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ABSTRACTS
10-th International Gamow Summer School "Astronomy and beyond: Astrophysics, Cosmology and Gravitation, Cosmomicrophysics, Radio-astronomy and Astrobiology"
(Ukraine, Odessa, Chernomorka, 23-28 August, 2010) MEMORIAL SESSION
SERGEY ALEKSANDROVICH SNEGOV (1910-1994) ­ OUSTANDING PHYSICIST, COSMOLOGIST, ASTRONOMER AND WRITER ­ VISIONARY TO A 100-ANNIVERSARY FROM BIRTHDAY Pahomov A.G. PFUM, Moscow It is possible to judge a condition of an astronomical science on literary works of time. From Iliada and disseya of Homer we find out, that Ancient Greeks of the archaic period knew Orion, the She-bear, the Evening and Morning star. They already, in so early time, had concept of space, as certain ordered, harmonious device. XX century, past in an atmosphere of development , astrophysics and nuclear physics, star and anagalactic astronomy, became for us already a history. In epoch new computer and nanotehnology, celebrations currents and occult sciences, celebrations of the last century become covered by a luminous fog. How to keep for descendants the saved up luggage of scientific knowledge? Where to gather the information on a scientific picture of the world prevailing once? In the twentieth century intensively developed and the literary genre of science fiction ­ when writers was very popular, leaning(basing) on a condition of a science and engineering of time, tried to predict achievements of the far future. For the description of conquest of space our far descendants the writer needed to know not by hearsay about a condition of an astronomical science. S.A.Snegov was born in Odessa in 1910. Has acted(arrived) on physical and mathematical faculty of the Odessa university, studied textbooks and treatises in physics, studied products of old philosophers and new thinkers. In intervals between the academic works did(made) tests of literary creativity. After the termination(ending) of the Odessa university of S.A.Snegov has moved to Leningrad, has acted(arrived) on a factory "Pyrometer" on a post engineer ­ physics, continued to write verses and the novel, has conceived the dissertation in theoretical physics. After a nuclear epopee Sergey Snegov has decided to engage in science fiction. The success of the novel "People as gods" has forced to concentrate on fantastic products. Except for a clear statement and nuclears-physical ideas and representations, their projections to the far future ­ the writer freely appears in the novels and stories concepts of the metrics, the curved space, a phase corner of time ­ the separate attention is deserved with the astronomical picture of the world twisted in an exotic reality. The bright, colourful, juicy, realistic description of the star sky can teach many authors of popular articles and textbooks on astronomy. . .. .., .. , .., , . .

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PLENARY SESSION
.., .., .. , .. HST, , . , , , , . THE COSMIC MICROWAVE BACKGROUND: FROM GAMOW HYPOTHESIS TO PLANCK OBSERVATORY B. Novosyadlyj Astronomical Observatory of Ivan Franko National University of Lviv 45 years ago the cosmic microwave background (CMB) radiation, predicted by George Gamow, was detected. Such prediction and discovering have founded the new fundamental trends of astrophysics ­ physical cosmology and CMB astronomy, which are key now for our understanding of structure and evolution of the Universe. The short history of CMB astronomy from Gamow's hypothesis to Planck observatory as well as its main advantages will be presented in this review talk. .. . .. , . , , , . , . , , . . 1987? .. , 1987 . , . , . . . . ULTRA HIGH ENERGY COSMIC RAYS: PROTON MODEL Hnatyk B. Astronomical Observatory of Taras Shevchenko National University of Kyiv We analyze the recent results of measurement of the energy spectrum and chemical composition of Ultra High Energy Cosmic Rays (UHECRs) presented by AUGER, HIRES and Kascade-Grange collaborations. We show that observed fluxes and spectra of UHECRs in ankle region can be reasonably explained in the frame of a dip model with proton dominated UHECR flux. The dip in proton model is a result of relativistic proton energy losses via electron-positron pair creation in p-gamma interaction with CMB photons Meantime the chemical composition measurements are contradictory, mainly due to the strong dependence on unknown physics of EAS development at ultra high energies E>1018 eV.
1 2

..1, .. 1,2, ..1 . .. ,



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PROBLEMATIC ASPECTS OF EXTRA DIMENSIONS Maxim Eingorn and Alexander Zhuk Astronomical Observatory and Department of Theoretical Physics, Odessa National University, Odessa, Ukraine In Kaluza-Klein model with toroidal extra dimensions, we obtain the metric coefficients in a weak field approximation for delta-shaped matter sources. These metric coefficients are applied to calculate the formulas for frequency shift, perihelion shift, deflection of light and parameterized post-Newtonian (PPN) parameters. In the leading order of approximation, the formula for frequency shift coincides with well known general relativity expression. However, for perihelion shift, light deflection, time delay and PPN parameters, these expressions demonstrate good agreement with experimental data only in the case of ordinary three-dimensional space. This result does not depend on the size of the extra dimensions. Therefore, in considered multidimensional Kaluza-Klein models the point-like masses cannot produce gravitational field which corresponds to the classical gravitational tests. We also obtain the exact 5-D soliton solution with correct non-relativistic Newtonian limit. The energy momentum tensor for this solution has clear physical interpretation. However, the classical tests for this metric do not satisfy the experimental data. Therefore, considered multidimensional Kaluza-Klein models face a severe problem. .1, .1,2, .2 1 . .. 2 , , , , . , . . , , . , ( ), , , , .

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THE LAMBDA CDM CUSP/CORE PROBLEM Antonino Del Popolo Catania University, Italy I review the Cusp/Core problem, namely the discrepancy between simulations and observations concerning the density profile of galaxies and clusters. After discussing the N-body predictions concerning density profiles and the observational results, and the implication for the LambdaCDM model, I describe the possible solutions to the problem. I will describe how the cusp/ core problem can be solved by means of an analytical calculation taking into account the effect of ordered and random angular momentum, dynamical friction, and baryons adiabatic contraction (AC). NUMERICAL METHODS FOR MHD PROBLEMS IN ASTROPHYSICS S.G.Moiseenko SRI RAS, Moskow In my talk I plan to review some popular methods for numerical simulations of MHD astrophysical problems. I plan to say about Lagrangian and Eulerian approach in MHD, Finite difference methods, Smooth Particle Hydrodynamics method, Godunov-type methods. Basic operators method. Problem of div(B)=0 in numerical simulations. NEW LOOK AT THE NATURE OF ANOMALOUS PULSARS I.F.Malov Pushchino Radio Astronomy Observatory Anomalous X-Ray Pulsars (AXP), Soft Gamma-Ray Repeaters (SGR), Rotational Radio Transients (RRAT), Compact Central Objects (CCO) and X-Ray Dim Isolated Neutron Stars (XDINS) belong to different classes of anomalous objects with neutron stars as the central bodies. We have shown that AXPs and SGRs can be described by the drift model in the framework of the preposition on usual properties of the central neutron star (rotation periods P~ 0.01 - 1 sec and surface magnetic fields B ~ 1011 ­1013 G). Here we shall show that some differences of the sources under consideration will be explained by their geometry (particularly, by the angle between their rotation and magnetic axes). Probably there is the bimodality of anomalous pulsars. AXPs, SGRs and some radio transients belong to the population of aligned rotators with the angle between the rotation axis and the magnetic moment < 200. These objects are described by the drift model, and their observed periods are connected with a periodicity of drift waves. Other sources have ~ 900, and switching on 's and switching off's of their radiation are caused by accretion phenomena connected with a relic disc surrounding them. XDINS and CCOs are probably neutron stars with rather low magnetic fields at the surface of neutron stars. When an SNR around any CCO disappears a new XDINS is created. Other known models of "anomalous" pulsars are discussed.

.. . .. boch@sai.msu.ru , ( ), , . () . , 100 . . . . . SOLAR GAMMA RAYS: ACHIEVEMENTS, PROBLEMS, PROSPECTS Leonty I. Miroshnichenko N.V. Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, Troitsk, Moscow Region, 142190, Russia, leonty@izmiran.ru We present and critically discuss some latest data on solar gamma rays from the point of view of particle acceleration at/near the Sun and sounding of elemental abundances and dynamical properties of the Sun's atmosphere during solar flares. All those aspects are of fundamental interest for solar and star physics. They may have important implications on the understanding of solar atmospheric dynamics, particle acceleration in space plasmas and Galactic chemical evolution. The main points of consideration are following: nuclear aspects of interaction of accelerated particles (solar cosmic rays, SCR) with the Sun's atmosphere (cross-sections, dependence on FIP etc.); acceleration mechanisms for different nuclei (resonant mechanism for 3He ions?); coronal magnetic structure (loop model); gamma-ray spectroscopy; photosphere density models (density enhancement?); enhanced abundance of 3 in the photosphere (?); production of light and rare elements in so-called i-j interactions between accelerated and background nuclei. Interestingly, that concentration of 3He in flare-accelerated particles, as it was found earlier, may be enhanced by a factor of 1000 over its possible photospheric value. As to the latest observational findings (discoveries?), we separate amongst them: 1) effect of density enhancement (EDE) in the photosphere (several major flares); 2) evidence of essential enhancement of 3He abundance in the photosphere (flare of 20 January 2005); 3) localization of the gamma-ray sources (two RHESSI flares ­ 23 July 2002 and 28 October 2003); 4) timing of the flare evolution by gamma-ray fluxes in energy range above 90 MeV; 5) influence of solar flares on the lower solar atmosphere from the Na D absorption line measured by GOLF/SOHO. To our opinion, the role of i-j interactions

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in the production of gamma-ray lines in solar flares still remains poor-understood. Another actual problem is related to the long duration and large extension gamma ray events. We incline to consider such phenomena as serious evidence of multiple acceleration processes at/near the Sun. Cosmological consequence of solar gamma-ray studies is reduced to the conclusion of that typical abundance of light elements 7Li, 4He, 2H, and, especially, 3He may not be a good baryometer of the Universe... MAGNETIC FIELD OF THE EARTH: ECOLOGICAL ASPECT M.I.Orliuk, A.O.Romenets Institute of Geophysics NAS of the Ukraine, Kyiv, Ukraine orlyuk@igph.kiev.ua The magnetic field of the Earth which is analyzed as the ecological factor is the magnetic ecological field Becol. This field is considered as the sum of harmonic and distortion fields: Becol = Bh + Bd As harmonic magnetic ecological field (Bh) necessary to consider a sum of fields: Bh = Bn + Bl + Byv + Bs-d + Bm-d + BPp where Bn ­ a normal field of Earth; Bl ­ a magnetic field of lithosphere: Byv ­ a field of yearly variations; Bs-d ­ a field of solar-day's variation by intensity 10-40 nT concerning to season; Bm-d ­ a field of moon-day's variation by intensity of firsts nanotesla; BPp ­ a field of periodical pulsations. These fields, variations and pulsations are stable in space and time. To distortion magnetic ecological field (Bd) there is belonged a sum of fields, which are insignificant in space of magnetic heterogeneities of lithosphere (anomalies with wavelengths less 60 km including to anomalies of anthropogenic origin) and unstable in the time, irregular variations and pulsations of outer and anthropogenic origin. The decision of the problem of geomagnetic ecology reduces to solution of series tasks: 1) the researches of spatial-temporary structure of geomagnetic field and the compiling of maps of geomagnetic ecological field; 2) the research of vital-active rhythms and magnetic fields of individuals; 3) joint analysis of magnetic ecological field with biological rhythms of biosystems and individuals; 4) Studying of the mechanism of influence of the magnetic field on organic systems.
B B B B B B B B B B B B

archy, test lepton number conservation. Dark matter remains one of the biggest unsolved mysteries in modern science. Particle physics provides a possible explanation for non-baryonic dark matter in the form of weakly interacting massive particles (WIMPs). The most likely WIMP candidate is the neutralino, predicted by supersymmetry models. It is expected that WIMPs interact with matter producing low energy recoils, which can be detected by ultra-low background underground detectors. Search for both extremely rare processes require development of particle detectors with very low radioactive contamination, high energy resolution, very low energy threshold, containing certain (or variety of) elements. Development of next generation dark matter and double beta decay experiments is discussed. A range of effects beyond the standard model of particles: violation of fundamental conservation laws, Pauli principle, search for hypothetical particles and interactions can be realized by similar experimental technique. BOREXINO . . Borexino , 03680 , ( , - ) 1956 . . . , . ( 3) Borexino ­ , . - (). (278 -, C9H12) (10­17 / ). + ~ : e + p e + n, 1.8 ( 40K). 256 , . , , 9.9+4.1-3.4 (68% C.L.) 252.6 ·. 3.9(+1.6-1.3) /(100 ·). « » (Bulk Silicate Earth) « », , . 3 95%.

RARE NUCLEAR AND SUB-NUCLEAR PROCESSES: PHYSICS BEYOND THE STANDARD MODEL OF PARTICLES Fedor Danevich Institute for Nuclear Research, MSP 03680 Kyiv, Ukraine Observations of neutrino oscillations manifest the nonzero neutrino mass and provide important motivation for high sensitivity experiments to search for neutrinoless double beta decay. Investigations of this process could clarify nature of neutrino (Majorana or Dirac particle), determine the absolute value of neutrino mass and neutrino mass hier-

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- .. e ds 2 = N 2 c 2 dt 2 - F - 1 d R 2 - R 2 d 2 , =e/c2=const. , M m . p m R (m) = 2 , p 2 = 2 4 - 1>0 2 c c (1+p ) M 1 M2
p m m 1+p
2

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r= rg 1 - f 2 ( R) sin

f ( R) 2 ,
2

- 0 ( R) =

rg 2(1 - f 2 ( R))
32

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-

m

2

M, m Q , m d M p 1 M2
= ± dm m m
±

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0

( - sin ) . 2 , - -, -«», . , - m( R ) sin 2 , r= d =
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m( R ) = f ( R ) ( R ) . . 1. .. , .56, . 1914, 1969. 2. R.Kantowski, R.K.Sachs J. of Math. Phis. V.7 3, p. 443, 1966. 3. K.Bronnikov, I.Dymnikova // arxiv: 0705.2368v1[grgc] May 2007. 4. O.B.Zaskavskii // arxiv: gr-gc/00509043v2 Sept. 2005.
SCALAR FIELD MODELS OF DARK ENERGY WITH BAROTROPIC EQUATION OF STATE: PROPERTIES AND OBSERVATIONAL CONSTRAINTS B. Novosyadlyj, O. Sergijenko Astronomical Observatory of Ivan Franko National University of Lviv A dark energy is treated as a minimally coupled classical or tachyonic scalar fields with a time-varying pa-

8 ( R, ) r 2 e 2 . c4



p2 +1

<0.

, (M/m)0=M0/m0 . m0, M0 R=R0. (Q2=M2), R>R0 () Q2>M2. , , , , . , -. , .

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rameter of generelised linear barotropic equation-of-state (EoS). The 7-year WMAP data on CMB anisotropy, the Union dataset on Supernovae Ia and SDSS DR7 on galaxies space distribution are used for constraining of parameters of such dark energy model along with other cosmological ones. Using a Monte Carlo Markov Chain technique the posterior likelihoods are computed. It is shown that current density and EoS dark energy parameters are determined well as adiabatic sound speed, playing the role of early EoS parameter, is determined worse. Meanwhile, the obtained results give possibility to conclude that current data prefer the scalar field models of dark energy with increasing EoS parameter. Such dark energy recedes their repulsion properties that will predermine in future decelerated expansion and recolapse. We note also, that cosmological scalar field models with zero adiabatic sound speed as well as $\Lambda$-models (adiabatic sound speed equals -1) are not excluded yet by these observational data at enough high confidence level. .. , . - , , , : ) , , ) ' , ) , . - , " ", "". , ' , . " -" - , " " , . -

, , . .. " " , , , , . , : ­ . , .. " ", , " ". , , . , - , 1077 . : - , , , 10100. ASYMPTOTIC EXPANSIONS AND AMPLIFICATION OF GRAVITATIONAL LENS NEAR THE FOLD CAUSTIC A.N. Alexandrov, V.I. Zhdanov Kyiv National University, Ukraine We present two different methods that enable us to obtain approximate solutions of the lens equation near the fold caustic up to arbitrary degree of accuracy. We obtain "post-linear" corrections to the well known linear caustic approximation formula for the total amplification of two critical images of a point source. In order to obtain the non-trivial corrections we had to take into account the Taylor expansion of the lens equation near caustic up to the fourth order. The result has been used to obtain amplification of the extended Gaussian source in the above "post-linear" order. The amplification is reduced to the

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form containing three parameters. The modified amplification formula is applied to the Q2237+0305 gravitational lens system light curve fitting in the vicinity of the high amplification events (HAE). We show that introduction of some of the "post-linear" corrections reduces chi-squared by 30% and enlarges the fitting interval in case of known HAE on the light curve of the image C (1999). These corrections may be important for a precise comparison of different source models on account of observational data. ANTIGRAVITY IN GRAVITY: SOME EXAMPLES R.Plyatsko, O.Stefanyshyn, M.Fenyk Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of NAS of Ukraine, Lviv Using the Mathisson-Papapetrou (MP) equations we investigate the significantly nongeodesic highly relativistic motions of a spinning particles starting near the Schwarzschild and Kerr black holes. Some of these motions, namely circular, are described by the analytical relationships following directly from the MP equations in the Boyer-Lindquist coordinates, other of them, noncircular and nonequatorial, are calculated numerically. For realization of these motions the spinning particle must possess the obital velocity corresponding to the relativistic Lorentz factor much grater than 1. All considered cases of the spinning particle motion are within the framework of validity of the test-particle approximation. Different cases of the nonequatorial motions are computed and illustrated by the typical figures. All these orbits exhibit the effects of the significant gravitational repulsion that are caused by the spin-gravity interaction. The situation with a macroscopic test particle moving relative to a massive body with high Lorentz factor is not realistic. However, the highly relativistic values of this factor are usual in astrophysics for the elementary particles. We can expect the effects of the significant space separation of some highly relativistic particles with different orientation of spin. It would be interesting to study the possible role of the highly relativistic spin-gravity interaction in the jet formation.

SATELLITE OBSERVATIONS OF THE EARTH AND GLOBAL WARMING Leonid Zotov Sternberg Astronomical Institute Moscow State University Satellite methods of monitoring of the Earth take more and more essential place in the present-day geodesy and geophysics. They are especially important for monitoring of the environmental changes because of their global coverage. In recent decades many satellites were launched by American NASA and European ESA space agencies to monitor changes in ocean level, gravity field, water balance, atmospheric contents, heat transfer, precipitation, solar irradiation, etc. Huge amount of data obtained needs advanced methods of processing and careful interpretation. We present the results of multichannel singular spectrum analysis for the first time applied to altimetry, gravity, and tropospheric CO2 maps from Jason, GRACE, Aqua satellites. This method allow to distinguish seasonal and secular changes in CO2 contents, ocean level, gravity changes caused by hydrological cycles, icesheet melting, postglacial rebound. Sea level rise of ~3 mm/yr, tropospheric CO2 rise of ~1.7 ppm/yr and evident gravity decrease in some Antarctica, Greenland and mounting regions proofs that we are living in the epoch of global warming. Though paleoclimatic data says us that we are at the beginning of a new ice age, the observations contradict it. IPCC reports show us warming trends. Extreme climate events are more often observed. Scientific community is debating over the cause. Models show, that anthropogenic factors can be responsible. We will try to look at this problem both from the satellites orbit and from the ground, discuss the probable scenarios.

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COSMOMICROPHYSICS, COSMOLOGY AND GRAVITATION

11- .. ­ ­ 11- . , . .., .. 70 (), 2MIG ( ., 2010) (Veron+2010). 6000 / , 1- 2 . , , . ­ , , , , .. 2MIG. 70 , . ( 4 ). .. 1,2, ..1,2, .. 1 1 2 . .. , : , .. .

, C10024+17 [1]. EGRET- , 4 14 [2]. () . , , . . , . , , . . . , , . 1. Jee M.J., et al., 2007, ApJ, 661, 728 2. de Boer W., Sander C., Zhukov V., Gladyshev A.V., Kazakov D.I., 2005, A&A, 444, 51 : , , ., ., . , ­ . , , . 2.6- « ». , .

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GENERAL PROPERTIES OF SUBSTELLAR OBJECTS OF GALAXY Ya.Pavlenko MAO NASU I review of current understanding of the nature and physical properties brown dwarfs and exoplanets. Low mass objects form the most numerous, but poorly known yet population of our Galaxy. A brief historical excursion on the opening and the existing progress of investigation of these objects is carried out. New aspects of researches of brown dwarfs and other low mass objects in the framework of our project Mikrocosmophysics2. .. , .. . 72, . , . , 49010, antonstupka@mail.ru, kopteva-L@yandex.ru , : r (1) divj + t = 0. (1) : r2 2 r r (2) S = + jA/c - - E dVdt , 8 G 2

: i h >> 0 h . - 4- T = c 2 u u . hik (7) h = h - - . hkk h11 = h22 = h33 , hkk = h00 - 2 0 , k . (5) (6) (8) h00 c 2 /2 , (9) Ai - h0i c 2 . (7) h0i = h0i - i 0 , h00 = h00 - 2 0 0 , (8) (9) r r A = A + c 2 0 , = - c t 0 . (10) (10) (4) 0 - / c . (4) , = 0 , , A . THE DEPENDENCE OF ELLIPTICITY FROM RICHNESS FOR GALAXY CLUSTERS AND GROUPS E.Panko Odessa National University The ellipticities for real galaxy clusters and groups of PF Catalogue of and simulated structures with different richness are compared. The real structures with N>50 have significantly larger ellipticity than the modeling objects. The difference in dependences of ellipticities from richness for real and simulated structures is discussed.

r

r j ­ r , A ­ , r , E ­ r r (3) E =- 1 t A - . c

: r r (4) + t A A - c , (2). (2) , ,

r divE = -4 G ,

(5) (6) DISTINCTIVE PROPERTIES OF RIEMANNIAN SPACE-TIMES WITH OWN COMPLEX OR ISOTROPIC EIGENVECTOR V. P. Olyeynik Odessa I.I.Mechnikov National University, Odessa, Ukraine, olyeyvp@onu.edu.ua We investigate the properties of particle-like models, which Riemannian space-time is described by a metric tensor with the off-diagonal contributions. The feature of spaces with off-diagonal metric with a signature



r r t E = 4 Gj ,

. (5), (6). : : g = + h , h << 1 ;

c : / c << 1 ;

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( + - - -) or ( - + + + ) is that its own complex or own
null vector may be only tangential to a surface in this space. There is a class of coordinate systems in which such a surface is a plane of Minkowski. The metric tensor in these coordinates will contain only one off-diagonal contribution. The distinctive properties of particle-like models with certain angular contributions of the electromagnetic and fermion fields are studied. STRONG GRAVITATIONAL LENSING AS A KEY TO DETECT DARK MATTER: THE RESULTS OF MONITORING PG1115+080 AND Q2237+0305 Shulga V.M.1, Tsvetkova V.S.1, Minakov ..1, Dudinov V.N.1,2, Vakulik V.G.1,2, Kochetov A.Ye. 1,2, Smirnov G.V. 2, Sergeyev A.V. 1,2 Institute of Radio Astronomy of the NAS of Ukraine, 4 Krasnoznamennaya Str., Kharkov 61002, Ukraine Institute of Astronomy of the Kharkiv V.N.Karazin National University, 35 Sumskaya Str., Kharkov 61022, Ukraine

Q2237+0305:
1

..1, ..1,2 . .. 2

1 2

In execution of the Program "Cosmomicrophysics" during 2007-2009, we investigated gravitationally lensed quasars PG1115+080 and Q2237+0305 ­ the objects produced by the phenomenon of strong gravitational lensing, which is presently believed to be the most promising way to detect dark matter and to study its abundance and distribution at different spatial scales in the Universe. In particular, from monitoring of quadruply lensed quasar PG1115+080 during 2001-2006, microlensing events were detected in images A1 and A2, which can well explain the observed anomaly of their mutual brightness. This does not exclude a possibility for the dark matter substructures to exist, but imposes a constraint on the upper limit of the typical mass msub of such structures: msub < 104 M В M5. New values of the time delays obtained for PG 1115+080 have made it possible to substantially decrease the inconsistency between the Hubble constant estimates obtained with the time delay method, and those ones taken with other methods, in particular, with the most recent estimates made from Cepheids. Our result is a strong argument in favor of mass models close to isothermal, which suggest presence of the dark matter halo in the PG 1115+080 lens galaxy. Histograms of microlensing magnification probability distributions were built for the first time for macroimages of the Q2237+0305 quadruply lensed quasar based on all the available data of long-term observations. Comparison of the histograms with the probability distributions obtained in simulations shows that, at distances from the galaxy centre corresponding to positions of macroimages, the dark matter fraction in the Q2237+080 galaxy is probably much less than 50%.

Q2237+0305, , 2001-2008 . ( 100 ) 1.5- -22 ( , ). (V-I) R. (V-I) R, 6- 4- , a = 0.30 ± 0.03 r = 0.82 ± 0.10. - , . , - , . r = 0.3 ± 0.2 rE V 1.3 ± 0.5, = 1.4 ± 0.6 R = 1.5 ± 0.8 I. , , V 1997 2000 OGLE II [Vakulik et al., MNRAS, 382, 2, 2007]. GRAVITATIONAL LENS SYSTEM WITH TWO SPATIAL SCALES OF INHOMOGENEITIES Berdina L.A., Minakov A.A. Institute of Radio Astronomy, Kharkov laberdina@gmail.com In the work, focusing of the quasar radiation by the gravitational field of a galaxy having two spatial scales of mass distribution was considered. As an extended component, the mass distribution in a galaxy averaged over an interstellar distance was analyzed. Separate star ­ microlens randomly located along the propagation path of a radiation acted as a compact component of the inhomogeneities. Analysis of the effect was performed within the framework of the Sobolev method. Isophots of the source images were computed and estimates of magnification factor of image brightness were obtained.

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CORRELATION FUNCTION OF QUASARS IN REAL AND REDSHIFT SPACE FROM SDSS DR7 G. Ivashchenko, V.I. Zhdanov, A.V. Tugay Kyiv National University, Ukraine We determine the quasar two-point correlation function (2pCF) within the redshift interval 0.8