Theory of galaxy formation In the commonly accepted CDM model the Universe is deemed to be spatially flat, homogeneous and isotropic at appropriate scale The dimension of this scale is changing with the growth of our knowledge of the Universe In this model, the structure was formed from the primordial adiabatic, nearly scale invariant, Gaussian random fluctuations
Galaxy formation scenarios Primordial turbulences (von Weizsacker 1951, Gamow 1952, Oziernoy1978 and Efstathiou and Silk 1983) accounts for the spin angular momentum as a remnant of the primordial whirl Hierarchical clustering (Peeble 1969, Doroshkevich 1970, Dekel 1985) large-scale structures in the Universe form "from bottom up", as a consequence of gravitational interactions between galaxies Zeldovich's pancake model (Sunayev and Zeldovich 1972, Doroshkevich 1973, Shandarin 1974, Doroshkevich, Saar, and Shandarin 1978, Zeldovich 1978), which provides that structures in the Universe form "from up to bottom " in the effect of asymmetrical collapse of a large structure Li Li-Xin (1998) model involving galaxy forming in a rotating universeas a consequence of the conservation of angular momentum in a rotating universe based on ideas of Gamow (1946), Goedel (1949) and Colins and Hawking (1973).
Different theories of the galaxy formation make predictions regarding to the angular momenta of galaxies (Peebles 1969, Doroshkevich 197373, Shandarin1974, Silk & Efstathiou 1983, Catelan & Theuns 1996, Li 1998, Lee & Pen 2000, 2001, 2002, Navarro et al. 2004, Trujillio et al. 2006) The analysis of an orientation of galaxies planes is regarded as a standard test of galaxies formation scenarios
In the 1975 Hawley and Peebles gave the proposal to use tree statistical tests for investigations of the galaxies orientation in the large structures. Since this time this method has been the standard method of searching for galactic alignments. We investigated the distributions of the angles giving information about galaxy angular momenta. The position angles of the galaxy major axes, as well as two angles ( D and ) describing the spatial orientation of galaxy plane can be tested for isotropy, by applying three different statistical tests.
Example – Cluster A2721 (all galaxies and face-on galaxies excluded)
Godłowski Szydłowski & Flin 2005 suggested that alignment of galaxies in cluster should increase with the number of objects in particular cluster. There is no clear empirical evidence that galaxy groups and clusters rotate (Hwang & Lee 2007). Thus, it can be accepted that the total angular momentum of galaxy structure is mainly connected with the galaxies' spins. Moreover, stronger alignment suggests greater total angular momentum of galactic groups or clusters. Usually this dependence between angular momentum and mass of the structure is presented as empirical relation J~M 5/3. Many attempts to explain this relations – it is rather difficult to explain the observed relation between the richness of galaxy cluster in the light of galaxy formation scenarios – possibilities: a) the alignment is due to tidal torque, as suggested by Catelan and Theuns (1996 ) b) Li Xin-Li model
Sample of 247 optically selected rich Abell clusters, having in the considered area at least 100 members - taken from PF catalogue Panko & Flin 2006 The values of analyzed statistics increase with the amount of galaxies' members, which is equivalent to the existence of the relation between anisotropy and number of galaxies in cluster. We found only weak correlation between the alignment and BM type. We found a strong correlation between BM type and the velocity dispersion. The velocity dispersion decreases with BM type.
Methods The question which arise, is if we could say that in analyzed sample of 247 Abell clusters we found an alignment. For this meaner, we analyze the distributions of position angles of galaxies belonging to investigated clusters using 2 test, Fourier tests and autocorrelation test as well as Kolmogorow test. For our sample of 247 Abell clusters, we compute the mean values of analyzed statistics. Our null hypothesis H_0 is that mean value of the analyzed statistics is as expected in the cases of a random distribution of analyzed angles. We compared our results with theoretical predictions as well as with results obtained from numerical simulations. Originally proposed by Hawley and Peebles (1975) tests was analyzed in details and some improvements are proposed.
We found that orientation of galaxies in analyzed clusters are not random i.e. we found an existence of alignment of galaxies in the our sample 247 rich Abell galaxy clusters. Statistical tests - Results
Above results were obtained with help of the analysis of position angles – WHAY??
Godłowski & Ostrowski MNRAS 303 50 (1999) (maps of 11 / ( 1 1) statistics) Based on the sample 18 Tully LSC groups The inclination angle was calculated according to the formula: cos 2 i=(q 2 -q 0 2 )/(1-q 0 2 ), where observed axial ratio q=b/a and q 0 is "true" axial ratio. Formula mentioned above is valid for oblate spheroids Holmberg 1946. Tully used standard value q 0 2 =0.2 – not including information about morphological types of galaxies
What is possible to do? Calculate the inclination angle calculated cos 2 i=(q 2 -q 0 2 )/(1-q 0 2 ), where q 0 2 is given from HHV–according morphological types of galaxies (Tully catalogue give information about morphological types)
When lack of information about morphological types ….. In clusters we are able estimated the fraction of galaxies with particular morphological types We simulate isotropic distribution of the inclination angle and position angle for each galaxy From the formulae cos 2 i=(q 2 -q 0 2 )/(1-q 0 2 ) we compute „observed” q=a/b (with taking into account distribution of morphological types of galaxies in clusters) We compute new value of cos 2 i assuming q 0 =0.2 and value of D and angles Now we obtained new „theoretical isotropic distributions” for D and angles which can be compared with „observational” (obtained with assumption that q 0 =0.2) one.
Conclusions Alignment of galaxies in cluster should increase with the number of objects in particular cluster. In rich Abell clusters alignment is observed In group of galaxies alignment is not observed Standard approximation q 0 =0.2 is wrong – IMPLICATIONS FOR TULLY FISHER RELATION It is still possible investigated spatial orientation galaxies in clusters taking into account fraction of galaxies according morphological types