Maria Teresa Crosta and Francois Mignard Small field relativistic experiment with Gaia: detection of...
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Transcript of Maria Teresa Crosta and Francois Mignard Small field relativistic experiment with Gaia: detection of...
Maria Teresa Crosta and Francois Mignard
Small field relativistic experiment with Gaia:
detection of the quadrupolar light
deflection
The GAREX project: GAia Relativistic Experiments
Investigation of observational strategies to test General Relativity with Gaia.
First task: how to exploit the observations close to the Jupiter’s limb
• Simulation of light deflection experiments of the stars behind Jupiter
• Estimation of gamma by comparison of small fields
• Evaluation of the reliability to detect the quadrupole effect due to the planet
Preliminary investigation for testing the quadrupolar effect
of Jupiter• Gaia will be able to observe close to Jupiter’s edge and therefore to perform many Eddington-like experiments
•Jupiter acts in the Solar System as a gravitational lens: the deflected angle can be computed as a positional vector
• Evaluation of (i) the number of times Jupiter will cross the Astrometric Focal Plane and (ii) the stellar density around the planet during the Gaia mission
Jupiter in a real starfield in mid 2013 near the galactic plane (plate from the Palomar digitalized survey). The faintest stars are around V=18.The red spots (UNSO-B2) are stars around V=20.
Jupiter on the background starfield during the Gaia mission
Visibility of Jupiter
Stellar density around Jupiter
V < 20
Light deflection produced by an axisymmetric body
dlUc
2
2Φ
A planet will act as a lens on the grazing light from a distant source. The deflection angle can be computed then as a vector
mzmznnztznΦ
2
2222
2
22
2
~
2211b
RJ
b
RJ
bc
GM
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 out of plane
Principle of the simulated measurements
• The observable is the relative displacement (along the scan) due to Jupiter gravitational presence with respect the zero-deflection position without Jupiter, each affected by the same error
• This means that we are comparing small fields around the planet within a short interval of time and avoiding the attitude restitution of the satellite
JJals ΦΦΦ
Steps of the simulation
1. Determination of the ephemerides (l,b) and spin axis of Jupiter as seen from L2
2. Determination of the stellar density corresponding to the given (l,b) for each magnitude bin in the range 12-20 (V-band)
3. Generation of a mock catalogue [epoch, x, y, V ]
4. Gaussian errors for each star position (V<12.5)
)15(2.010 Va
Parameters used in the simulation
Number of stars simulated
Crossing of the galactic plane
We expected:
• to disentagle a deflection vector field due only to the quadrupole
• to have a detection for the first time of the effect of the quadrupole of Jupiter on the light path 100 µas
The theoretical distribution of the stellar deflected positions due to the presence of J2
Light deflection diplacements around Jupiter from the observer’s point of view: mid2012
total deflection monopole quadrupole
number of simulated stars
monopole quadrupole total deflection
number of the simulated stars
Epoch 2013
Epoch mid2013
monopole quadrupoletotal deflection
number of the simulated stars
Epoch end 2013 total deflection
monopole quadrupole
number of the simulated stars
total deflection
Epoch mid 2014
monopole quadrupole
number of the simulated stars
total deflection
Epoch mid 2015
monopole quadrupole
number of the simulated stars
total deflection
Epoch 2016monopole
quadrupole
number of the simulated stars
total deflection Epoch 2017
monopolequadrupole
number of the simulated stars
total deflection
Epoch 2018monopole quadrupole
number of the simulated stars
total deflection
End mid 2018
monopole quadrupole
number of the simulated stars
Monopole displacement vector field
between mid2012-mid2018(obs view)
Quadrupole displacement vector field between
mid2012-mid2018
angular positions of the spin axis w.r.t. the direction towards the observer
Magnitude of the simulated light deflections
Monopole and Quadrupole versus epoch
Error analysis•N observations correspond to a system of N equations where the unknowns are the uncorrelated paramers and
•The errors are estimated by computing the partial derivative with respect to them in each observation equation
•A least-square fitting is applyed to the over-determinated system of observed equations generated by the large number of observations
•A Student ratio test filters the observations too noisy
•Montecarlo experiment, where each run contains a least square fit and provides the mean value of and together with their standard deviation
•After nrun Montecarlo, evaluation of the mean and the scatter
Results on ~
Results on
Results of the Montecarlo runs
This simulation is a nominal experiment It includes the ephemerides of Jupiter as seen from L2 and a
positional accuracy given by the current error budget analysis Computation of the effect considering Jupiter as a moving lens The velocity of the deflector has not been considered
Next steps
Further simulations with the final error budget studies (i.e. straylight profile, across scan, etc...)
Extension of the simulation to the case of the Saturn Investigation on the indirect determination of the center of
gravity of the planet throughout the light displacement vector field around it.