Relativity test with Gaia

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Relativity test with Gaia Powered By Docstoc
					  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  105 107
 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
                 1.110   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

				
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posted:3/25/2011
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