MICROSCOPE Space Mission Research Articles

Ultralight scalar dark matter detection with ZAIGA

Zhaoshan long-baseline atom interferometer gravitation antenna (ZAIGA) is a proposed underground long-baseline atom interferometer (AI) facility, aiming for experimental research on gravitation and related problems. In this paper, we study the possibility of detecting the ultralight scalar dark matter (DM) with ZAIGA. According to a popular scalar DM model, the DM field contains a background oscillation term and a local exponential fluctuation term. In order to calculate the proposed constraints on DM coupling parameters, we need to first compute the DM signals in ZAIGA. For the case of two AIs vertically separated by 300[Formula: see text]m, the DM-induced differential phase consists of three contributions, coming from the DM-induced changes in atomic internal energy levels, atomic masses and the gravitational acceleration. For the case of two AIs horizontally separated by several kilometers, the signal comes from the DM-induced changes in atomic internal energy levels. With the current and future technical parameters of ZAIGA, we then obtain the proposed constraints on five DM coupling parameters. It turns out that our proposed constraints could be several orders of magnitude better than the ones set by the MICROSCOPE space mission.

New Test of Lorentz Invariance Using the MICROSCOPE Space Mission

We use data from the T-SAGE instrument on board the MICROSCOPE space mission to search for Lorentz violation in matter-gravity couplings as described by the Lorentz violating standard model extension (SME) coefficients (a[over ¯]_{eff})_{μ}^{w}, where (μ=T, X, Y, Z) and (w=e, p, n) for the electron, proton, and neutron. One of the phenomenological consequences of a nonzero value of those coefficients is that test bodies of different composition fall differently in an external gravitational field. This is similar to "standard" tests of the universality of free fall, but with a specific signature that depends on the orbital velocity and rotation of Earth. We analyze data from five measurement sessions of MICROSCOPE spread over a year finding no evidence for such a signature, but setting constraints on linear combinations of the SME coefficients that improve on best previous results by 1 to 2 orders of magnitude. Additionally, our independent linear combinations are different from previous ones, which increases the diversity of available constraints, paving the way towards a full decorrelation of the individual coefficients.

Testing the Universality of Free Fall towards Dark Matter with Radio Pulsars.

The violation of the weak equivalence principle (EP) in the gravitational field of Earth, described by the Eötvös parameter η_{⊕}, was recently constrained to the level |η_{⊕}|≲10^{-14} by the MICROSCOPE space mission. The Eötvös parameter η_{DM}, pertaining to the differential couplings of dark matter (DM) and ordinary matter, was only tested to the level |η_{DM}|≲10^{-5} by the Eöt-Wash group and lunar laser ranging. This test is limited by the EP-violating driving force in the solar neighborhood that is determined by the galactic distribution of DM. Here we propose a novel celestial experiment using the orbital dynamics from radio timing of binary pulsars, and obtain a competing limit on η_{DM} from a neutron-star-white-dwarf (NS-WD) system, PSR J1713+0747. The result benefits from the large material difference between the NS and the WD and the large gravitational binding energy of the NS. If we can discover a binary pulsar within ∼10 pc of the galactic center, where the driving force is much larger in the expected DM spike, precision timing will improve the test of the universality of free fall towards DM and constrain various proposed couplings of DM to the standard model by several orders of magnitude. Such a test probes the hypothesis that gravity is the only long-range interaction between DM and ordinary matter.

Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data

The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10^-15 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. This code has been integrated in the official MICROSCOPE data processing 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. The main improvement has been obtained using a prior on the power spectrum of the colored-noise that can be directly derived from the incomplete data. We show that after reconstructing missing values with this new algorithm, a least-squares fit may allow us to significantly measure an EPV signal with a 0.96x10^-15 precision in the inertial mode and 1.2x10^-15 precision in the spin mode. 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. The improved inpainting software, called ICON, is freely available at http://www.cosmostat.org/software/icon.

Gaussian regression and power spectral density estimation with missing data: The MICROSCOPE space mission as a case study

We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging, based on the circulant approximation of the complete data covariance. After initialization with an autoregessive fit of the noise, a few iterations of estimation/reconstruction steps are performed until convergence of the regression and PSD estimates, in a way similar to the expectation-conditional-maximization algorithm. The estimation can be performed for an arbitrary PSD provided that it is sufficiently smooth. The algorithm is developed in the framework of the MICROSCOPE space mission whose goal is to test the weak equivalence principle (WEP) with a precision of $10^{-15}$. We show by numerical simulations that the developed method allows us to meet three major requirements: to maintain the targeted precision of the WEP test in spite of the loss of data, to calculate a reliable estimate of this precision and of the noise level, and finally to provide consistent and faithful reconstructed data to the scientific community.

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.

Regression analysis with missing data and unknown colored noise: Application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events, or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method that cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the weak equivalence principle (WEP) with a precision of $1{0}^{\ensuremath{-}15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor of 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.

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.

Validation of the in-flight calibration procedures for the MICROSCOPE space mission

The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of 10-15. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.

MICROSCOPE – fabricating test masses for an in‐orbit test of the equivalence principle

The MICROSCOPE space mission is to test in 2016 the Weak Equivalence Principle (WEP) with an accuracy of 10−15. This fundamental physics mission should provide answers to the basic question of the universality of free‐falling bodies in a uniform gravity field. During 18 months, the mission should improve the current ground experiments by at least two orders of magnitude. The payload is composed of two electrostatic differential space accelerometers that exhibit a resolution of 2×10−12 m s−2 Hz−1/2. By measuring the difference of acceleration between two concentric test masses at the orbital frequency, a possible WEP violation signal is extracted from the measurement where the gravity gradient effect dominates by a factor of one hundred.This paper addresses the scientific objective of the space mission and describes how the performance drives the specification. A particular focus is made on the work jointly performed by ONERA and PTB to fulfil the fabricating requirements.

The MICROSCOPE experiment, ready for the in-orbit test of the equivalence principle

Deviations from standard general relativity are being intensively tested in various aspects. The MICROSCOPE space mission, which has recently been approved to be launched in 2016, aims at testing the universality of free fall with an accuracy better than 10−15. The instrument has been developed and most of the sub-systems have been tested to the level required for the detection of accelerations lower than one tenth of a femto-g. Two concentric test masses are electrostatically levitated inside the same silica structure and controlled on the same trajectory at better than 0.1 Å. Any dissymmetry in the measured electrostatic pressures shall be analysed with respect to the Earth's gravity field. The nearly 300 kg heavy dedicated satellite is defined to provide a very steady environment to the experiment and a fine control of its attitude and of its drag-free motion along the orbit. Both the evaluations of the performance of the instrument and the satellite demonstrate the expected test accuracy. The detailed description of the experiment and the major driving parameters of the instrument, the satellite and the data processing are provided in this paper.

Drop Tower Microgravity Improvement Towards the Nano-g Level for the MICROSCOPE Payload Tests

The Bremen drop tower at the Center of Applied Space Technology and Microgravity (ZARM) provides high quality micro-g condition needed for many high precision tests. This is even more improved by the development of a free flyer technology. This new technology is used for a free fall test of the MICROSCOPE differential accelerometers which only can work with a residual acceleration disturbance level below 25 nano-g in the high resolution mode. The French MICROSCOPE space mission for testing the Weak Equivalence Principle is scheduled for 2012/2013. The free fall accelerometer test campaign at ZARM is an important part of the pre-mission test program. In this article the new free flyer technology, its performance as well as the accelerometer tests are described.

The Microscope Mission and Its Uncertainty Analysis

The accurate test of the Universality of Free Fall may demonstrate a violation of Einstein Equivalence Principle (EP) as most attempts of Grand Unification theories seem to conduct. The MICROSCOPE space mission aims at an accuracy of 10−15 with a small drag free satellite and a payload based on electrostatic inertial sensors. The two test-masses made of Platinum and Titanium alloys are forced to follow accurately the same orbit. The sets of surrounding electrodes carried by gold coated silica parts allows the generation of electrical fields and electrostatic pressures on the masses. Common forces and torques are exploited to control the satellite drag compensation system and its fine inertial or rotating pointing. Difference in the force along the Earth gravity monopole is accurately measured and interpreted for the test. After a short presentation of the mission and the instrument, most of the relevant parameters to the experiment performance are detailed as well as the associated technologies to reach the expected levels of accuracy. Present error budgets confirm the test expected accuracy of better than 10−15.

Overview

the scientific objectives of the MICROSCOPE space mission impose a very fine calibration of the on-board accelerometers. However the required performance cannot be achieved on ground because of the presence of high disturbing sources. On-board the CHAMP satellite, accelerometers similar in the concept to the MICROSCOPE instrument, have already flown and analysis of the provided data then allowed to characterise the vibration environment at low altitude as well as the fluctuation of the drag. The requirements of the in-orbit calibration procedure for the MICROSCOPE instrument are demonstrated by modelling the expected applied acceleration signals with the developed analytic model of the mission. The proposed approach exploits the drag-free system of the satellite and the sensitivity of the accelerometers. A specific simulator of the attitude control system of the satellite has been developed and tests of the proposed solution are performed using nominal conditions or disturbing conditions as observed during the CHAMP mission.

Microscope in orbit calibration procedure for a test of the equivalence principle at 10 −15

the scientific objectives of the MICROSCOPE space mission impose a very fine calibration of the on-board accelerometers. However the required performance cannot be achieved on ground because of the presence of high disturbing sources. On-board the CHAMP satellite, accelerometers similar in the concept to the MICROSCOPE instrument, have already flown and analysis of the provided data then allowed to characterise the vibration environment at low altitude as well as the fluctuation of the drag. The requirements of the in-orbit calibration procedure for the MICROSCOPE instrument are demonstrated by modelling the expected applied acceleration signals with the developed analytic model of the mission. The proposed approach exploits the drag-free system of the satellite and the sensitivity of the accelerometers. A specific simulator of the attitude control system of the satellite has been developed and tests of the proposed solution are performed using nominal conditions or disturbing conditions as observed during the CHAMP mission.

MICROSCOPE, testing the equivalence principle in space

The test of the equivalence principle can be performed in space with orders of magnitude better resolution than in the laboratory, because of the outstanding steady and soft environment of the in-orbit experiment. The expected new experimental results will contribute to the unification of the four interactions, demonstrate the existence of extra scalar interaction or participate in the research for a quantum gravity theory. The MICROSCOPE space mission is being developed within the framework of the Cnes scientific program with the objective of testing the universality of free fall with a 10 −15 accuracy. The concept and the design of the experiment are discussed and the major performance drivers of the room temperature instrument are pointed out. The launch of the drag-free satellite is scheduled for late 2004. By its specific technology demonstration, the mission will open the way to even more accurate acceleration measurements for other space missions in fundamental physics.