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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. 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

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  1. GR tests and micro-arcsecond light bending parameters by global and differential Gaia mesurements Maria Teresa Crosta Astronomical Observatory of Turin INAF - OATo

  2. 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

  3. Relativistic Astrometry Why? Tests of General Relativity (and alternative theories) m-arcsecond accuracy Relativistic models of Light propagation

  4. Global astrometry 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

  5. The physical link • 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

  6. 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) • 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 )

  7. Known Unknown Unknown Unknown Unknown Unknown Unknown Unknown . . . . . . . The mathematical problem • 1 observation 1 condition equation BUT …

  8. The mathematical problem • 1 observation 1 condition equation b=Ax Over-determined system of equations to be solved with least-squares method ATb=ATAx

  9. Gaia expected precision No other foreseen measurements of g can challenge Gaia in the next decade! Vecchiato A et al. A&A, 399, 2003

  10. 2.TheGAREXproject 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

  11. Light deflection produced by an oblate body • 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

  12. Light deflection diplacements around Jupiter from the observer’s point of view: mid2013 monopole quadrupole

  13. Cumulative effect (mid2012 -mid2018) monopole quadrupole

  14. Results of the Montecarlo runs g e

  15. Strategy for the actual experiments 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

  16. …but in 2019! II.Open cluster against the galactic plane crossed by Jupiter M18, Sagittarius V=13 V=12

  17. 3. 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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