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International Centre for Theoretical Physics on the Dermination of The IC/90/316 R INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ON THE DERMINATION OF THE HUBBLE CONSTANT V.G. Gurzadyan V.V. Harutyunyan and A.A. Kocharyan INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1990 MIRAMARE- TRIESTE IC/90/316 International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ON THE DETERMINATION OF THE HUBBLE CONSTANT • V.G. Gurzadyan ** International Centre for Theoretical Physics, Trieste, Italy, V.V. Harutyunyan and A.A. Kocharyan Department of Theoretical Physics, Yerevan Physical Institute, 375036 Yerevan, USSR. ABSTRACT The possibility of an alternative determination of the the distance scale of the Universe and the Hubble constant based on the numerical analysis of the hierarchical nature of the large scale Universe (galaxies, clusters and superclusters) is proposed. The results of computer experiments performed by means of special numerical algorithm are represented. MIRAMARE - TRIESTE October 1990 * Submitted for publication. ** Permanent address: Department of Theoretical Physics, Yerevan Physical Institute, 375036 Yerevan, USSR. Many powerful methods are developed for determination of the distance scale of the Universe and thue to obtain the Hubble constant. Much efforts have been Bade, particularly for analyzing the dynamical characteristics of nearby galaxies and clusters (local test); fron the data on corresponding peculiar velocities and our motion respect to the Microwave background the value of Hubble ratio can be estimated. However, e.g. the data for galaxies on distances D ^ 35 Mpc; as is well known^ have lead to controversial results: 101±2 km s Hpc (for 600 "best observed" galaxies) (de Vaucouleurs and Peters,1984) and 52*2 km B Hpc" (Tammann and Sandage, 1985). The reason of thie controversy can be connected with the estimation of contribution of Local velocity anomaly, i.e. the infall of the Local Group toward the Virgo Cluster (Virgocentric flow) (Tully, 1988). Rather effective is also the determination of Hubble ratio by means of IR Tully-Fisher empirical relation, i.e. the infrared magnitude of the galaxy/H 1 velocity width dependence. Though the validity of TF relation is established also for the blue band and even its non-sensitivity on galaxy morphology is shown {Aaronson and Mould, 1983; Aaronson et al, 1986; Botinelli et al, 1988; and references therein), the role of number of selection effects (isophotal diameters, surface brightness of galaxies, Malmquist bias, etc) does remain crucial. Evidently the latter fact ie a typical feature of any empirical law. Below we propose a possibility of determination of Hubble constant without making use of any empirical law and by means of observational information not only of nearby galaxies but that of much farther ones (cf. Lynden-Bell's (1977)method concerning the dynamical of double quasars with superluminar velocities ). The idea of the method is based on one of main properties of the matter distribution of the observed Universe - its hierarchical nature. A special algorithm developed in our recent paper (Gurzadyan, Harutyunyan and Kocharyan, 1990) for statistical investigation of large scale Universe just via construction of hierarchy of subsystems to a given system. The initial problem is as follows: the description of the -2- global dynamics of an hierarchical system proceeding from the information on spatial and velocity distributions of the particles (or a United part of this information). Let ue give the mathematical definition of the problem (for details see (Gurzadyan, Harutyunyan and Kocharyan,1990). Assume N particlee given in R with coordinates and velocities (x,v)eR as well as parameters \eA describing the internal properties of the particles. He define a bounded system of AcN particles respect to ordinarity classes * (x.v.X) if c dc c : RxA - B , ceE and 3 c<=R such that for V i«=A Mention that there exiBts a function via vhich to each system is made to correspond a point in E . The problem is solved by means of the following simple algorithm: 1. The set of M particles is splitted into minimal number of subsets; 2. The formed subsystems are reduced to characteristic points; 3. The procedure is continued until trivial splitting is found. Based on this scheme the initial N particle system is reduced to another n-particle one. The investigation of the latter just gives the information on the global dynamics of the initial system. Consider now the case when N systems are participating in a global flow (e.g. of a Hubble type) of: Let L. particles from each of them have masses M. ., coordinates and velocities x.,v. (l^i^N, l<j^L.). All those data except N and H are initial for our algorithm. Replacing each system by a characteristic point with a coordinates and velocities of the center of inertia. Whence one has „ new , .new H.-z. / ±. Ae a result of a number of numerical experiments we have obtained 0.9 < H./H < 1.1. -3- The inaccuracy appears due to the fact that certain particles can be nenber of more than one eyeten. This inaccuracy in principle can be diminished if the "additional" particlee are including with a coefficient less than one. For the experiment represented on Figuree 1-7 the initial data has been as follows: N=5, L.^50-60, M. .=sl. 1 1J ACKNOWLEDGMENTS One of the authors (V.G.G.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste. -4- REFERENCES. Aaronson M., Mould J. 1983 Ap.J.,£65,l. Aaronson M. , Bothun G.D.,Mould J., Huchra J., Schonner B.A., Cornell M.E. 1986 Ap.J-,3O3, 536. Botinelli L. , Gouguenheim L., Teerrikorpi P. 1988 Astr.Ap.,196,17. de Vaucouleurs G., Peters W.L. 1984 Ap.J.,287, 1. Gurzadyan V.G., Harutyunyan V.V., Kocharyan A.A. (in press). Lynden-Bell D. 1977 Nature, 270, 396. Tamann G.A. , Sandage A. 1985 Ap. J. ,^94, 81. Tully R. in: Large Scale Motions in the Universe: A Vatican Study Week; ed. V.C.Rubin, G.V.Coyne, Vatican, 1988. Figure Captione. Fig.l. The initial pattern of the galaxy distribution inveetigated respect to the existence of subsystems. The radix of circles indicate the distance from the observer in logarithmic scale; the radial lines-the peculiar velocities of galaxies in the sane scale. Fig.2-6. The separated clusters of galaxies. Fig.7. The global dynamics of clusters of galaxies: the circles indicate their centers of inertia. -6- Fig.l -7- Fig. 2 Fig. 3 -8- Fig. 4 Fig.5 -9- Fig. 6 Fig. 7 -10- T Starapato in proprio nella tipografia del Centro Internazionale di Fisica Teorica.
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