Recovering the Internal Dynamics and the Shapes of Galaxy Clusters: Virgo Cluster

We describe a method for recovering of the substructure, internal dynamics and geometrical shapes of clusters of galaxies. Applying the method to the Virgo cluster, we, first, reveal the substructure of the central 4 arc degree field of the Virgo cluster by means of S-tree technique. The existence of three main subgroups of galaxies is revealed and their dynamical characteristics are estimated. Then, using the previously suggested technique (Gurzadyan and Rauzy 1997), the bulk flow velocities of the subgroups are evaluated based on the distribution of the redshifts of the galaxies. The results enable us also to obtain a secure indication of the elongation of the Virgo cluster and its positional inclination.Comment: to appear in Int.Journ.Mod.Phys.

Kolmogorov stochasticity parameter measuring the randomness in Cosmic Microwave Background

The Kolmogorov stochasticity parameter (KSP) is applied to quantify the degree of randomness (stochasticity) in the temperature maps of the Cosmic Microwave Background radiation maps. It is shown that, the KSP for the WMAP5 maps is about twice higher than that of the simulated maps for the concordance \LambdaCDM cosmological model, implying the existence of a randomizing effect not taken into account in the model. As was revealed recently, underdense regions in the large scale matter distributions, i.e the voids, possess hyperbolic and hence randomizing properties. The degree of randomness for the Cold Spot appears to be about twice higher than the average over the mean temperature level spots in the sky, which supports the void nature of the Cold Spot. Kolmogorov's parameter then acts as a quantitative tracer of the voids via CMB.Comment: A&A Lett (in press), 2 pages, 1 Tabl

Collective relaxation of stellar systems revisited

The chaos in stellar systems is studied using the theory of dynamical systems and the Van Kampen stochastic differential equation approach. The exponential instability (chaos) of spherical N-body gravitating systems, already known previously, is confirmed. The characteristic timescale of that instability is estimated confirming the collective relaxation time obtained by means of the Maupertuis principle.Comment: A & A (in press), 3 pages, to match the published versio

Towards investigation of evolution of dynamical systems with independence of time accuracy: more classes of systems

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended, now including systems that are; (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.Comment: Eur. Phys. Journ. C (in press), to match the published version, 4 page

The cosmological constant derived via galaxy groups and clusters

The common nature of dark matter and dark energy is argued in [1] based on the approach that the cosmological constant \Lambda enters the weak-field General Relativity following from Newton theorem on the "sphere-point mass" equivalency [2]. Here we probe the \Lambda-gravity description of dark matter in galaxy systems, from pairs up to galaxy clusters using the data of various sources, i.e. of Local Supercluster galaxy surveys, gravity lensing and Planck satellite. The prediction that the cosmological constant has to be the lower limit for the weak-field \Lambda obtained from galaxy systems of various degree of virialization is shown to be supported by those observations. The results therefore support the \Lambda-gravity nature of dark matter in the studied systems, implying that the positivity of the cosmological constant might be deduced decades ago from the dynamics of galaxies and galaxy clusters far before the cosmological SN surveys.Comment: To appear in Eur Phys J C, 7 page

On the Numerical Study of the Complexity and Fractal Dimension of CMB Anisotropies

We consider the problem of numerical computation of the Kolmogorov complexity and the fractal dimension of the anisotropy spots of Cosmic Microwave Background (CMB) radiation. Namely, we describe an algorithm of estimation of the complexity of spots given by certain pixel configuration on a grid and represent the results of computations for a series of structures of different complexity. Thus, we demonstrate the calculability of such an abstract descriptor as the Kolmogorov complexity for CMB digitized maps. The correlation of complexity of the anisotropy spots with their fractal dimension is revealed as well. This technique can be especially important while analyzing the data of the forthcoming space experiments.Comment: LATEX, 3 figure