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Testing Relativity with Space Astrometry Missions

Testing Relativity with Space Astrometry Missions. Sergei A.Klioner. Lohrmann-Observatorium, Technische Universität Dresden SKA/LISA/Gaia workshop, Birmingham, 31 March 2006. naked eye. telescopes. space. 0. 1400. 1500. 1600. 1700. 1800. 1900. 2000. 2100. Hipparchus. Ulugh Beg.

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Testing Relativity with Space Astrometry Missions

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  1. Testing Relativity with Space Astrometry Missions Sergei A.Klioner Lohrmann-Observatorium, Technische Universität Dresden SKA/LISA/Gaia workshop, Birmingham, 31 March 2006

  2. 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

  3. Relativity as a driving force for Gaia

  4. 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

  5. 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

  6. The BCRS is suitable to model processes in the whole solar system Barycentric Celestial Reference System

  7. The version of the GCRS for a massless observer: The gravitational field of external bodies is represented only in the form of relativistic tidal potentials. Local Reference System of an Observer • the BCRS-induced tetrad is the local coordinate basis at the origin of that • reference system… • Modelling of any local phenomena: • observation, • attitude, • local physics (if necessary)

  8. 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:

  9. 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

  10. 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?

  11. Gaia’s goals for testing relativity

  12. 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

  13. Any kind of inconsistency is very dangerous for the quality and reliability of • the estimates • The whole data processing and all the auxiliary information should be • assured to be compatible with the PPN formalism (or at least GR) • planetary ephemeris: coordinates, scaling, constants • Gaia orbit: coordinates, scaling, constants • astronomical constants • ??? • Monitoring of the consistency during the whole project Necessary condition: consistency of the whole data processing chain

  14. Z Y E L2 X Sun Z Y • Gaia have very tough requirements for the accuracy of its orbit: • 1-2 mm/s in velocity • (this allows to compute aberration with an accuracy of 1 as) • Example of the non-Schwarzschild relativistic effects for a Lissajous orbit the Lagrange point L2 over 200 days (km) Example: consistency of the Gaia orbit

  15. It is natural to divide all tests into two groups: • global tests • are related to the global solution • should use the whole Gaia data or at least as much as possible • local tests • special additional solutions (e.g. differential or orbital ones) • relatively small amount of data Global vs. local tests

  16. Depending on the final design and clock synchronization mode • it could be possible to test the gravitational red shift of the on-board clock • (Local Positional Invariance) • Currently, the best accuracy for the red shift comes from the GP-A: 10 –4 • (Vessot, 1979) • Several dedicated and semi-dedicated missions were cancelled Global test: gravitational red shift

  17. The mean rate of the proper time on a Lissajous orbit is different • from Terrestrial Time only • by 4 ×10 –12 • Cancellation: lower potential and larger velocity than on the Earth • The gravity term is still 6 ×10 –10 Global test: gravitational red shift • We could be sensitive to for the secular drift • Still unclear if technically feasible…

  18. } standard Lorentz transformations • Mansouri & Sexl (1977) suggested a test framework against which • one can test special relativity • Robertson (1949) discussed similar ideas • Lorentz transformations with additional numerical parameters • Many experiments can be interpreted in terms of constrains • on those parameters: e.g. Michelson-Morley and similar • The idea is to use Gaia data to check • if the special-relativistic formula for aberration is correct Global test: local Lorentz invariance

  19. Several kinds of gravitational fields deflecting light at the 1 muas level • monopole field • quadrupole field • gravitomagnetic field due to translational motion • gravitomagnetic field due to rotational motion Global test: PPN  from light deflection

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

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

  22. 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

  23. Most precise test possible with Gaia Preliminary analysis: ESA, 2000; Mignard, 2001; Vecchiato et al., 2003: Global test: PPN  from light deflection • Advantages of the Gaia experiment • optical, • deflection (not Shapiro), • wide range of angular distances, • full-scale simulations of the experiments • Problems with some of the „current best estimates“ of  • 1. special fits of the post-fit residuals of a standard solution • (missed correlations lead to wrong estimates of the uncertainty); • 2. no special simulations with simulated data to check what kind • of effects we are really sensitive to

  24. Specific Gaia-related problems in the test: • Correlations: • parallax zero point (90%) • special kinds of systematic errors in the velocity of the satellite • … • Special care should be taken with the stability of the estimate: • barely undetected binaries, • source structure and stability, • … • A series of global deflection tests! Global test: PPN  from light deflection

  25. Main experiment: one single  for all deflecting bodies. • highest accuracy expected • other bodies (Jupiter) de-correlate  and parallaxes • Individual  for each deflecting body (at least: Sun, Jupiter, Earth) • Jupiter • Earth • Saturn • …important since this can be interpreted in terms of Equivalence Principle Global test: PPN  from light deflection

  26. III. Stability check: dependence of  on various parameters • data divided into several time spans • linear drift in  (equivalent to linear drifts in M and/or G) • dependence on the brightness • dependence on the angular distance to the Sun • … • Alternative angular dependence: higher-order PPN/PPL terms • Alternative angular dependence: a • (-1 in General Relativity) • VI. Alternative non-radial deflection patterns: vector spherical harmonics Global test: PPN  from light deflection

  27. Secular change of the secular aberration due to acceleration of the Solar system relative to the Galaxy. • Deflection on very low frequency gravitational waves: • - constrain the flux at 10-7 to 10-8 Hz • - detailed sensitivity study: to be done • similar study done for VLBI: Pyne et al. 1996, 1997 • Deflection pattern due to hypothetical unknown massive body • within the Solar system • - case with almost no proper motion: Gaudi & Bloom 2005 Global test: pattern matching in positions/proper motions

  28. 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 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. O. Sovers, 1988: first attempts to use geodetic VLBI data M.Eubanks, S.Klioner, …, 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:

  29. The accuracy of ephemerides is not sufficient (by a factor of 100!) to predict • deflection with an accuracy of 1 as: exclude from the global solution. • Differential solution could allow one to • measure the light-deflection parameters γ for each of these planets • (NOTE: this is independent of global solution) • quadrupole light defection (Crosta, Mignard, 2004,…) • measure the light deflection due to the gravimagnetic field induced by translational motion of the planets Local test: differential deflection due to Jupiter and Saturn

  30. I. Schwarzschild effects due to the Sun: perihelion precession Historically the first test of general relativity Local test: relativistic effects in asteroids

  31. Perihelion precession (the first 20001 asteroids)

  32. Perihelion precession (12.09.05: 253113)

  33. I. Schwarzschild effects due to the Sun: perihelion precession Mignard, 2001; Hestroffer, Berthier, 2005: Preliminary results with limited number of sources and with perihelion advance only: Local test: relativistic effects in asteroids

  34. II. Non-Schwarzschild effects • Orbital consequences of the EIH equations for asteroids are still poorly known. • Especially interesting for resonant asteroids for which the relativistic effects of e.g. Jupiter can be enhanced Local test: relativistic effects in asteroids

  35. 20000 Integrations over 200 days Maximal „post-Sun“ perturbations in meters

  36. III. Special test: SEP with Trojan and other resonant asteroids • The effect is historically the first example of observable effect due to a violation of the Strong Equivalence Principle: (Nordtvedt, 1968) • shift of L4 and L5 by 1” for =1 • The effect is hidden in the PPN-EIH equations of motion • Orellana, Vucetich, 1988-1993: =-0.54±0.48 • 12 Trojans, 100-200 observations for each, accuracy 1”: • One can hope to do much betterwith Gaia • Rigorous theoretical analysis still has to be done… Local test: relativistic effects in asteroids

  37. A short-arc (5 years) ephemeris with highest possible accuracy is necessary • Observations relevant for the solar system ephemeris: • direct observations of the giant planets • indirect: from differential light deflection • indirect: from natural satellites • masses of hundreds of asteroids • (marginally important for the giant planets) Global/local tests: improve ephemeris and redo

  38. 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!

  39. The mission would survive without fundamental physics tests: • the tests cannot be “too heavy” so that they “disturb” the main goals… • But the tests are more than welcome and they are “for free”: Search for the optimal strategy for Gaia

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