Space test of the Equivalence Principle: first results of the MICROSCOPE mission
|Authors:||P. Touboul, G. Metris, M. Rodrigues, Y. André, Q. Baghi, J. Bergé, D. Boulanger, S. Bremer, R. Chhun, B. Christophe, V. Cipolla, T. Damour, P. Danto, H. Dittus, P. Fayet, B. Foulon, P.-Y. Guidotti, E. Hardy, P.-A. Huynh, C. Lämmerzahl, V. Lebat, F. Liorzou, M. List, I. Panel, S. Pires, B. Pouilloux, P. Prieur, S. Reynaud, B. Rievers, A. Robert, H. Selig, L. Serron, T. Sumner, P. Viesser|
|Journal:||Classical and Quantum Gravity|
|Download:||ADS | arXiv|
The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of 10^-15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter = [-1 +/- 9(stat) +/- 9 (syst)] x 10^-15 (both 1 uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1 uncertainties leads to a current limit on of about 1.3 x 10^-14.
Weak Lensing provides a unique method to directly map the distribution of dark matter in the universe. Ongoing efforts are made to improve the detection of cosmic shear on existing telescopes and future instruments dedicated to survey are planned. Several methods are used to derive the lensing shear from the shapes of background galaxies. But the shear map obtained is always noisy, and when it is converted into a map of the projected mass map, the result is dominated by the noise.
MRLens offers a new algorithm for the reconstruction of Weak Lensing mass maps.
MRLens (Multi-Resolution tools for gravitational Lensing) is a software written in C++ with an IDL interface. This method uses the Multiscale Entropy concept (which is based on wavelets) and the False Discovery Rate (FDR) which allows us to derive robust detection levels in wavelet space. MRLens has been used to process the COSMOS map (see Figure above)..
More than a software dedicated to a new reconstruction method, MRLens software includes many other tools useful to process, analyze and visualize lensing data. The user manual introduces Weak Lensing field and describes the MRLENS tools. Some results are presented and an accurate description of IDL routines are available.
Fast download : (Only binaries)
Standard Download : (Binaries and data)
System Requirements : 1- Make sure you have approximately 400 MB of disk space available. After installation MRLENS package occupies approximately 56 MB or 205MB (version with data) of disk space.
2- The binaries C++ called by IDL routines are not available under all the systems therefore you cannot use the package on all platforms. The supported platforms are : SUN-Solaris, PC-Linux, Mac OS X. Next release will include PC Windows.
Software Requirements : The IDL MRLENS software requires that IDL (version 6.0 or later) to be installed on your computer. Starting IDL using the script program mrl.pro allows the user to add the MRLENS software to the IDL environment.
Thus, all routines described in the user manual can be called.
An online help is available by using the mrh.pro program.oftwares are required:
This package is a compilation of some algorithms and methods which were developed and/or used successfully in the applications reported in the 2 following publications:
Weak Lensing Mass Reconstruction using Wavelets, J.-L. Starck, S. Pires and A. Réfrégier, Astronomy and Astrophysics, March 2006
Map of the universe's Dark Matter scaffolding, R. Massey, J. Rhodes, R. Ellis, N. Scoville, A. Leathaud, A. Finoguenov, P. Capak, D. Bacon, H. Aussel, J.-P. Kneib, A. Koekemoer, H. McCracken, B. Mobasher, S. Pires, A. Réfrégier, S. Sasaki, ,J.-L. Starck, Y. Taniguchi and J. Taylor, Nature, January 2007
Sunyaev-Zeldovich cluster reconstruction in multiband bolometer camera surveys, S. Pires, J.-B. Juin, D. Yvon, Y. Moudden, S. Anthoine and E. Pierpaoli, Astronomy and Astrophysics, April 2006
More than a software dedicated to a new reconstruction method, this package includes many other tools useful to process, analyze and visualize lensing data.
Please acknowledge use of the code in any resulting work, citing Starck, et al, 2006. We would be interested to collaborate with anyone requiring more advanced applications, and are always interested to hear about new applications. For questions and feedback or to be informed of the forthcoming versions, send an email to Sandrine Pires.
The analysis of weak lensing data requires to account for missing data such as masking out of bright stars. To date, the majority of lensing analyses uses the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. The two-point correlation function is unbiased by missing data but its direct calculation will soon become a burden with the exponential growth of astronomical data sets. The power spectrum is fast to estimate but a mask correction should be estimated. Others statistics can be used but these are strongly sensitive to missing data.
The solution that is proposed by FASTLens is to properly fill-in the gaps with only NlogN operations, leading to a complete weak lensing mass map from which we can compute straight forwardly and with a very good accuracy any kind of statistics like power spectrum or bispectrum. The inpainting method relies strongly on the notion of sparsity and on the construction of sparse representations in large redundant dictionaries.
FASTLens (Fast STatistics for weak Lensing) is a package written in C++ that includes:
- An inpainting code to derive complete weak lensing mass maps from incomplete shear maps
- A power spectrum estimator
- A bispectrum estimator (for equilateral and isoscele configurations)
We propose also a new method to compute fastly and accurately the power spectrum and the bispectrum with a polar FFT algorithm.
The user manual introduces the missing data problem in statistic estimation and presents the available routines. An accurate description of IDL routines is given.
The IDL FASTlens software requires IDL (version 6.0 or later) to be installed on your computer.
The binaries C++ called by IDL routines are not available under all the systems therefore you cannot use the package on all platforms. The supported platforms are : PC-Linux and Mac OS X.
Inpainting routines (inpainting for weak lensing)
Statistic routines (power spectrum and bispectrum estimators)
FASTLens (FAst STatistics for weak Lensing) : Fast method for weak lensing statistics and map making, S. Pires, J.-L. Starck, A. Amara, A. Refregier and J. Fadili, MNRAS, 395, 1265-1279, 2009
Please acknowledge use of the code in any resulting work, citing Pires, et al, 2009. We would be interested to collaborate with anyone requiring more advanced applications, and are always interested to hear about new applications. For questions and feedback or to be informed of the forthcoming versions, send an email to Sandrine Pires.
The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 1015 precision. To reach this performance requires an accurate and robust data analysis method, especially since the possible WEP violation signal will be dominated by a strongly colored noise. An important complication is brought by the fact that some values will be missing –therefore, the measured time series will not be strictly regularly sampled. Those missing values induce a spectral leakage that significantly increases the noise in Fourier space, where the WEP violation signal is looked for, thereby complicating scientific returns.
Recently, we developed an inpainting algorithm to correct the MICROSCOPE data for missing values (in red, fig 4). This code has been integrated in the official MICROSCOPE data processing and analysis pipeline because it enables us to significantly measure an equivalence principle violation (EPV) signal in a model-independent way, in the inertial satellite configuration. In this work, we present several improvements to the method that may allow us now to reach the MICROSCOPE requirements for both inertial and spin satellite configurations (green curve, fig. 4).
The code ICON
The code corresponding to the paper is available for download here.
Although, the inpainting method presented in this paper has been optimized to the MICROSCOPE data, it remains sufficiently general to be used in the general context of missing data in time series dominated by an unknown colored-noise.
Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data, S. Pires, J. Bergé, Q. Baghi, P. Touboul, G. Métris, accepted in Physical Review D, December 2016
Dealing with missing data: An inpainting application to the MICROSCOPE space mission, J. Bergé, S. Pires, Q. Baghi, P. Touboul, G. Metris, Physical Review D, 92, 11, December 2015