arXiv subjects
Publications and source records attributed to V. G. Gurzadyan.
Some points related to the exponential instability of N-body gravitating systems and which are misinterpreted in various papers are clarified. Exponential instability is a phenomenon essentially responsible for the relaxation, evolutionary, morphological and other properties of certain type of galaxies and star clusters.
The properties of the Cosmic Microwave Background (CMB) radiation must be different in flat, positively and negatively curved universes. This fact leads to a direct way of determining the geometry of the universe. The signature of the predicted effect of geodesic mixing, i.e., of the `chaotic' behavior of photon beams in negatively curved spaces peculiar to Anosov systems with strong statistical properties, has been detected while studying the COBE-DMR 4-year data \cite{GT}. This possible observation of the negative curvature of the universe suggests the need to search for more effective ways to analyze the CMB data expected from forthcoming high precision experiments. Information theory offers such a descriptor for the CMB sky maps - the Kolmogorov complexity - as well as provides novel insight into the problem of the loss of information and time asymmetry in a hyperbolic universe.
The relation between the thermodynamical and cosmological arrows of time is usually viewed in the context of the initial conditions of the Universe. It is a necessary but not sufficient condition for ensuring the thermodynamical arrow. We point out that in the Friedmann-Robertson-Walker Universe with negative curvature, k=-1, there is the second necessary ingredient. It is based on the geodesic mixing - the dynamical instability of motion along null geodesics in hyperbolic space. Kolmogorov (algorithmic) complexity as a universal and experimentally measurable concept can be very useful in description of this chaotic behavior using the data on Cosmic Microwave Background radiation. The formulated {\it curvature anthropic principle} states the negative curvature as a necessary condition for the time asymmetric Universe with an observer.
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.
The information theory approach is suggested to the Cosmic Microwave Background (CMB) problem for negatively curved homogeneous and isotropic Universe. Namely, the Kolmogorov complexity of anisotropy of spots in CMB sky maps is proposed as a new descriptor for revealing crucial cosmological information, particularly on the curvature of the Universe. Such profound descriptor can be especially valuable while analyzing the data of forthcoming space and ground based experiments MAP, Planck surveyor, CAT, etc.
The problem of the relative motion of the substructures of the Local Group of galaxies revealed via S-tree method, as well as of the velocity of the Local Group itself, is considered. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. Once the bulk motion of substructures is estimated, in combination with the observed CMB dipole we also consider the mean velocity of the Local Group itself. Assigning the Local Group the mean motion of its main substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)= (-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668 km/s towards l=265 and b=42. This estimation is in good agreement, within 1 sigma level, with the estimation of Yahil et al (1977).
The results of an analysis of the substructure of 1 degree field galaxies of the Virgo cluster by means of the S-tree technique developed by Gurzadyan et al, are represented. 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 of Cepheids in that spirals.
The geodesics followed by cosmic microwave background (CMB) photons show different behaviours depending on the geometry of space. Namely, the effect of `mixing geodesics' predicts a distinct signature in CMB maps: threshold-independent elongated anisotropy spots in negatively curved geometries. We have found statistically significant sign for spot elongation in the COBE four year maps. This can be a direct indication for the negative curvature of the Universe.
The S-tree method is used to estimate the redshift of the core of Coma cluster - $cz = 6953$ km s$^{-1}$ and dispersion $σ=949$ km s$^{-1}$. The existence of three subgroups of galaxies is revealed, one of them is associated with the cD galaxy NGC 4874, another - with NGC 4889. It is argued that these subgroups are 'galaxy associations', i.e. galactic dynamical entities moving through the main cluster. The non-stationarity of the dynamical processes ongoing in the Coma core is concluded.
The results of the analysis of the subclustering in a sample of ESO Nearby Abell Cluster Survey (ENACS) galaxy clusters, with data complemented from other studies, are presented. The analysis is performed by using the S-tree method enabling one to study the hierarchical properties of clusters, namely by the detection of the main physical cluster and of its subgroups. The results indicate: (a) systematically lower genuine cluster velocity dispersions than known from previous studies; (b) existence of 2-3 subgroups in each cluster. Due to certain properties of specific dynamical entities, we denote these subgroups as galaxy associations, which can become an essential challenge for formation mechanisms of galaxy clusters.
The problem of reconstruction of the 3D velocities of clusters of galaxies from the redshift distribution of galaxies of the cluster is formulated. Though numerical simulations show the impossibility of direct use of Ambartsumian's formula derived for the stellar systems because of the small number of objects in the clusters, an additional physical assumption on the form of the searched velocity distribution can lead to the possibility of obtaining the transverse velocity of the cluster. The accuracy of the proposed reconstruction procedure is estimated.
The existence of period-doubling bifurcations is shown for the Konishi-Kaneko map. The value of the control parameter $k_{\infty}$ corresponding to the transition to the chaotic phase is estimated, along with the Feigenbaum universal number. This type of facts can be crucial in diagnosis of chaos in stellar dynamics.
When considering the statistical properties of a bundle of cosmic microwave background (CMB) photons propagating through space, the effect of `mixing geodesics' appears with a distinct signature that depends on the geometry of space. In a Universe with negative curvature this effect is expected to produce elongated anisotropy spots on CMB maps. We used COBE-DMR data to look for such effect. Based on the analysis of a measure of eccentricity of hot spots it appears that there is a clear indication of an excess eccentricity of hot spots with respect to that expected from noise alone. This result must be interpreted with caution as this effect can be due in part to galactic emission. If the detected eccentricity of anisotropy spots can be attributed to the effect of mixing it implies the negative curvature of the Universe and a value of $Ω< 1$.
Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available data on two pulsars PSR 2129+1210A and PSR 2129+1209D seem to exclude the existence of a black hole, the presence of which was instead supported by recent Hubble Space Telescope data on surface brightness profile (Yanny et al. 1994). The fluctuations of the gravitational field caused by the stars of the system are enough to explain the acceleration observed for both pulsars. In the case of the Galactic center, additional data are needed for similar definite conclusions.
We report the results of an analysis of the hierarchical properties of the cluster of galaxies Abell 119. Observational data from the ESO Nearby Abell Cluster Survey (ENACS) are used, complemented by data from previous studies, while the analysis is performed with the S-tree method. The main physical system and its three subgroups with truncated Gaussian velocity distributions are identified; due to their remarkable physical features and possible cosmogonical mission we call these subgroups ``galaxy associations''. The mass centre of the core of main system is shown to coincide with the X-ray centre of the cluster. An alignment of the mass centres of the 3 galaxy associations is also shown.
As was shown before (Gurzadyan and Kocharyan, 1992, 1993ab) the statistical properties (exponential mixing) of motion of CMB photon beams in Friedmann Universe with negative curvature can have definite observable consequences including the decrease of the CMB anisotropy amplitude after the last scattering, distortion of images on CMB sky maps. Here we consider one more consequence concerning the behaviour of temperature autocorrelation function C(θ,β), where θis the modulation (separation) angle, and βthe observing beam effective angle. We prove that in the Universe with negative curvature any spectrum of perturbations at last scattering epoch becomes a scale-invariant by present time. It is also predicted that the temperature autocorrelation function should increase while obtained from measurements with small beam sizes within some mixing beam angle.