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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. Summary. 1. PPN γ measurement through global astrometry

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Gr tests and micro arcsecond light bending parameters by global and differential gaia mesurements

GR tests and micro-arcsecond light bending parameters by global and differential Gaia mesurements

Maria Teresa Crosta

Astronomical Observatory of Turin

INAF - OATo


Summary
Summary global and differential Gaia mesurements

  • 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


Relativistic Astrometry global and differential Gaia mesurements

Why?

Tests of General Relativity

(and alternative theories)

m-arcsecond accuracy

Relativistic models of

Light propagation


Gaia relativity tests within the solar system

Global astrometry global and differential Gaia mesurements

PPN parameterg

[amount of curvature by unit rest mass]

Light deflection

Orbit fitting of asteroids

PPN parameter b[amount of non-linearity in the superposition law of gravitational fields]

Precession of the perihelion

new tests to be set from the relativistic modelling

Gaia relativity tests within the Solar System

Small field astrometry: Eddington-like experiments

Local relativistic effects => new parameters + g


The physical link
The physical link global and differential Gaia mesurements

  • for GR g =1, alternative theories, called scalar-tensor predict small deviations from GR values:

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

Cassini-Earth Sun conjunction

(B. Bertotti, L.Iess & P.Tortora, Nature, 425, 2003)

Current best estimate :

  • GPB expected precision


1. global and differential Gaia mesurementsLight 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)

  • 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 )


The mathematical problem

Known global and differential Gaia mesurements

Unknown

Unknown

Unknown

Unknown

Unknown

Unknown

Unknown

. . . . . . .

The mathematical problem

  • 1 observation 1 condition equation

BUT …


The mathematical problem1
The mathematical problem global and differential Gaia mesurements

  • 1 observation 1 condition equation

b=Ax

Over-determined system of equations to be solved with least-squares method

ATb=ATAx


Gaia expected precision
Gaia global and differential Gaia mesurements expected precision

No other foreseen measurements of g can challenge Gaia in the next decade!

Vecchiato A et al.

A&A, 399, 2003


2. global and differential Gaia mesurementsTheGAREXproject

GAiaRelativisticExperiments

astro-ph/0512359

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

  • New estimate ofgby comparison of small fields

  • Detection of the Quadrupole Efficiency Factoredue to the planet:e= 0 no multipole light effect, =1 validation of GR prediction


Light deflection produced by an oblate body global and differential Gaia mesurements

  • PPN formalism, locally perturbed minkowskian geometry

  • the deflection angle is a vectorDF

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 somewhere out of plane


Light deflection diplacements around jupiter from the observer s point of view mid2013
Light deflection diplacements around Jupiter from the observer’s point of view: mid2013

monopole

quadrupole


Cumulative effect mid2012 mid2018
Cumulative effect (mid2012 -mid2018) observer’s point of view: mid2013

monopole

quadrupole


Results of the montecarlo runs
Results of the Montecarlo runs observer’s point of view: mid2013

g

e


Strategy for the actual experiments
Strategy for the actual experiments observer’s point of view: mid2013

I.Evolution of the errors on g and e with the magnitude

for various impact parameters & for various epochs

sg

se

o=2013 =>crossing of the galactic plane

  • = Full Gaia field


…but in 2019 observer’s point of view: mid2013!

II.Open cluster against the galactic plane crossed

by Jupiter

M18, Sagittarius

V=13

V=12


3. observer’s point of view: mid2013 Conclusion & Perspectives

Our simulations

  • prove that the expected accuracy of Gaia in the determination of the PPN gparameter 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.


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