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  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  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

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 (V-band) 3.Generation of a mock catalogue [epoch, x, y, V ] 4.Gaussian errors for each star position (V<12.5)

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 quadrupole total deflection number of the simulated stars

Epoch end 2013 total deflection monopole quadrupole number of the simulated stars

total deflection Epoch mid 2014 monopolequadrupole number of the simulated stars

total deflection Epoch mid 2015 monopolequadrupole number of the simulated stars

total deflection Epoch 2016 monopole quadrupole number of the simulated stars

total deflection Epoch 2017 monopole quadrupole number of the simulated stars

total deflection Epoch 2018 monopole 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 n run 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.