Testing general relativity with Gaia's astrometric core solution

Testing general
relativity with Gaia’s
astrometric core
solution
David Hobbs
Lund Observatory

proper
motion
(µ α* , µ δ )
position at
reference
epoch
(α 0 , δ 0 )
Parallax (π)
Radiation Task Force meeting, 14 Apr 2008

Gaia Scientific Return
• Galactic structure and evolution: Accurate data for 1,000,000,000 objects → a revolution
in stellar dynamics, formation and evolution.
• Astrometric, photometric and spectroscopic properties: Dynamics, Temperatures,
Ages, Luminosities and Metallicities.
• Extrasolar planets: 10 000 Jupiter-mass planets within 50 pc and P =1.5-9 years.
• Solar System: 300,000 Solar system bodies will be detected and their orbits determined.
• Binaries: 10 million binaries up to 250 parsecs and 60 million in total.
• Brown Dwarfs: Large numbers of faint brown dwarfs near the Sun.
• Reference Frame: 1 or 2 orders of magnitude improvement for optical ICRF.
• General Relativity: Light bending caused by the Sun, planets and moons will be used to test
GR to unprecedented accuracy.

What is the PPN formalism
The parameterized post-Newtonian (PPN) formalism is a tool to compare classical theories of gravity in
the limit of weak fields and slow motion compared to c
It is a generalization for all possible metric theories of gravity (GR is the simplest)
The formalism has 10 ad hoc parameters which characterize different gravitational effects
The two most fundamental parameters are PPN-γ and PPN-β
γ How much space curvature is produced by unit rest mass ?
β How much nonlinearity is there in the superposition law of gravity ?
In general relativity γ = β = 1
Some scalar-tensor cosmological models predict
for γ -1 a deviation from GR between 10 -5 and 10 -8

Currently the best estimates:
γ-1 = (2.1±2.3)×10 -5
(Cassini: Shapiro time delay)
β-1 = (1.2±1.1)×10 -4
from (4β-γ-3=4.3×10 -4 ) (LLR)
From Turyshev (2008)
Experimental Tests of General Relativity

Determining PPN-γ with Gaia
Gaia will detect the light bending by the Sun and major planets continuously during its 5 year mission
At right angles to the Sun the bending is ~4000 µas, while for a ray grazing Jupiter it is ~16270 µas.
These measurements can be used in the Gaia’s core solution to determine PPN-γ by analyzing the
residuals between observations and calculated observations based on a model of general relativity
Combining millions of measurements will map these effects to unprecedented accuracy
It has been
suggested that
Gaia can test
GR (γ = 1) to
the order of
γ-1 ~ 2-5×10 -7
Image ESA

Preliminary results
Solving for only PPN-γ-1 gives slow
convergence due to a strong correlation
with the parallax zero point
Solving for PPN-γ with an artificial
constraint equal to zero on the parallax zero
point accelerates convergence
Correlation between PPN-γ and the parallax
zero point is ~ 91% which affects the
accuracy of PPN-γ
Running 100 simulations allows the distribution of
the errors in γ to be calculated
Extrapolate to large scale simulations (ESAC & Gaia)
Correct the total weight of observations in all
magnitude bins to give a realistic estimate for Gaia
Pessimistic estimate: γ-1 = 4.01×10 -6
Optimistic estimate : γ-1 = 1.27×10 -6
Correlation with the parallax zero point is a problem
TODO: Confirm results in AGIS with ~2.5 million *
TODO: Need to investigate BA variations

Determining PPN-β with Gaia
Gaia will also measure large numbers (~300,000) of Solar System objects (asteroids and NE objects)
Precession of perihelion (due to GR and solar oblateness) for eccentric asteroids β-1 of ~5×10 -4
Tests of the solar quadrupole moment J2 ~ 1.5×10 -8 (current ~2×10 -7 )
Variations of the gravitational constant Ġ/G ~ 2×10 -12 year -1 (current LLR ~(5±6)×10 -13 )
Acceleration of solar system’s barycenter
Gaia can measure the acceleration of the solar system’s
barycenter relative to remote sources (quasars)
This acceleration causes a change of secular aberration
measured as a pattern of proper motions
a ~ 4.5 µas-yr -1
Measurable ±10% over a 5 years giving the first direct
measurement of this effect
The algorithms have already been implemented by the Lund
team in the Gaia data processing chain.