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Relativity and microarcsecond astrometry

Sergei A.Klioner

Lohrmann-Observatorium, Technische Universität Dresden

The 3rd ASTROD Symposium , Beijing, 16 July 2006

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• New face of astrometry

• Relativity for microarcsecond astrometry

• Microarcsecond astrometry for relativity

Content

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New face of astrometry

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Accuracy of astrometric observations

1 mas

1 µas10 µas

100 µas

10 mas

100 mas

1“

10”

100”

1000”

1 µas10 µas

100 µas

1 mas

10 mas

100 mas

1”

10”

100”

1000”

1400 1500 1700 1900 2000 21000 1600 1800

Ulugh Beg

Wilhelm IVTycho Brahe

HeveliusFlamsteed

Bradley-Bessel

FK5

Hipparcos

Gaia

SIM

ICRF

GC

naked eye telescopes space

1400 1500 1700 1900 2000 21000 1600 1800

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

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Standard presentation of Gaia goals…

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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 RELATIVITYAPPLIED RELATIVITY

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Relativity for microarcsecond astrometry

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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

14 -1/ 5 10 yrG G

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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 RSof an observer

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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

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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:

t

observedrelated to the light raydefined in the BCRS coordinates

Klioner, Astron J, 2003; PhysRevD, 2004:

91 10 objects 30 years!s

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Sequences of transformations

• Stars:

0 0 0 0

(1) (2) (3) (4) (5)

( ) ( ), , , , ,t ts n k l l

• Solar system objects:

(1) (2,3) (6)

orbitkns

(1) aberration(2) gravitational deflection(3) coupling to finite distance(4) parallax(5) proper motion, etc.(6) orbit determination

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Aberration: s n

• Lorentz transformation with the scaled velocity of the observer:

2

1/ 22 2

2

1( 1) ,

(1 / )

1 / ,

21 ( , )o o

c v c

v c

w tc

nvn v

v x x

snv

• 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: 1 as 0.6 mm/so xs

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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

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Monopole gravitational light deflection

body (as) >1as

Sun 1.75 180

Mercury 83 9

Venus 493 4.5

Earth 574 125

Moon 26 5

Mars 116 25

Jupiter 16270 90

Saturn 5780 17

Uranus 2080 71

Neptune 2533 51

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

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Monopole gravitational light deflection

body (as) >1as

Sun 1.75 180

Mercury 83 9

Venus 493 4.5

Earth 574 125

Moon 26 5

Mars 116 25

Jupiter 16270 90

Saturn 5780 17

Uranus 2080 71

Neptune 2533 51

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

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Gravitational light deflection

• A body of mean density produces a light deflection not less than if its radius:

1/ 2 1/ 2

3650 km

1 g/cm 1μasR

Ganymede 35Titan 32Io 30Callisto 28Triton 20Europe 19

Pluto 7Charon 4Titania 3Oberon 3Iapetus 2Rea 2Dione 1Ariel 1Umbriel 1Ceres 1

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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

a bnk

d 2. the standard gravitational lens limit:

, a d b d Both schemes fail for Gaia! A combination of both is needed

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Parallax and proper motion: k l l0, 0, 0

• All formulas here are formally Euclidean:

0 0 0

( ) ( ) ( ), ,

| ( ) ( ) | | ( ) |

( ) ( ) ( ) ( )

o o s e s e

o o s e s e

s e s e s e e e

t t t

t t t

t t t t t

x X X

x X X

X X V

k l

• Expansion in powers of several small parameters:

1 AU | ( ) |,

| ( ) | | ( ) |

,

s e

s e s e

t

t t

0

V

X X

k l l l

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Relativistic description of the Gaia orbit

L2 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

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Relativistic description of the Gaia orbit

Real orbit in co-rotating coordinates:

L2

L2 X

Y

Z

Sun E

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Relativistic description of the Gaia orbit

Relativistic effects for the Lissajous orbits around L2 (Klioner, 2005)

Example: Differences between position for Newtonian and post-Newtonianmodels in km vs. time in days

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Relativistic description of the Gaia orbit

Deviations grow exponentially for about 250 days:

Log(dX in km) Log(dV in mm/s)

NewtonS

S+ES+E+JS+E+M

Optimal force model can be chosen…S – Sun

Bodies in the post-Newtonian force: J – Jupiter E – Earth M – Moon

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Relativistic description of the motion of sources

( cty) ( cty)e ( )a AU e ( )i Object

Mercury 42.98 8.84 0.39 0.21 7.00

Venus 8.62 0.06 0.72 0.01 3.39

Earth 3.84 0.06 1.00 0.02 0.00

Mars 1.35 0.12 1.52 0.09 1.85

Schwarzschild effects due to the Sun: perihelion precession

Historically, the first test of general relativity

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Perihelion precession (the first 20001 asteroids)

( cty) ( cty)e ( )a AU e ( )i Object number

Mercury 42.98 8.84 0.39 0.21 7.00

Phaethon 3200 10.13 9.01 1.27 0.89 22.17

Icarus 1566 10.06 8.31 1.08 0.83 22.85

Talos 5786 9.98 8.25 1.08 0.83 23.24

Hathor 2340 7.36 3.31 0.84 0.45 5.85

Ra-Shalom 2100 7.51 3.28 0.83 0.44 15.75

Cruithne 3753 5.25 2.70 1.00 0.51 19.81

Khufu 3362 5.05 2.37 0.99 0.47 9.92

1992 FE 5604 5.55 2.25 0.93 0.41 4.80

Castalia 4769 4.30 2.08 1.06 0.48 8.89

Epona 3838 2.72 1.91 1.50 0.70 29.25

Cerberus 1865 4.05 1.89 1.08 0.47 16.09

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Perihelion precession (253113 asteroids)( cty) ( cty)e ( )a AU e ( )i Object number

Mercury 42.98 8.84 0.39 0.21 7.00

2004 XY60 32.14 25.63 0.64 0.80 23.79

2000 BD19 26.83 24.02 0.88 0.90 25.68

1995 CR 19.95 17.33 0.91 0.87 4.03

1999 KW4 66391 22.06 15.19 0.64 0.69 38.89

2004 UL 15.06 13.96 1.27 0.93 23.66

2001 TD45 17.12 13.30 0.80 0.78 25.42

1999 MN 18.48 12.30 0.67 0.67 2.02

2000 NL10 14.45 11.80 0.91 0.82 32.51

1998 SO 16.39 11.45 0.73 0.70 30.35

1999 FK21 85953 16.19 11.38 0.74 0.70 12.60

2004 QX2 11.05 9.97 1.29 0.90 19.08

2002 AJ129 10.70 9.79 1.37 0.91 15.55

2000WO107 12.39 9.67 0.91 0.78 7.78

2005 EP1 12.50 9.60 0.89 0.77 16.19

Phaethon 3200 10.13 9.01 1.27 0.88 22.17

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Maximal „post-Sun“ perturbations in meters

2 | |N Sun pNx x

1 2 3 4 5

0.5

1

5

10

50

0 0.2 0.4 0.6 0.8

0.01

0.1

1

10

100a

e

2 4 6 8

20

40

60

80

e

20000 Integrations over 200 days

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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…

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Microarcsecond astrometry for relativity

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Relativity as a driving force for Gaia

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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

14 -1/ 5 10 yrG G

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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:

5 81 4 10 5 10

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Gaia’s goals for testing relativity

2

6 7

4 5

7 8

10 10

10 10

10 10

a lot more...

J

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Fundamental physics with Gaia

Global tests Local 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

/G G

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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

2 6, 5 6, 8 6 /x y za a a as yr

4.2 1.5, 2.6 1.6, 6.1 2.3 / x y za a a as yr

0.2, 3.7, 2.1 / x y za a a as yr Circular orbit about the galactic centre gives:

O. Titov, S.Klioner, 2003-…: > 3.2 106 observations, OCCAM

M.Eubanks, …, 1992-1997: 1.5 106 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.

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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-1 9 28

V1003 ScoGROJ1655-40

17 16

V616 MonA0620-00

18 16

V404 CygGS2023+338

19 50

V381 NorXTEJ1550-564

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• Already known objects:

• Unknown objects, e.g. binaries with “failed supernovae” (Gould, Salim, 2002)

• Gaia advantage: we record all what we see!