Transcript Lecture 1: The Scale of the Cosmos

"Some observational aspects of
rotation”
Włodzimierz Godłowski
Institute of Physics Opole University
Ustroń 2011
Cosmic web: structures and voids
Theory of galaxy formation
• In the commonly accepted LCDM 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
(dD and h) 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~M5/3.
• 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 c2 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.
Statistical tests
Statistical tests II
Statistical tests - Results
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.
Above results were obtained with help
of the analysis of position angles
– WHAY??
Godłowski &
Ostrowski MNRAS
303 50 (1999)
(maps of D11/s(D11)
statistics)
Based on the sample 18 Tully LSC groups
The inclination angle was calculated
according to the formula:
cos2 i=(q2 -q02 )/(1-q02), where observed
axial ratio q=b/a and q0 is "true" axial
ratio. Formula mentioned above is valid for
oblate spheroids Holmberg 1946. Tully
used standard value q02=0.2 – not
including information about morphological
types of galaxies
What is possible to do?
Calculate the inclination angle calculated
cos2 i=(q2 -q02 )/(1-q02), where q02 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 cos2 i=(q2 -q02 )/(1-q02) we compute
„observed” q=a/b (with taking into account distribution of
morphological types of galaxies in clusters)
• We compute new value of cos2 i assuming q0=0.2 and value
of dD and h angles
• Now we obtained new „theoretical isotropic distributions” for
dD and h angles which can be compared with
„observational” (obtained with assumption that q0=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 q0=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