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 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” Ulugh Beg Wilhelm IV Tycho Brahe Hevelius Flamsteed Bradley-Bessel FK5 Hipparcos Gaia SIM ICRF GC naked eye telescopes space 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

5 Standard presentation of Gaia goals…

6 Why general relativity? 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 

7 Relativity for microarcsecond astrometry

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

9 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, Damour, Soffel, Xu, Klioner, Voinov, 1993 Soffel, Klioner, Petit et al., 2003 BCRS GCRS Local RS of an observer

10 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

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

13 Aberration: s  n Lorentz transformation with the scaled velocity of the observer: 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 Gravitational light deflection: n    k 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

15 Monopole gravitational light deflection body (  as)>1  as Sun 1.75  180  Mercury83 9 Venus  Earth  Moon26 5  Mars Jupiter  Saturn  Uranus Neptune Monopole light deflection: distribution over the sky on at 16:45 equatorial coordinates

16 Monopole gravitational light deflection body (  as)>1  as Sun 1.75  180  Mercury83 9 Venus  Earth  Moon26 5  Mars Jupiter  Saturn  Uranus Neptune Monopole light deflection: distribution over the sky on at 16:45 equatorial coordinates

17 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

18 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: d ab n k  2. the standard gravitational lens limit: Both schemes fail for Gaia! A combination of both is needed 

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

20 Relativistic description of the Gaia orbit L2L2 X Y Z Sun E 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) F. Mignard, 2003

21 Relativistic description of the Gaia orbit Real orbit in co-rotating coordinates: L2L2 L2L2 X Y Z Sun E

22 Relativistic description of the Gaia orbit Relativistic effects for the Lissajous orbits around L 2 (Klioner, 2005) Example: Differences between position for Newtonian and post-Newtonian models in km vs. time in days

23 Relativistic description of the Gaia orbit Deviations grow exponentially for about 250 days: Log(dX in km) Log(dV in mm/s) 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 Relativistic description of the motion of sources Object Mercury Venus Earth Mars Schwarzschild effects due to the Sun: perihelion precession Historically, the first test of general relativity

25 Perihelion precession (the first asteroids) Objectnumber Mercury Phaethon Icarus Talos Hathor Ra-Shalom Cruithne Khufu FE Castalia Epona Cerberus

26 Perihelion precession ( asteroids) Objectnumber Mercury XY BD CR KW UL TD MN NL SO FK QX AJ WO EP Phaethon

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

28 Beyond the standard model 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…

29 Microarcsecond astrometry for relativity

30 Relativity as a driving force for Gaia

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

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

33 Gaia’s goals for testing relativity

34 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

35 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, …, : 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.

36 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 GROJ V616 Mon A V404 Cyg GS V381 Nor XTEJ Already known objects: Unknown objects, e.g. binaries with “failed supernovae” (Gould, Salim, 2002) Gaia advantage: we record all what we see!