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GR tests and micro-arcsecond
light bending parameters by
global and differential Gaia
mesurements
Maria Teresa Crosta
Astronomical Observatory of Turin
INAF - OATo
March 31 2006,
Birmingham
Summary
1. PPN γ measurement through global
astrometry
2. PPN γ and detection of the quadrupole
effect due to a planet with differential
astrometric measurements
3. Conclusions & perspectives
March 31 2006,
Birmingham
Relativistic Astrometry
Why?
m-arcsecond accuracy
Tests of General Relativity
Relativistic models of (and alternative theories)
Light propagation
March 31 2006,
Birmingham
Gaia relativity tests within the Solar System
Global astrometry
PPN parameter g
[amount of curvature by unit rest mass]
Light deflection
Small field astrometry: Eddington-like
experiments
Local relativistic effects => new
parameters + g
Precession of the
perihelion Orbit fitting of asteroids
PPN parameter b [amount of non-
linearity in the superposition law of
gravitational fields]
new tests to be set from the
March 31 2006,
relativistic modelling
Birmingham
The physical link
• for GR g =1, alternative theories, called scalar-tensor
predict small deviations from GR values:
γ 1 105 107
a remnant of a long range scalar field would violate GR (the assumptions
in the equivalence principle, lack of universality of the constants of
microphysics etc..)
The exact amount of the violations depends on the particular
scalar-tensor theory adopted=>quantization of gravity
Current best estimate : γ 1 (2.1 2.3) 10 5 Cassini-Earth Sun
conjunction
(B. Bertotti, L.Iess &
P.Tortora, Nature, 425,
2003)
• GPB expected precision γ 1 3 10 -5
March 31 2006,
Birmingham
1.Light deflection: the PPN g global experiment with Gaia
The adopted metric is the PPN expression for the
Schwarzschild metric in isotropic coordinate (in
geometrized units)
M Sun 2 2
[
2
2 M Sun 2 M Sun
ds (1
2
2b c dt 1 g dr 2 r 2 ( d 2 sin 2 d 2 )
r r r
•Geodesics for light rays: kv kµ;n = 0
Relativistic astrometry models: the RAMOD project
Bucciarelli B , Crosta MT, de Felice F, Lattanzi MG,
and Vecchiato A (ESA SP 576 - p 259 ) cos f ( i , i , i , mi g , i )
March 31 2006,
Birmingham
The mathematical problem
1 observation 1 condition equation
Known Unknown Unknown Unknown Unknown
∂f ∂f ∂f ∂f
sin i(1) i(1) i i i g
∂i
∂i
∂i g
∂
BUT …
∂f ∂f ∂f ∂f
sin i( 2 ) i( 2 ) i i i g
∂i
∂i
∂i g
∂
. . . . . . .
∂f ∂f ∂f ∂f
sin (n)
(n)
i i i g
g
i i
∂i ∂i ∂i ∂
March 31 2006,
Birmingham
The mathematical problem
1 observation 1 condition equation
b=Ax
Over-determined
system of
equations to be
·
solved with least-
·
squares method
ATb=ATAx
March 31 2006,
Birmingham
Gaia expected
precision
g 1 5 10 7
No other foreseen
measurements of g can
challenge Gaia in the next
decade!
Vecchiato A et al.
A&A, 399, 2003
March 31 2006,
Birmingham
2. The GAREX project
GAia Relativistic Experiments
Investigation of observational strategies to test General
Relativity with Gaia.
First experiment: quadrupolar light deflection
Simulation of light deflection experiments of the stars behind Jupiter:
the observable is the relative displacement due to Jupiter’s presence
with respect to the zero-deflection position without Jupiter
Φals Φ J Φ J
New estimate of g by comparison of small fields
Detection of the Quadrupole Efficiency Factor e due to the planet: e =
0 no multipole light effect, =1 validation of GR prediction
March 31 2006, astro-ph/0512359
Birmingham
Light deflection produced by an oblate body
PPN formalism, locally perturbed
minkowskian geometry
the deflection angle is a vector F
Observer view. The position of the
star is displaced both in the radial (-
n) and orthoradial (m) directions.
The spin axis of the planet lies
March 31 2006, somewhere out of plane
Birmingham
Light deflection diplacements around
Jupiter from the observer’s point of
view: mid2013
monopole quadrupole
March 31 2006,
Birmingham
Cumulative effect (mid2012 -mid2018)
monopole quadrupole
March 31 2006,
Birmingham
Results of the Montecarlo runs
g e
March 31 2006,
Birmingham
1.110 3
3
Strategy for the actual experiments
I. Evolution of the errors on g and e with the magnitude
for various impact parameters & for various epochs
g e
o=2013
=>crossing of
the galactic
plane
• = Full Gaia
field
March 31 2006,
Birmingham
II. Open cluster against the galactic plane crossed
by Jupiter M18, Sagittarius
…but in 2019 !
V=12 V=13
March 31 2006,
Birmingham
3. Conclusion & Perspectives
Our simulations
prove that the expected accuracy of Gaia in the determination of the
PPN g parameter is 10-7 !
give a prerequisite for a first evidence of the quadrupole light
deflection due a Jupiter
In a close future
Realistic simulations with the final error budget and initial condition of
scanning law (real field, background noise + straylight profile etc...)
Test models of the light deflection with a moving body => speed of
gravity?
Extension of the simulation to the case of Saturn
Investigation on the indirect determination of the center of
gravity/mass of the planet throughout the light displacement vector
field around it.
March 31 2006,
Birmingham
