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Relativity and microarcsecond astrometry

This symposium explores the new face of astrometry, focusing on the application of relativity in microarcsecond astrometry. Topics include the accuracy of astrometric observations, the significance of general relativity, and the current accuracies of relativistic tests. Additionally, the establishment of relativistic astronomical reference systems and the effects of gravitational light deflection are discussed.

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Relativity and microarcsecond astrometry

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  1. Relativity and microarcsecond astrometry Sergei A.Klioner Lohrmann-Observatorium, Technische Universität Dresden The 3rd ASTROD Symposium , Beijing, 16 July 2006

  2. New face of astrometry • Relativity for microarcsecond astrometry • Microarcsecond astrometry for relativity Content

  3. New face of astrometry

  4. naked eye telescopes space 0 1400 1500 1600 1700 1800 1900 2000 2100 Hipparchus Ulugh Beg 1000” 1000” 100” 100” Wilhelm IV Tycho Brahe Flamsteed 10” Hevelius 10” Bradley-Bessel 1“ 1” GC 100 mas 100 mas FK5 10 mas 10 mas Hipparcos further 4.5 orders in 20 years 1 mas 1 mas ICRF 100 µas 100 µas 10 µas Gaia 10 µas 1 µas SIM 1 µas 0 1400 1500 1600 1700 1800 1900 2000 2100 Accuracy of astrometric observations 4.5 orders of magnitude in 2000 years 1 as is the thickness of a sheet of paper seen from the other side of the Earth

  5. Standard presentation of Gaia goals…

  6. Newtonian models cannot describe high-accuracy • observations: • many relativistic effects are many orders of • magnitude larger than the observational • accuracy • space astrometry missions or VLBI would not work without relativistic modelling • The simplest theory which successfully describes all • available observational data: • APPLIED RELATIVITY Why general relativity? 

  7. Relativity for microarcsecond astrometry

  8. Several general-relativistic effects are confirmed with the following precisions: • VLBI ± 0.0003 • HIPPARCOS ± 0.003 • Viking radar ranging ± 0.002 • Cassini radar ranging ± 0.000023 • Planetary radar ranging ± 0.0001 • Lunar laser ranging I ± 0.0005 • Lunar laser ranging II ± 0.007 • Other tests: • Ranging (Moon and planets) • Pulsar timing: indirect evidence for gravitational radiation Current accuracies of relativistic tests

  9. BCRS GCRS Local RS of an observer • Three standard astronomical reference systems were defined • BCRS (Barycentric Celestial Reference System) • GCRS (Geocentric Celestial Reference System) • Local reference system of an observer • All these reference systems are defined by • the form of the corresponding metric tensors. • Technical details: Brumberg, Kopeikin, 1988-1992 • Damour, Soffel, Xu, 1991-1994 • Klioner, Voinov, 1993 • Soffel, Klioner, Petit et al., 2003 The IAU 2000 framework

  10. particular reference systems in the curved space-time of the Solar system Relativistic Astronomical Reference Systems • One can • use any • but one • should • fix one

  11. General structure of the model • s the observed direction • n tangential to the light ray • at the moment of observation •  tangential to the light ray • at • k the coordinate direction • from the source to the observer • l the coordinate direction • from the barycentre to the source •  the parallax of the source • in the BCRS • The model must be optimal: observed related to the light ray defined in the BCRS coordinates Klioner, Astron J, 2003; PhysRevD, 2004:

  12. Stars: Sequences of transformations • Solar system objects: (1) aberration (2) gravitational deflection (3) coupling to finite distance (4) parallax (5) proper motion, etc. (6) orbit determination

  13. Lorentz transformation with the scaled velocity of the observer: Aberration: s n • For an observer on the Earth or on a typical satellite: • Newtonian aberration 20 • relativistic aberration  4 mas • second-order relativistic aberration 1 as • Requirement for the accuracy of the orbit:

  14. Several kinds of gravitational fields deflecting light in Gaia observations at the level of 1 as: • monopole field • quadrupole field • gravitomagnetic field due to translational motion Gravitational light deflection: n  k

  15. Monopole light deflection: distribution over the sky on 25.01.2006 at 16:45 • equatorial coordinates Monopole gravitational light deflection

  16. Monopole light deflection: distribution over the sky on 25.01.2006 at 16:45 • equatorial coordinates Monopole gravitational light deflection

  17. A body of mean density  produces a light deflection not less than  • if its radius: Gravitational light deflection Pluto 7 Charon 4 Titania 3 Oberon 3 Iapetus 2 Rea 2 Dione 1 Ariel 1 Umbriel 1 Ceres 1 Ganymede 35 Titan 32 Io 30 Callisto 28 Triton 20 Europe 19

  18. k  n a b d  Both schemes fail for Gaia! A combination of both is needed Example of a further detail: light deflection for solar system sources Two schemes are available: 1. the standard post-Newtonian solution for the boundary problem: 2. the standard gravitational lens limit:

  19. All formulas here are formally Euclidean: Parallax and proper motion: k  l  l0, 0, 0 • Expansion in powers of several small parameters:

  20. Z Y E L2 X Sun • Gaia has very tough requirements for the accuracy of its orbit: • 0.6 mm/s in velocity • (this allows to compute the aberration with an accuracy of 1 as) Relativistic description of the Gaia orbit F. Mignard, 2003

  21. Z Y E L2 X Sun Real orbit in co-rotating coordinates: Relativistic description of the Gaia orbit L2

  22. Relativistic effects for the Lissajous orbits around L2(Klioner, 2005) Example: Differences between position for Newtonian and post-Newtonian models in km vs. time in days Relativistic description of the Gaia orbit

  23. Deviations grow exponentially for about 250 days: Log(dX in km) Log(dV in mm/s) Relativistic description of the Gaia orbit Newton S S+E S+E+J S+E+M Optimal force model can be chosen… S – Sun Bodies in the post-Newtonian force: J – Jupiter E – Earth M – Moon

  24. Schwarzschild effects due to the Sun: perihelion precession Historically, the first test of general relativity Relativistic description of the motion of sources

  25. Perihelion precession (the first 20001 asteroids)

  26. Perihelion precession (253113 asteroids)

  27. 20000 Integrations over 200 days Maximal „post-Sun“ perturbations in meters

  28. Gravitational light deflection caused by the gravitational fields • generated outside the solar system • microlensing on stars of the Galaxy, • gravitational waves from compact sources, • primordial (cosmological) gravitational waves, • binary companions, … • Microlensing noise could be • a crucial problem • for going well below 1 microarcsecond… Beyond the standard model

  29. Microarcsecond astrometry for relativity

  30. Relativity as a driving force for Gaia

  31. Several general-relativistic effects are confirmed with the following precisions: • VLBI ± 0.0003 • HIPPARCOS ± 0.003 • Viking radar ranging ± 0.002 • Cassini radar ranging ± 0.000023 • Planetary radar ranging ± 0.0001 • Lunar laser ranging I ± 0.0005 • Lunar laser ranging II ± 0.007 • Other tests: • Ranging (Moon and planets) • Pulsar timing: indirect evidence for gravitational radiation Current accuracies of relativistic tests

  32. Just an example… • Damour, Nordtvedt, 1993-2003: • Scalar field (-1) can vary on cosmological time scales so that it asymptotically vanishes with time. • Damour, Polyakov, Piazza, Veneziano, 1994-2003: • The same conclusion in the framework string theory and inflatory cosmology. • Small deviations from general relativity are predicted for the present epoch: Why to test further?

  33. Gaia’s goals for testing relativity

  34. Improved ephemeris Fundamental physics with Gaia Consistency checks Global tests Local tests Local Positional Invariance Differential solutions Pattern matching Local Lorentz Invariance Monopole Light deflection SS acceleration Quadrupole Primordial GW One single  Gravimagnetic Unknown deflector in the SS Four different ‘s Asteroids Stability checks for  Perihelion precession Non-Schwarzschild effects Higher-order deflection SEP with the Trojans Alternative angular dependence J_2 of the Sun Non-radial deflection

  35. Acceleration of the Solar system relative to remote sources leads to • a time dependency of secular aberration: 5 as/yr • constraint for the galactic model • important for the binary pulsar test of relativity (at 1% level) Global test: acceleration of the solar system O. Sovers, 1988: first attempts to use geodetic VLBI data Very hard business: the VLBI estimates are not reliable (dependent on the used data subset: source stability, network, etc) Gaia will have better chances, but it will be a challenge. M.Eubanks, …, 1992-1997: 1.5 106 observations,CALC/SOLVE O. Titov, S.Klioner, 2003-…: > 3.2 106 observations, OCCAM Circular orbit about the galactic centre gives:

  36. Fuchs, Bastian, 2004: Weighing stellar-mass black holes in binaries • Astrometric wobble of the companions (just from binary motion) Gaia provides the ultimate test for the existing of black holes? • Already known objects: • Unknown objects, e.g. • binaries with • “failed supernovae” • (Gould, Salim, 2002) • Gaia advantage: • we record all what we see!

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