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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
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
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 RELATIVITYAPPLIED RELATIVITY
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Relativity for microarcsecond astrometry
8
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
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, 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
17
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
19
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…
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 ± 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
32
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
34
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
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
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
20 18
• Already known objects:
• Unknown objects, e.g. binaries with “failed supernovae” (Gould, Salim, 2002)
• Gaia advantage: we record all what we see!