)
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.
![Page 57: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/57.jpg)
From the presented analysis of the orientation of galaxy groups in the Local Supercluster thefollowing picture of the structure formation appears. The two brightestgalaxies were formed first. They originated in the filamentary structuredirected towards the centre of the protocluster. This is the place wherethe Virgo cluster centre is located now.Due to gravitational clustering, the groups are formed in such a mannerthat galaxies follow the line determined by the two brightest objects.Therefore, the alignment of structure position angle and line joining twobrightest galaxies is observed. The other groups are forming on thesame or nearby filament. The flatness of the LSC additionally contributesto the observed alignment of galaxy groups. The majority of the groups lieclose to us. Due to completeness of the Catalog, the lack of groupsfurther than the Virgo Cluster centre is observed, but nearby groups arevery 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, theformation is occurring on the filamentary structure.
![Page 58: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/58.jpg)
a) Turbulencje
b) Pancake (naleśnik)
c) Hierarchiczne grupowanie się (momenty skręcające)
Iye & Sugai, 1991ApJ 374, 12
![Page 59: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/59.jpg)
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000
-1500
-1000
-500
0
500
1000
1500
![Page 60: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/60.jpg)
![Page 61: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/61.jpg)
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
The division of ACO clusters corresponding to PF structures according to structure richness and B-M morphological types.
PJF 2009, AJ 138, 1709
![Page 62: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/62.jpg)
Cen & Ostriker (2006)
![Page 63: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/63.jpg)
![Page 64: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/64.jpg)
![Page 65: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/65.jpg)
![Page 66: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/66.jpg)
![Page 67: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/67.jpg)
![Page 68: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/68.jpg)
![Page 69: Monika Biernacka Włodzimierz Godłowski Teresa Juszczyk Paulina Piwowarska Elena Panko](https://reader036.vdocuments.site/reader036/viewer/2022062323/56815950550346895dc68ea1/html5/thumbnails/69.jpg)