Equivalence Principle Violation Signal Research Articles

Dealing with missing data: An inpainting application to the MICROSCOPE space mission

Missing data are a common problem in experimental and observational physics. They can be caused by various sources, either an instrument's saturation, or a contamination from an external event, or a data loss. In particular, they can have a disastrous effect when one is seeking to characterize a colored-noise-dominated signal in Fourier space, since they create a spectral leakage that can artificially increase the noise. It is therefore important to either take them into account or to correct for them prior to e.g. a Least-Square fit of the signal to be characterized. In this paper, we present an application of the {\it inpainting} algorithm to mock MICROSCOPE data; {\it inpainting} is based on a sparsity assumption, and has already been used in various astrophysical contexts; MICROSCOPE is a French Space Agency mission, whose launch is expected in 2016, that aims to test the Weak Equivalence Principle down to the $10^{-15}$ level. We then explore the {\it inpainting} dependence on the number of gaps and the total fraction of missing values. We show that, in a worst-case scenario, after reconstructing missing values with {\it inpainting}, a Least-Square fit may allow us to significantly measure a $1.1\times10^{-15}$ Equivalence Principle violation signal, which is sufficiently close to the MICROSCOPE requirements to implement {\it inpainting} in the official MICROSCOPE data processing and analysis pipeline. Together with the previously published KARMA method, {\it inpainting} will then allow us to independently characterize and cross-check an Equivalence Principle violation signal detection down to the $10^{-15}$ level.

Determination of the Equivalence Principle Violation Signal for the MICROSCOPE Space Mission: Optimization of the Signal Processing

The MICROSCOPE space mission aims at testing the Equivalence Principle (EP) with an accuracy of $10^{-15}$. The test is based on the precise measurement delivered by a differential electrostatic accelerometer on-board a drag-free microsatellite which includes two cylindrical test masses submitted to the same gravitational field and made of different materials. The experiment consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless at a well-known frequency. This high precision experiment is compatible with only very little perturbations. However, aliasing arises from the finite time span of the measurement, and is amplified by measurement losses. These effects perturb the measurement analysis. Numerical simulations have been run to estimate the contribution of a perturbation at any frequency on the EP violation frequency and to test its compatibility with the mission specifications. Moreover, different data analysis procedures have been considered to select the one minimizing these effects taking into account the uncertainty about the frequencies of the implicated signals.

Modelling of the MICROSCOPE Mission

The French space mission MICROSCOPE aims at testing the Equivalence Principle (EP) up to an accuracy of 10−15. The experiment will be carried out on a satellite which is developed and produced within the CNES Myriade series. The measuring accuracy will be achieved by means of two high-precision capacitive differential accelerometers that are built by the French institute ONERA, see Touboul and Rodrigues (Class. Quantum Gravity 18:2487–2498, 2001). At ZARM, which is a member of the science team, the data evaluation process is prepared. Therefore, a comprehensive simulation of the real system including the science signal and all error sources is built for the development and testing of data reduction and data analysis algorithms to extract the EP violation signal. Currently, the ZARM Drag-Free simulator, a tool to support mission modelling, is adapted for the MICROSCOPE mission in order to simulate test mass and satellite dynamics. Models of environmental disturbances like solar radiation pressure are considered, also. Additionally, detailed modelling of the on-board capacitive sensors is done. The actual status of the mission modelling will be presented. Particularly, the modelling of disturbances forces will be discussed in detail.

Modelling and simulation of the space mission MICROSCOPE

AbstractThe French space mission MICROSCOPE aims at testing the weak Equivalence Principle (EP) with an accuracy of 10−15. The payload, which is developed and built by the French institute ONERA consists of two high-precision capacitive differential accelerometers. The detection of the test mass movement and their control is done via a complex electrode system. The German department ZARM is member of the MICROSCOPE performance team. In addition to drop tower tests, mission simulations and the preparation of the mission data evaluation are realized in close cooperation with the French partners CNES, ONERA and OCA. Therefore a comprehensive simulation of the real system including the science signal and all error sources is built for the development and testing of data reduction and data analysis algorithms to extract the EP violation signal. In this context the focus lays on the correct modeling of the environmental disturbances. Currently new effort to study the influence of the solar radiation and the Earth albedo to the MICROSCOPE mission scenario is underway.

TEPEE/GReAT (General Relativity Accuracy Test in an Einstein Elevator): Advances in the detector development

This paper reports the development of an experiment (TEPEE/GReAT) to test the Equivalence Principle (EP) at a level of accuracy equal to 5 × 10-15 , by means of a differential accelerometer free falling in a cryogenic vacuum capsule released from a stratospheric balloon. Such an accuracy requires resolving a very small signal out of the instrument's intrinsic noise and the noise associated with the instrument's motion. Imperfections in the construction of the detector introduce gravity gradient noise that it is possible to separate from the violation signal spinning the detector around an horizontal axis in order to have the EP violation signal and the gravity gradients one modulated at two different frequencies. Experimental results on prototype instruments showing high sensitivity and common mode rejection factor are shown.

Nutational Oscillatory Effect of the Test Body in Space Equivalence Principle Experiments**The project supported by National Natural Science Foundation of China under Grant Nos. 10205005 and 10121503

The significance of quadrupole gravitational force is discussed for test mass in equivalence principle (EP), and the angular moment acting on a cylindrically symmetrical body due to quadrupole force is calculated, which will result in nutational oscillatory effect. The oscillations contain a perturbation with the same frequency of EP violation signal, which is mitigated by two different methods as in Galileo Galilei (GG) mission and μSCOPE. In GG the sensor for readout is sensitive to differential forces in the orbital plane perpendicular to spin axis of test cylinders. In order to mitigate the nutational oscillatory effect, test mass should be rapidly rotated with the spin axis. However, in μSCOPE, the readout sensitive axis is the symmetry axis in the orbital plane. This nutational oscillation will produce a second order effect in the rotation amplitude at twice the signal frequency, and could be subtracted easily, too.

Tidal effects in space experiments to test the equivalence principle: implications on the experiment design

Experiments to test the equivalence principle (EP) in low Earth orbit require to detect the effects of an extremely small non-classical differential acceleration between test masses of different composition. In all proposed experiments the test masses are concentric coaxial cylinders, so as to reduce classical tidal effects which are differential too. Perfect centring being impossible, tidal effects need to be carefully investigated as they impose severe constraints on the basic features of the experiment design. The present analysis shows that with free flying (uncoupled) test masses an EP violation signal could be detected if the initial conditions of the masses were finely adjusted for them to remain at a fixed distance relative to each other while orbiting around the Earth. However, such an experiment is severely limited by non-gravitational effects. If the test cylinders are weakly coupled in 2D in the plane perpendicular to their symmetry axis (close to the orbit plane), while rapidly spinning around it, a position of relative equilibrium is provided by physical laws which makes tidal effects widely separated from the signal. Weak coupling in 1D along the symmetry axis (to lie and slowly rotate in the orbit plane) is viable but less advantageous.

“Galileo Galilei (GG) on the Ground-GGG”: experimental results and perspectives

The GGG differential accelerometer is made of concentric coaxial test cylinders weakly coupled in the horizontal plane and spinning in supercritical regime around their symmetry axis. GGG is built as a full scale ground based prototype for the proposed “Galileo Galilei-GG” space experiment aiming to test the equivalence principle (EP) to 10 −17 at room temperature. We report measured Q values of 95000 at 1.4 Hz, and expect even better ones at typical spin frequencies of a few Hz. An EP violation signal in the field of the Sun would appear as a low frequency displacement in the horizontal plane of the laboratory, and it can be separated out from a much larger whirl motion of the test masses at their natural differential frequency. So far we have managed to reduce the amplitude of this whirl to about 0.1 μm. We discuss how to improve these results in view of the very high accuracy GG experiment in space, and/or to reach a 10 −13 sensitivity in the lab which would allow us to either confirm or rule out recent predictions of violation to this level.

Radiometer effect in the μSCOPE space mission

Space experiments to test the Equivalence Principle (EP) are affected by a systematic radiometer effect having the same signature as the target signal. In [PhRvD 63 (2001) 101101(R)] we have investigated this effect for the three proposed experiments currently under study by space agencies: μSCOPE, STEP and GG, setting the requirements to be met—on temperature gradients at the level of the test masses—for each experiment to reach its goal. We have now re-examined the radiometer effect in the case of μSCOPE and carried out a quantitative comparative analysis, on this issue, with the proposed heliocentric LISA mission for the detection of gravity waves. We find that, even assuming that the μSCOPE spacecraft and payload be built to meet all the challenging requirements of LISA, temperature gradients along its test masses would still make the radiometer effect larger than the target signal of an EP violation because of flying in the low geocentric orbit required for EP testing. We find no way to separate with certainty the radiometer systematic disturbance from the signal. μSCOPE is designed to fly a second accelerometer whose test masses have the same composition, in order to separate out systematic effects which—not being composition dependent like the signal—must be detected by both accelerometers. We point out that this accelerometer is in fact insensitive to the radiometer effect, just as it is to an EP violation signal, and therefore even having it onboard will not allow this disturbance to be separated out. μSCOPE is under construction and it is scheduled to fly in 2004. If it will detect a signal to the expected level, it will be impossible to establish with certainty whether it is due to the well known classical radiometer effect or else to a violation of the equivalence principle—which would invalidate General Relativity. The option to increase the rotation speed of the spacecraft (now set at about 10 −3 Hz) so as to average out the temperature gradients which generate the radiometer effect, is allowed in the GG design, not in that of STEP and μSCOPE.

The “Galileo Galilei” (GG) project: Testing the Equivalence Principle in space and on Earth

“ GALILEO GALILEI” ( GG) is a proposal for a small, low orbit satellite devoted to testing the Equivalence Principle ( EP) of Galileo, Newton and Einstein to 1 part in 10 17. At the end of 1997 GG has been selected and funded by ASI (Agenzia Spaziale Italiana) for a 1-year Phase A study. The main novelty of GG is that the concentric hollow test cylinders whose relative motion (in the plane perpendicular to the spin axis) would be affected by an EP violation, spin together with the read-out capacitance sensors placed in between them. The nominal spin rate is 2 Hz, and this is the frequency at which the putative EP violation signal is modulated by the sensors. As compared to other experiments the modulation frequency is increased by more than a factor 10 4, thus reducing 1 f (low frequency) electronic and mechanical noise. GG will have FEEP ion thrusters for drag compensation. The required amount of propellant is of a few grams only. The experiment works at room temperature. To demonstrate the feasibility of the space experiment a payload prototype for EP testing on the ground ( GGG - GG on the Ground) is under development in the laboratories of Laben. The challenge in this field is to fly an experiment able to improve by many orders of magnitude the current best ground sensitivity (≅10 −12). This requires spurious relative motions of the test bodies to be greatly reduced, leaving them essentially motionless. Doing that with more than one pair of bodies appears to be an unnecessary complication. This is why GG is now proposed with a single pair of test masses. Information, research papers and photographs of the ground apparatus are available on the Web ( http://tycho.dm.unipi.it/nobili).

A Note on the Solar Radiation Perturbations of Lunar Motion

Solar-radiation and thermal-force effects acting on the Earth and the Moon are studied in detail. Their essential contribution to the lunar geocentric motion consists of a synodic “in-phase” oscillation with 3.65 ± 0.08 (realistic error) millimeters amplitude. This correction must be taken into account when searching for a hypothesized equivalence principle violation signal in the lunar laser ranging data.