1. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 1 Практические приложения фундаментальной теории Д.ф.-м.н. Сергей М. Копейкин Университет штата Миссури, США

2. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 2 SIM SIM PlanetQuest is designed as a space-based 9-m baseline optical Michelson interferometer operating in the visible waveband. This mission will open up many areas of astrophysics, via astrometry with unprecedented accuracy. Over a narrow field of view (1°), SIM aims to achieve an accuracy of 1 µas in a single measurement.

3. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 3 OBSS OBSS is an astrometric satellite designed to determine with unprecedented accuracy the positions, distances, and motions of a billion stars within our galaxy. It is a collaborative effort between the U.S. Naval Observatory and several other institutions. OBSS will measure stellar positions to less than 10 microarcseconds. (= the width of a typical strand of human hair from a distance of 650- 900 miles.)

4. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 4 GAIA During its operational lifetime, Gaia will continuously scan the sky, roughly along great circles, according to a carefully selected pre-defined scanning law. The characteristics of this law, combined with the across-scan dimension of the astrometric fields of view, result in the above pattern for the distribution of the predicted number of transits on the sky in ecliptic coordinates. The fixed solar aspect angle (45 degrees), i.e., the angle between the Sun and Gaia's spin axis, favours observations of stars around ecliptic latitudes plus and minus 90 - 45 = 45 degrees. Gaia will scan the sky continuously according to a pre-defined pattern. The satellite will rotate around its spin axis at a rate of 60 arcsec/s, equivalent to a spin period of 6 hours. The spin axis itself precesses at a fixed angle of 45 degrees to the Sun. The line of sight of the two astrometric instruments are separated by the 'basic angle', which is 106.5 degrees.

5. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 5 JASMINE JASMINE is abbreviation of the position astronomical satellite plan (Japan Astrometry Satellite Mission for INfrared Exploration). It will surwey the Milky Way and its buldge in the infrared band around 1 milli-micron, measure positions, distances, and proper motion of several hundred million stars at high accuracy approaching 10 microarcsecond.

6. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 6 Square Kilometer Array (SKA) The SKA will be an interferometric array of individual antenna stations, synthesizing an aperture with diameter of up to several 1000 kilometers. The SKA is a new generation radio telescope that will be 100 times as sensitive as the best present-day instruments. It will unlock information from the very early Universe and, using novel capabilities, be able to undertake entirely new classes of observation including VLBI with a microarcsecond resolution.

7. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 7 VERA VERA (VLBI Exploration of Radio Astrometry) is the first VLBI array dedicated to phase- referencing astrometry. S269 (Sharpless 269) is a massive star forming region toward constellation Orion. VERA has successfully measured its trigonometric parallax of 189 +/- 8 micro-arcsecond. This is the smallest parallax ever measured, corresponding to a source distance to 17,250 light year.

8. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 8 Gravitational Light Deflection by Multipoles in Cosmology Object: Abell 2218 Type: Giant Arc Image credits: J.-P. Kneib, R.S. Ellis, I. Smail, W.J. Couch, R.M. Sharples

9. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 9 Gravitational Light-Ray Deflection by Planetary Multipoles Gravitational Field Model Propagation of Light Model Deflection Patterns Interpretation of Observations and Gravitational Physics

10. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 10 Gravitational Field Model 1.Linearized general relativity 2.The harmonic gauge 3.The gravity field equation (c = 1 units)

11. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 11 The metric, the waves, and the multipoles the retarded time:

12. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 12 The Light-ray Perturbations The unperturbed equation of light ray The perturbed equation of light ray The Christoffel symbols The wave vector decomposition The light-ray geodesic

13. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 13 The Unperturbed Light-ray Trajectory

14. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 14 The light-ray deflection angle Time argument is the retarded time: s = t - r The slowly evolving "Coulomb component" of the gravitational field can not transfer information about position of the source of the gravitational field with the speed (of gravity) faster than the speed of light.

15. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 15 The Minkowski diagram of the interaction of gravity and light Observer Observer’s world line Star’s world line Planet’s world line Future gravity null cone Light null cone

16. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 16 The bi-characteristic interaction of gravity and light in general relativity Any type of gravitational field obeys the principle of causality, so that even the slowly evolving "Coulomb component" of the gravitational field can not transfer information about position of the source of the gravitational field with the speed faster than the speed of light.

17. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 17 Retardation of gravitational field in a light-ray deflection experiment Observer and planet are at rest Planet moves uniformly relative to observer

18. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 18 The deflection equations and the central inverse mapping

19. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 19 Snapshot deflection patterns Monopole Dipole Quadrupole

20. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 20 Dynamic deflection patterns Circle Cardioid Caley’s sextic March 21, 1988 Treuhaft & Lowe DSN JPL NASA September 8, 2002 Fomalont & Kopeikin VLBA+MPfRA Not measured as yet SIM? SKA? Gaia? JASMINE? VERA?

21. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 21 Measuring the dipolar deflection of light. The «speed of gravity» experiment. Position of Jupiter taken from the JPL ephemerides Position of Jupiter determined from the gravitational deflection of light by Jupiter Measured with 20% of accuracy, thus, proving a direct evidence that the null cone is a bi-characteristic hypersurface (speed of gravity = speed of light) 10 microarcseconds = the width of a typical strand of a human hair from a distance of 650 miles.

22. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 22 Gravitational deflection maps gravity field Optical position of Jupiter Gravitational position of Jupiter measured from the light deflection of stars

23. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 23 The «Speed of Gravity» Experiment Edward Fomalont (NRAO) (observation + data processing) Sergei Kopeikin (UMC) (theory + interpretation) The Team

24. 24 The Very Long Baseline Array Effelsberg, Germany Green Bank, Virginia

25. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 25 Basic Interferometry in about one minute for ‘sufficiently strong’ radio sources (S/N>1)

26. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 26 VLBI Limitations to Positional Accuracy Location of Radio Telescope Position on earth (~ 1 cm) Earth Rotation and orientation (~ 5 cm) Time synchronization (~ 50 psec) Array stability (~ 5 cm) Propagation in troposphere and ionosphere Very variable in time and space (~ 5 cm in 10 min) CONVERSION FACTORS: 1 cm = 30 psec = 300 microarcsec 0.03cm = 1 psec = 10 microarcsec

27. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 27 The Experiment

28. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 28 Motion of Jupiter

29. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 29 Source Structure Stability Over Experiment 2 mas ticks Source Stability

30. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 30 Factor of 3 increase in accuracy using 2 calibrators Effect of Troposphere Two calibrators – phase-referencing technique. Reconstruction of the wave front with accuracy 10 microarcseconds – a human hair at 500 miles !

31. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 31 residualresidual Measured Delays for Each Source

32. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 32 Residual Delays for J0842 Compared on Several Days for a Few Baselines

33. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 33 Jupiter’s retarded position from the gravitational time delay (green points) versus Jupiter’s retarded position from JPL ephemeris (magenta) magnetosphere

34. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 34 Results of Experiment

35. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 35 Is the large-scale structure of spacetime shaped by relic gravitational waves? & How to detect them ? Detection of Ultra-Long Gravitational Waves via Astrometry Sergei M. Kopeikin and Valeri V. Makarov

36. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 36 Short and Ultra-Long Gravitational Waves Orbiting binary stars, supernova explosions, coalescence of binary neutron stars and encounters of stars in dense clusters are thought to generate ripples in spacetime propagating far from the source (~ 1/r law). They cause tensor-type 2 transverse deflection of light rays from background sources (quasars, masers, etc.). As a rule, General Relativity predicts negligibly small astrometric effects from these sources (Kopeikin et al, Phys. Rev. D, 1999, 2001, 2002). Plane long-period cosmological waves, on the other hand, may be detectable at the (sub) μas level of accuracy via specific patterns of proper motions of light sources, expressed mostly by vector spherical harmonics of a second order. secular aberrationresidual rotationgravitational waves (quadrupole modes)

37. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 37 Patterns of apparent proper motions of quasars Simulated proper motion field of distant quasars induced by a set of plane cosmological waves. Gravitational waves of different phase and orientation superpose to make up a complicated vector field pattern mostly represented by several vector spherical harmonics of second order. The amplitude of the effect depends on the dimensionless strain of the GW packet. Such a pattern, if it exists, could be determined by precision global astrometry at a high signal-to-noise ratio if the astrometric grid includes > 100 quasars.

38. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 38 Differential Wide-Angle Astrometry of Quasars Detection of the apparent motion of a very distant light source induced by the propagating long wave can be done with an astrometric instrument capable of (sub) microarcsecond relative measurements over wide angles (~ 90°)

39. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 39 Tentative design Two Michelson interferometers with articulating siderostats and mutually orthogonal baseline vectors, plus two guide interferometers to monitor attitude changes by locking on guide stars, tied into a rigid external metrology system

40. 1-я школа по астрометрии, Москва, Октябрь 22-26, 2007 40 Triangulation grid of quasars 6 quasars separated by ~ 90 degrees make a simple celestial triangulation grid >100 quasars needed to investigate the global pattern of gravitational waves Since only relative proper motions are required, a set of independent triangulation sextuplets is sufficient Proper motion amplitude proportional to frequency ω and dimensionless stress h Estimate: primordial gravitational waves of h = 3·10 -9 at ω = 10 -2 yr -1 or of h = 3·10 -11 at ω = 1 yr -1 can be detected by the global astrometric triangulation Conclusions: - alternative detection of GW; - the method is feasible; - deeper study is required.