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

2. 2 Accuracy of astrometric observations 1 mas 1 µas 10 µas 100 µas 10 mas 100 mas 1“ 10” 100” 1000” 1 µas 10 µas 100 µas 1 mas 10 mas 100 mas 1” 10” 100” 1000” 140015001700190020002100016001800 Ulugh Beg Wilhelm IV Tycho Brahe Hevelius Flamsteed Bradley-Bessel FK5 Hipparcos Gaia SIM ICRF GC naked eye telescopes space 140015001700190020002100016001800 Hipparchus 4.5 orders of magnitude in 2000 years further 4.5 orders in 20 years 1  as is the thickness of a sheet of paper seen from the other side of the Earth

3. 3 Relativity as a driving force for Gaia

4. 4 The IAU 2000 framework 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 BCRS GCRS Local RS of an observer

5. 5 Relativistic Astronomical Reference Systems particular reference systems in the curved space-time of the Solar system One can use any but one should fix one

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

7. 7 Local Reference System of an Observer 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. 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. 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. 9 Current accuracies of relativistic tests 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

10. 10 Why to test further? 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:

11. 11 Gaia’s goals for testing relativity

12. 12 Fundamental physics with Gaia Global testsLocal tests Local Positional Invariance Local Lorentz Invariance Light deflection One single  Four different  ‘s Differential solutions Asteroids Pattern matching Perihelion precession Non-Schwarzschild effects SEP with the Trojans Stability checks for  Alternative angular dependence Non-radial deflection Higher-order deflection Improved ephemeris SS acceleration Primordial GW Unknown deflector in the SS Monopole Quadrupole Gravimagnetic Consistency checks J_2 of the Sun

13. 13 Necessary condition: consistency of the whole data processing chain 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

14. 14 Example: consistency of the Gaia orbit L2L2 X Y Z Sun E 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)

15. 15 Global vs. local tests 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

16. 16 Global test: gravitational red shift 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

17. 17 Global test: gravitational red shift 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 We could be sensitive to for the secular drift Still unclear if technically feasible…

18. 18 Global test: local Lorentz invariance 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 standard Lorentz transformations }

19. 19 Global test: PPN  from light deflection 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

20. 20 Monopole gravitational light deflection body (  as)>1  as Sun 1.75  180  Mercury83 9 Venus493 4.5  Earth574 125  Moon26 5  Mars116 25 Jupiter16270 90  Saturn5780 17  Uranus2080 71 Neptune2533 51 Monopole light deflection: distribution over the sky on 25.01.2006 at 16:45 equatorial coordinates

21. 21 Monopole gravitational light deflection body (  as)>1  as Sun 1.75  180  Mercury83 9 Venus493 4.5  Earth574 125  Moon26 5  Mars116 25 Jupiter16270 90  Saturn5780 17  Uranus2080 71 Neptune2533 51 Monopole light deflection: distribution over the sky on 25.01.2006 at 16:45 equatorial coordinates

22. 22 Gravitational light deflection A body of mean density  produces a light deflection not less than  if its radius: Ganymede 35 Titan 32 Io 30 Callisto 28 Triton 20 Europe 19 Pluto 7 Charon 4 Titania 3 Oberon 3 Iapetus 2 Rea 2 Dione 1 Ariel 1 Umbriel 1 Ceres 1

23. 23 Global test: PPN  from light deflection Most precise test possible with Gaia Preliminary analysis: ESA, 2000; Mignard, 2001; Vecchiato et al., 2003: 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. 24 Global test: PPN  from light deflection 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!

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

26. 26 Global test: PPN  from light deflection 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 … IV.Alternative angular dependence: higher-order PPN/PPL terms V.Alternative angular dependence:  a (  -1 in General Relativity) VI.Alternative non-radial deflection patterns: vector spherical harmonics

27. 27 Global test: pattern matching in positions/proper motions I. Secular change of the secular aberration due to acceleration of the Solar system relative to the Galaxy. II. 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 III. Deflection pattern due to hypothetical unknown massive body within the Solar system - case with almost no proper motion: Gaudi & Bloom 2005

28. 28 Global test: acceleration of the solar system 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) O. Sovers,  1988: first attempts to use geodetic VLBI data Circular orbit about the galactic centre gives: O. Titov, S.Klioner, 2003-…: > 3.2  10 6 observations, OCCAM M.Eubanks, S.Klioner, …, 1992-1997: 1.5  10 6 observations,CALC/SOLVE 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.

29. 29 Local test: differential deflection due to Jupiter and Saturn 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 I.measure the light-deflection parameters γ for each of these planets (NOTE: this is independent of global solution) II.quadrupole light defection (Crosta, Mignard, 2004,…) III.measure the light deflection due to the gravimagnetic field induced by translational motion of the planets

30. 30 Local test: relativistic effects in asteroids Object Mercury42.98 8.840.390.21 7.00 Venus 8.62 0.060.720.01 3.39 Earth 3.84 0.061.000.02 0.00 Mars 1.35 0.121.520.09 1.85 I. Schwarzschild effects due to the Sun: perihelion precession Historically the first test of general relativity

31. 31 Perihelion precession (the first 20001 asteroids) Objectnumber Mercury42.98 8.840.390.21 7.00 Phaethon320010.13 9.011.270.8922.17 Icarus156610.06 8.311.080.8322.85 Talos5786 9.98 8.251.080.8323.24 Hathor2340 7.36 3.310.840.45 5.85 Ra-Shalom2100 7.51 3.280.830.4415.75 Cruithne3753 5.25 2.701.000.5119.81 Khufu3362 5.05 2.370.990.47 9.92 1992 FE5604 5.55 2.250.930.41 4.80 Castalia4769 4.30 2.081.060.48 8.89 Epona3838 2.72 1.911.500.7029.25 Cerberus1865 4.05 1.891.080.4716.09

32. 32 Perihelion precession (12.09.05: 253113) Objectnumber Mercury42.98 8.840.390.21 7.00 2004 XY6032.1425.630.640.8023.79 2000 BD1926.8324.020.880.9025.68 1995 CR19.9517.330.910.87 4.03 1999 KW46639122.0615.190.640.6938.89 2004 UL15.0613.961.270.9323.66 2001 TD4517.1213.300.800.7825.42 1999 MN18.4812.300.67 2.02 2000 NL1014.4511.800.910.8232.51 1998 SO16.3911.450.730.7030.35 1999 FK218595316.1911.380.740.7012.60 2004 QX211.05 9.971.290.9019.08 2002 AJ12910.70 9.791.370.9115.55 2000WO10712.39 9.670.910.78 7.78 2005 EP112.50 9.600.890.7716.19 Phaethon320010.13 9.011.270.8822.17

33. 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. 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. 35 Maximal „post-Sun“ perturbations in meters 20000 Integrations over 200 days

36. 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 better with Gaia Rigorous theoretical analysis still has to be done… Local test: relativistic effects in asteroids

37. 37 Global/local tests: improve ephemeris and redo 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)

38. 38 Gaia provides the ultimate test for the existing of black holes? Fuchs, Bastian, 2004: Weighing stellar-mass black holes in binaries Astrometric wobble of the companions (just from binary motion) V(mag)  (  as) Cyg X-1928 V1003 Sco GROJ1655-40 1716 V616 Mon A0620-00 1816 V404 Cyg GS2023+338 1950 V381 Nor XTEJ1550-564 2018 Already known objects: Unknown objects, e.g. binaries with “failed supernovae” (Gould, Salim, 2002) Gaia advantage: we record all what we see!

39. 39 Search for the optimal strategy for Gaia 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”: