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The power spectrum is obtained for the Kolmogorov stochasticity parameter map for WMAP's cosmic microwave background (CMB) radiation temperature datasets. The interest for CMB Kolmogorov map is that it can carry direct information about voids in the matter distribution, so that the correlations in the distribution of voids have to be reflected in the power spectrum. Although limited by the angular resolution of the WMAP, this analysis shows the possibility of acquiring this crucial information via CMB maps. Even the already obtained behavior, some of which is absent in the simulated maps, can influence the development of views on the void correlations at the large-scale web formation.

A new map of the sky representing the degree of randomness in the cosmic microwave background (CMB) temperature has been obtained. The map based on estimation of the Kolmogorov stochasticity parameter clearly distinguishes the contribution of the Galactic disk from the CMB and reveals regions of various degrees of randomness that can reflect the properties of inhomogeneities in the Universe. For example, among the high randomness regions is the southern non-Gaussian anomaly, the Cold Spot, with a stratification expected for the voids. Existence of its counterpart, a Northern Cold Spot with almost identical randomness properties among other low-temperature regions is revealed. By its informative power, Kolmogorov's map can be complementary to the CMB temperature and polarization sky maps.

We continue investigation of the hidden plane-mirror symmetry in the distribution of excursion sets in cosmic microwave background (CMB) temperature anisotropy maps, previously noticed in the three-year data of the Wilkinson microwave anisotropy probe (WMAP), using the WMAP 5 years maps. The symmetry is shown to have higher significance, $\chi^2 < 1.7$, for low multipoles $\ell < 5$, while disappearing at larger multipoles, $\chi^2 > 3.5 $for $\ell > 10$. The study of the sum and difference maps of temperature inhomogeneity regions, along with simulated maps, confirms its existence. The properties of these mirroring symmetries are compatible with those produced by the Sachs-Wolfe effect in the presence of an anomalously large component of horizon-size density perturbations, independent of one of the spatial coordinates, and/or a slab-like spatial topology of the Universe.

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.

The plane-mirror symmetry previously noticed in the Cosmic Microwave Background (CMB) temperature anisotropy maps of Wilkinson Microwave Anisotropy Probe is shown to possess certain anomalous properties. The degree of the randomness determined by the Kolmogorov stochasticity parameter in both symmetry regions appears to have identical values which, however, essentially differ from the corresponding values for other sky regions. If the mirroring were of cosmological origin, this would imply either additional randomizing properties in those directions of the Universe or their different line-of-sight depth. This analysis also provides a way to test the hypothesis of a link between the nature of dark energy and inhomogeneities.

Statistical properties of many-dimensional dynamical systems-stellar systems of different types, are investigated by means of new definition of relative chaos based on the estimation of the Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos.

It is shown that emission lines, first of all the ultraviolet resonance doublet 2800 Mgii, can be used to decipher the internal dynamic structure of QSOs and active galactic nuclei. The electron temperatures of the emission regions of these objects are determined. A hypothesis is proposed explaining the observed broad profiles of the 2800 Mgii line as a summary effect of emission clouds with a Maxwellian velocity distribution. The main physical parameters of emission clouds in QSOs are obtained. A mechanism of formation of emission clouds is suggested: namely, tidal disruption of stars near to a massive compact object.

The subclustering within the Local Group is studied by means of the recently developed treediagram technique, enabling one to establish substructures of different boundness. Thirty-two galaxies from 39 listed are shown to form an interacting system which includes Milky Way and M31 giant spirals; we define the Local Group as that interacting system only. Second-level boundness indicates two clear subsystems, influenced by Milky Way and that of M31. The search of systems bound stronger, specifies several pair galaxies of similar morphology.

The stochastic and regular properties of disk stellar systems being dynamical systems with non-negative curvature are investigated. It is shown that the existence of regions of regular (ordered) and stochastic motion is their typical property (RS-systems). The stochastic regions of two-dimensional systems consisting of ergodic components with positive KS-entropy is shown not to be AnosovU-systems and to have no transversal fibers. As an example the Hénon-Heiles system is studied: the existence ofstrongly stable solutions is proved. The results indicate the crucial role of chaos and order in the dynamics of spiral galaxies of different classes.

The results of analysis of the substructure of 1 degree field galaxies of the Virgo cluster by means of the Stree technique developed by Gurzadyan et al. are presented. The existence of 3 main subgroups is shown and their dynamical parameters are obtained. The mass centers of the subgroups appear to be aligned in the direction parallel to the elongation of the Virgo cluster. The morphological analysis shows some domination of dwarf galaxies in the subgroup A containing M 87, and existence of two spiral galaxies N4425 and N4461; the latter fact can be crucial for the estimation of the distance of the Virgo cluster by means of the search for Cepheids in the spirals.

Ambartsumian's life spanned the whole period of existence of the USSR and illustrates both the difficulties of working under that system and the remarkable talents necessary to surmount them. He founded a flourishing school of astronomy in Armenia and the Byurakan Observatory. Within the Soviet Union his political skills made him a member of the Supreme Soviet and one of the most powerful scientists of his time. In astronomy, he discovered basic results in the theory of the transfer of radiation through matter. He discovered stellar associations and showed that most stars were born in such unbound expanding associations rather than in bound clusters. He came to believe, therefore, that stars were born explosively. Extending this to galaxies, he was the first to emphasize the importance of activity and explosions in the nuclei of galaxies long before quasars and black holes were discovered there. He was a pioneer of astronomical research from Soviet spacecraft.

The results are here presented of an analysis of the subclustering in a sample of galaxy clusters from the European Southern Observatory (ESO) Nearby Abell Cluster Survey (ENACS), along with complementary data from other studies. The analysis is performed by using the S‐tree method, enabling us to study the hierarchical properties of clusters by the detection of the main physical cluster and of its subgroups. The results indicate (a) systematically lower genuine cluster velocity dispersions than were known from previous studies, and (b) the existence of 2–3 subgroups in each cluster. As a result of certain properties of a new class of dynamical entities, we denote these subgroups as galaxy associations; these may become an essential challenge for the formation mechanisms of galaxy clusters.

We consider the problem of the relative motion both of the substructures of the Local Group of galaxies (revealed via the S‐tree method), and of the velocity of the Local Group itself. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via a 3D reconstruction procedure, which uses information on the radial velocities of the galaxies but does not take account of their distances. Once the bulk motion of the substructures is estimated we also consider, in combination with the observed cosmic microwave background (CMB) dipole, the mean velocity of the Local Group itself. Assigning to the Local Group the mean motion of its main substructures, we evaluate its peculiar velocity in Milky Way frame VLG→MW= (−7 ± 303, −15 ± 155, +177 ± 144) or 178 km s−1toward galactic coordinates l= 245 and b= +85. Combined with the CMB dipole VMW→CMB, we obtain a Local Group velocity in CMB frame: VLG→CMB= (−41 ± 303, −497 ± 155, 445 ± 144) or 668 km s−1towards l= 265 and b= 42. This estimation is in good agreement, within the 1 σ level, with the estimation of Yahil et al.

We show that the understanding of the problem of time asymmetry can be reached proceeding from the hypothesis of typicalness of the Universe. We come to the following consequences: 1) the cosmological arrow of time, in general, should not coincide with the thermodynamic one; 2) the thermodynamic arrow should not change its direction, while the Universe turns from the expanding phase to the contracting one; 3) CPT-invariance has to be violated. The last prediction, in principle, allows experimental verification.

The degree of randomness in the cosmic microwave background (CMB) maps has been shown to be measurable and indicative of the hyperbolic effect of voids on the propagation of the photon beams. In terms of an introduced porosity parameter, we now obtain the criterion for a hyperbolicity due to domination of voids in the line-of-sight direction. The criterion seems to be supported by the parameters of 30 Mpc scale voids revealed by the galactic redshift surveys. The importance of the geometrical effect of the voids is also due to their possible role in the temperature independent ellipticity of the excursion sets, as well as in the nature of dark energy. The role of possible larger scale inhomogeneities, from superclusters to semi-Hubble scale, in this effect remains yet unclear. ?

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 as high as that of the simulated maps for the concordance ΛCDM cosmological model, implying that a randomizing effect exists that has not been taken into account by the model. As was revealed earlier, 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 as high as the average of 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 by means of the CMB.

STELLAR collisions and/or tidal break-up of stars by a massive black hole1–3accompanied by subsequent accretion of the released gas onto the hole play a crucial part in most black hole models of quasars and active galactic nuclei. It is usually assumed that an accretion disk forms around the hole due to the large orbital momentum of a disrupting star. However, we show here that the accretion mostly has disk characteristics only when M < Mcrand becomes quasi-spherical when M ≫ Mcr.

Data on the cosmic microwave background (CMB) radiation by the Wilkinson Microwave Anisotropy Probe (WMAP) had a profound impact on the understanding of a variety of physical processes in the early phases of the Universe and on the estimation of the cosmological parameters. Here, the 7-year WMAP data are used to trace the disk and the halo of the nearby giant spiral galaxy M 31. We analyzed the temperature excess in three WMAP bands (W, V, and Q) by dividing the region of the sky around M 31 into several concentric circular areas. An asymmetry in the mean microwave temperature in the M 31 disk along the direction of the M 31 rotation is observed with a temperature contrast up to  ≃ 130   μK/pixel. We also find a temperature asymmetry in the M 31 halo, which is much weaker than for the disk, up to a galactocentric distance of about 10° (≃ 120 kpc) with a peak temperature contrast of about 40   μK/pixel. We studied the robustness of these possible detections by considering 500 random control fields in the real WMAP maps and simulating 500 sky maps from the best-fitted cosmological parameters. By comparing the obtained temperature contrast profiles with the real ones towards the M 31 galaxy, we find that the temperature asymmetry in the M 31 disk is fairly robust, while the effect in the halo is weaker. Although the confidence level of the signal is not high, if estimated purely statistically, which could be expected due to the weakness of the effect, the geometrical structure of the temperature asymmetry points towards a definite effect modulated by the rotation of the M 31 halo. This result might open a new way to probe these relatively less studied galactic objects using high-accuracy CMB measurements, such as those with the Planck satellite or planned balloon-based experiments, which could prove or disprove our conclusions.

Cosmic microwave background (CMB) radiation is characterized by well-established scales, the 2.7 K temperature of the Planckian spectrum and the 10-5amplitude of the temperature anisotropy. These features were instrumental in indicating the hot and equilibrium phases of the early history of the Universe and its large-scale isotropy, respectively. We now reveal one more intrinsic scale in CMB properties. We introduce a method developed originally by Kolmogorov, which quantifies a degree of randomness (chaos) in a set of numbers, such as measurements of the CMB temperature in a given region. Considering CMB as a composition of random and regular signals, we solve the inverse problem of recovering of their mutual fractions from the temperature sky maps. Deriving the empirical Kolmogorov’s function in the Wilkinson Microwave Anisotropy Probe’s maps, we obtain the fraction of the random signal to be about 20 per cent; i.e., the cosmological sky is a weakly random one. The paper is dedicated to the memory of Vladimir Arnold (1937–2010).