Space-based Gravitational Wave Research Articles

Compact advanced pure tilt actuator for testing tilt-to-length coupling in space-based gravitational wave detection

Tilt-to-length (TTL) coupling, caused by the jitter of test masses or satellites, is a major noise source in space-based gravitational wave detection. Calibrating and suppressing TTL coupling noise at the sub-nanometer level is essential. A key challenge in current ground-based TTL coupling testing is the residual translational movement of the tilt actuator. This paper presents the development of a compact advanced pure tilt actuator (APTA) specifically designed for testing TTL coupling. The APTA enables precise tilt motion, monitored by a four-beam interferometer measuring the displacement of attached retroreflectors. Detailed theoretical models and experimental setups are given. Experimental results demonstrate that the APTA test bed can achieve sub-nanometer-level TTL coupling calibration. Additionally, a typical test-mass interferometer tested by the APTA test bed demonstrated that the imaging system effectively suppresses TTL coupling errors. The TTL coupling coefficients were reduced from over ±30 μm/rad to within ±5 μm/rad across a range of ±200 μrad. The APTA test bed offers a compact, high-precision solution for ground-based TTL coupling tests and has the potential for broader application in related experimental setups.

Dragging of the particle spin and spin–spin coupling effect on its periapsis shift

Abstract The periapsis shift (PS) of spinning test particles in the equatorial plane of an arbitrary stationary and axisymmetric spacetime is studied using the post-Newtonian method. The result is expressed as a half-integer power series of $M/p$, where $M$ is the spacetime mass and $p$ is the semilatus rectum. The coefficients of the series are polynomials of the particle spin, the asymptotic expansion coefficients of the metric functions, and the eccentricity of the orbit. The particle spin is shown to have a similar effect as the Lense-Thirring (LT) effect on the PS, and both of them appear from the $(M/p)^{-3/2}$ order in the PS. The coupling between the spacetime and particle spins will increase (or decrease) the PS if they are parallel (or antiparallel). For Jupiter and Saturn rotating around the Sun and exceptionally designed satellites around Mercury and Moon, and the space-based gravitational wave observatories LISA and TaiJi around the Sun, the particle spin effect can be comparable to or even larger than the LT one in size. The PS in other spacetime studied are is not distinguishable from that in the Kerr spacetime to the $(M/p)^{-3/2}$ order.

Clock noise evaluation of space-based gravitational wave detectors based on time-delay interferometry

The heterodyne measurements are adopted in space-based gravitational wave detectors to detect gravitational wave signals in the millihertz range. Due to the difficulty in maintaining the equal distance between these spacecrafts in the detector, laser phase noise is a main noise in the detection process, so time-delay interferometry combination is adopted to eliminate this noise by synthesizing virtual equal arm interferometry. However, when conducting heterodyne laser interferometry measurements in space-based gravitational wave detection, clock noise is also introduced into the measurement, but the analytical results of clock noise have been ignored in previous studies. Based on time-delay interferometry combination, we analyze the impact of clock noise and provide analytical results of the total noise in various data combinations. Through this result, we evaluate the required clock accuracy of 10−16 for the gravitational wave detector when clock noise is not reduction, so the analytical result can more intuitively reflect how the clock noise effects the sensitivity of the detector.

Ground-based simulation of laser link acquisition for inter-satellite laser interferometry

Laser link acquisition and pointing technique is one of the essential techniques for the inter-satellite laser interferometry for space-based gravitational waves detection and next-generation Earth gravity measurement missions. The first step of building up inter-satellite laser link is using an acquisition camera to capture the inter-satellite laser beam signals within a pre-scanning uncertain cone. Subsequently, high-precision angle measurement technology, namely differential wavefront sensing, is used to achieve a high pointing precision required. Due to the distance constraint of a ground-based simulation experiment, it is difficult to verify directly the feasibility of an inter-satellite laser link acquisition and pointing control scheme. By means of controlling the optical properties of the received laser beam, the long-distance beam propagation is simulated with two optical benches of an inter-satellite interferometer, and the process of a laser link acquisition experiment has been demonstrated. The experimental results show that the inter-satellite laser beams could establish the dual-way locking successfully. The fluctuation of the laser beam pointing direction (in-loop) can be suppressed to about 5 µrad in atmospheric environment. The results verify the feasibility of the laser link acquisition scheme. The experimental setup can be extended to conduct experiments with various parameters, providing technical support for further testing of the inter-satellite laser link acquisition and pointing control methods.

Detecting Gravitational-wave Bursts from Black Hole Binaries in the Galactic Center with LISA

Stellar-mass black hole binaries (BHBs) in galactic nuclei are gravitationally perturbed by the central supermassive black hole (SMBH) of the host galaxy, potentially inducing strong eccentricity oscillations through the eccentric Kozai–Lidov mechanism. These highly eccentric binaries emit a train of gravitational-wave (GW) bursts detectable by the Laser Interferometer Space Antenna (LISA)—a planned space-based GW detector—with signal-to-noise ratios up to ∼100 per burst. In this work, we study the GW signature of BHBs orbiting our galaxy’s SMBH, Sgr A*, which are consequently driven to very high eccentricities. We demonstrate that an unmodeled approach using a wavelet decomposition of the data effectively yields the time-frequency properties of each burst, provided that the GW frequency peaks between 10−3 and 10−1 Hz. The wavelet parameters may be used to infer the eccentricity of the binary, measuring log10(1−e) within an error of 20%. Our proposed search method can thus constrain the parameter space to be sampled by complementary Bayesian inference methods, which use waveform templates or orthogonal wavelets to reconstruct and subtract the signal from LISA data.

Removing spikes in TianQin-1 inertial sensor data using machine learning method

Abstract The spikes in the inertial sensor data have been found to impact on the retrieval of the non-gravitational signals and the evaluation of the inertial sensor performance. Removing the spikes in the inertial sensor is critical for studies of gravitational reference sensors in space-based gravitational wave detection missions and accelerometers in gravity satellite missions. Thanks to a long period of inertial sensor data without thruster spikes, we can conduct machine learning based on this data to remove spikes. In this paper, a machine learning model called bi-directional long short-term memory (Bi-LSTM) neural network was built based on the inertial sensor data of TianQin-1 (TQ-1) mission. We use the machine learning method to remove the spikes in the inertial sensor data. After removing the spikes in the inertial sensor data, acceleration noise is suppressed form 2.0×10-7ms-2Hz-1/2 to the 2.8×10-10ms-2 Hz-1/2 at 0.1 Hz, which is far better than the existing methods, including the linear interpolation, data substitution and mean value of adjacent data.

Low-dimensional signal representations for massive black hole binary signals analysis from LISA data

The space-based gravitational wave observatory LISA will provide a wealth of information to analyze massive black hole binaries with high chirp masses, beyond $10^5$ solar masses. The large number of expected MBHBs (one event a day on average) increases the risk of overlapping between events. As well, the data will be contaminated with non-stationary artifacts, such as glitches and data gaps, which are expected to strongly impact the MBHB analysis, which mandates the development of dedicated detection and retrieval methods on long time intervals. Building upon a methodological approach we introduced for galactic binaries, in this article we investigate an original non-parametric recovery of MBHB signals from measurements with instrumental noise typical of LISA in order to tackle detection and signal reconstruction tasks on long time intervals. We investigated different approaches based on sparse signal modeling and machine learning. In this framework, we focused on recovering MBHB waveforms on long time intervals, which is a building block to further tackling more general signal recovery problems, from gap mitigation to unmixing overlapped signals. To that end, we introduced a hybrid method called SCARF (sparse chirp adaptive representation in Fourier), which combines a deep learning modeling of the merger of the MBHB with a specific adaptive time-frequency representation of the inspiral. Numerical experiments have been carried out on simulations of single MBHB events that account for the LISA response and with realistic realizations of noise. We checked the performances of the proposed hybrid method for the fast detection and recovery of the MBHB.

Dark matter phenomenology and phase transition dynamics of the next-to-minimal composite Higgs model with a dilaton

In this paper, we conduct a comprehensive study of the next-to-minimal composite Higgs model (NMCHM) extended with a dilaton field χ (denoted as NMCHMχ). A pseudo-Nambu-Goldstone boson (pNGB) η, resulting from the SO(6)→SO(5) breaking, serves as a dark matter (DM) candidate. The inclusion of the dilaton field is helpful for evading the stringent constraints from dark matter direct detection, as it allows for an accidental cancellation between the amplitudes of DM-nucleon scattering, an outcome of the mixing between the dilaton and Higgs fields. The presence of the dilaton field also enriches the phase transition patterns in the early universe. We identify two types of phase transitions: (i) a 1-step phase transition, where the chiral symmetry and electroweak symmetry breaking (EWSB) occur simultaneously, and (ii) a 2-step phase transition, where the chiral symmetry breaking transition takes place first, followed by a second phase transition corresponding to EWSB. Since the first-order phase transitions can be strong due to supercooling in our model, we also examine the stochastic background of gravitational waves generated by these phase transitions. We find that these gravitational waves hold promise for detection in future space-based gravitational wave experiments, such as LISA, Taiji, BBO, and DECIGO. Published by the American Physical Society 2024

Detecting ultralight dark matter gravitationally with laser interferometers in space

Ultralight dark matter (ULDM) is one of the leading well-motivated dark matter candidates, predicted in many theories beyond the standard model of particle physics and cosmology. There has been increasing interest in searching for ULDM in physical and astronomical experiments, mostly assuming there are additional interactions other than gravity between ULDM and normal matter. Here we demonstrate that even if ULDM has only gravitational interaction, it shall induce gravitational perturbations in solar system that may be large enough to cause detectable signals in future gravitational-wave (GW) laser interferometers in space. We investigate the sensitivities of Michelson time-delay interferometer to ULDM of various spins, and show vector ULDM with mass m≲10−18 eV can be probed by space-based GW detectors aiming at μHz frequencies. Our findings exhibit that GW detectors may directly probe ULDM in some mass ranges that otherwise are challenging to examine. Published by the American Physical Society 2024

Lomb-Scargle spectral analysis of plasma’s noise for space-based laser interferometric gravitational wave antennas

In space-based laser interferometric gravitational wave antennas, plasma from the solar wind is an important noise floor source for laser interferometric measurements between two distant spacecraft. In this study, we aim to analyze the impact of solar wind on the inter-satellite laser interferometric measurements of the Taiji mission, a space-based laser interferometric gravitational wave antenna proposed by the University of Chinese Academy of Sciences. Based on the 6.5-year electron number density data from the National Aeronautics and Space Administration Wind spacecraft and considering the uneven sampling characteristics of the data, we employed the Lomb–Scargle spectral analysis method to study the impact of solar wind plasma on intersatellite laser interferometric measurements within the frequency range of 1×10-6 Hz to 0.01 Hz. The study shows that the effect of the plasma on the intersatellite laser interferometric measurement is approximately 1 pm/Hz at 3.3 mHz, which is one order of magnitude smaller than the requirements on the displacement noise of the interferometric measurement of the Taiji mission, indicating that the noise due to plasma will not affect the aim of the Taiji mission to detect gravitational waves. The research can be applied to Taiji, Laser Interferometer Space Antenna, and future gravitational wave detection missions.

Nonlinear modeling and validation of spacecraft dynamics for space-based gravitational wave detector

The development of the Drag-Free and Attitude Control System is crucial for space-based gravitational wave detectors. The Drag-Free and Attitude Control System includes for spacecraft attitude control, drag-free control, moving optical subassemblies pointing control, and test masses electrostatic control during multiple phases of the mission lifetime. An accurate model of the spacecraft dynamics model is not only a precondition for the control design of Drag-Free and Attitude Control System, but also can serve as a valuable reference to assess the noise budget of gravitational wave detectors. This paper presents a generic, nonlinear mathematical model that describes the multi-body dynamics for the gravitational wave detectors. The model fully considers the couplings between the bodies involved, with a particular focus on the impact of the moving optical subassemblies on the spacecraft attitude. Additionally, a corresponding reduced model for the control design of the science mode is divided. Both models are validated numerically by Monte Carlo simulations and motion analysis, respectively.

Analysisof Beam Walk in Inter-Satellite Laser Link: Implications for Differential Wavefront Sensing in Gravitational Wave Detection

Achieving space-based gravitational wave detection requires the establishment of an interferometer constellation. It is necessary to establish and maintain stable laser interferometric links using the differential wavefront sensing (DWS) technnique. When the distant measurement beam experiences pointing jitter, it causes beam walk on the surface of the local detector. The reduced overlap between the local reference spot and the distant spot increases the nonlinear errors in the DWS technique, which need to be suppressed. Numerical analysis was conducted on the spatial beam interference signals of the DWS technique when the distant measurement beam experienced pointing jitter. An experimental measurement system was designed, and the beam walk was suppressed using a conjugate imaging system. The results show that within a range of 300 μrad, the optical path with the imaging system can reduce measurement errors by at least 83%. This way also helps to reduce pointing jitter noise in inter-satellite links, thereby improving laser pointing control accuracy.This method would provide a valuable reference for future DWS measurement systems.

Challenges in space-based gravitational wave data analysis and applications of artificial intelligence

Challenges in space-based gravitational wave data analysis and applications of artificial intelligence

Exploring Time Delay Interferometry ranging as a practical ranging approach in the Bayesian framework

Time Delay Interferometry (TDI) is an indispensable step in the whole data processing procedure of space-based gravitational wave detection, as it mitigates the overwhelming laser frequency noise, which would otherwise completely bury the gravitational wave signals. Knowledge on the inter-spacecraft optical paths (i.e. delays) is one of the key elements of TDI. Conventional method for inter-spacecraft ranging mainly relies on the pseudo-random noise (PRN) code signal modulated onto the lasers. To ensure the reliability and robustness of this ranging information, it would be highly beneficial to develop other methods which could serve as cross-validations or backups. This paper explores the practical implementation of an alternative data-driven approach – time delay interferometry ranging (TDIR) – as a ranging technique independent of the PRN signal. Distinguished from previous research, our TDIR algorithm significantly relaxes the stringent requirement for clock synchronization imposed by traditional TDI procedure. By framing TDIR as a Bayesian parameter estimation problem and employing a general polynomial parametrization, we demonstrate our algorithm with simulated data based on the numerical orbit of Taiji. In the presence of laser frequency noise and secondary noises, the estimated median values of delays are only 5.28 ns away from the ground truths, capable of suppressing laser frequency noise to the desired level. Additionally, we have also analyzed the requirements of mitigating optical bench noise and clock noise on TDIR, and presented an illustrative example for the impact of laser locking.

Gravitational Waves from First-Order Phase Transition in an Electroweakly Interacting Vector Dark Matter Model

Abstract We discuss gravitational waves (GWs) in an electroweakly interacting vector dark matter (DM) model. In the model, the electroweak gauge symmetry is extended to SU(2)$_0 \times$SU(2)$_1 \times$SU(2)$_2 \times$U(1)$_Y$ and spontaneously broken into SU(2)$_L \times$U(1)$_Y$ at TeV scale. The model has an exchange symmetry between SU(2)$_0$ and SU(2)$_2$. This symmetry stabilizes some massive vector bosons associated with the spontaneous symmetry breaking described above, and an electrically neutral one is a DM candidate. In a previous study, it was found that the gauge couplings of SU(2)$_0$ and SU(2)$_1$ are relatively large to explain the measured value of the DM energy density via the freeze-out mechanism. With the large gauge couplings, the gauge bosons potentially have a sizable effect on the scalar potential. In this paper, we focus on the phase transition of SU(2)$_0 \times$SU(2)$_1 \times$SU(2)$_2 \rightarrow$ SU(2)$_L$. We calculate the effective potential at finite temperature and find that the phase transition is first-order and strong in a wide range of the parameter space. The strong first-order phase transition generates GWs. We calculate the GW spectrum and find that it will be possible to detect the GWs predicted in the model by future space-based GW interferometers. We explore the regions of the parameter space probed by the GW detection. We find that the GW detection can probe the region where the mass of $h^{\prime }$, a CP-even scalar in the model, is a few TeV.

Configuration uncertainty propagation of gravitational-wave observatory using a directional state transition tensor

Configuration stability is essential for a space-based Gravitational-Wave (GW) observatory, which can be impacted by orbit insertion uncertainties. Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories. Current methods suffer from drawbacks related to high computational burden. To this end, a Radial-Tangential-Ddirectional State Transition Tensor (RT-DSTT)-based configuration uncertainty propagation method is proposed. First, two sensitive directions are found by capturing the dominant secular terms. Considering the orbit insertion errors along the two sensitive directions only, a reduced-order RT-DSTT model is developed for orbital uncertainty propagation. Then, the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using high-order derivatives. The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors. The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented. The performance of the proposed method is validated on the Laser Interferometer Space Antenna (LISA) project. Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.

Testing space-time non-commutativity with TianQin

The direct detection of gravitational waves offers a powerful tool to explore the nature of gravity and the structure of space-time. This paper focuses on the capabilities of space-based gravitational wave detectors in testing space-time non-commutativity. Our findings indicate that TianQin has the potential to impose constraints on the non-commutative scale at a sub-Planckian level using massive black hole binaries. Additionally, we have developed a pipeline tailored to this specific topic.

Orbital Stability Study of the Taiji Space Gravitational Wave Detector

Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main sources. Numerical simulation is an effective method to investigate the impact of perturbation on spacecraft orbits. This study shows that, in the context of the Taiji project, Earth’s gravity is an essential factor in the change in heliocentric formation configuration, contributing to the relative acceleration between spacecrafts in the order of O(10−6)m·s−2. Considering 00:00:00 on 27 October 2032 as the initial orbiting moment, under the influence of Earth’s gravitational perturbation, the maximum relative change in armlengths and variation rates of armlengths for Taiji is 1.6×105km, 32m·s−1, respectively, compared with the unperturbed Keplerian orbit. Additionally, by considering the gravitational perturbations of Venus and Jupiter, the armlength and relative velocity for Taiji are reduced by 16.01% and 17.45%, respectively, compared with when only considering that of Earth. The maximum amplitude of the formation motion indicator changes with the orbit entry time. Results show that the relative velocity increase between the spacecrafts is minimal when the initial orbital moment occurs in July. Moreover, the numerical simulation results are inconsistent when using different ephemerides. The differences between ephemerides DE440 and DE430 are smaller than those between DE440 and DE421.

On point-ahead angle control strategies for TianQin

Pointing-related displacement noises are crucial in space-based gravitational wave detectors, where point-ahead angle control of transmitted laser beams may contribute significantly. For TianQin that features a geocentric concept, the circular high orbit design with a nearly fixed constellation plane gives rise to small variations of the point-ahead angles within ±25 nrad in-plane and ±10 nrad off-plane, in addition to a static bias of 23 µrad predominantly within the constellation plane. Accordingly, TianQin may adopt fixed-value compensation for the point-ahead angles and absorb the small and slow variations into the pointing biases. To assess the in-principle feasibility, the far-field tilt-to-length (TTL) coupling effect is discussed, and preliminary requirements on far-field wavefront quality are derived, which have taken into account of TTL noise subtraction capability in post processing. The proposed strategy has benefits in simplifying the interferometry design, payload operation, and TTL noise mitigation for TianQin.

Constraints on Einstein-dilaton Gauss-Bonnet gravity with Taiji

In the 2030s, space-based gravitational-wave (GW) detectors will exhibit unprecedented sensitivity in the millihertz frequency band, greatly expanding the potential for testing theories of gravity compared to ground-based GW detectors. Inspired by effective string theory, Einstein-dilaton Gauss–Bonnet (EdGB) gravity introduces an extra dilaton scalar field that is directly coupled to higher curvature terms. Here, we investigate the capability of Taiji to constrain the parameters of EdGB gravity by analyzing GWs from massive black hole binaries (MBHBs). We utilize the parameterized post-Einsteinian (ppE) waveform with the leading order EdGB corrections for the inspiral phase of MBHBs. The constraints on the coupling constants are obtained by performing Fisher matrix analysis. With different mass ratios and spins χi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _i$$\\end{document} at redshifts z=2,3,4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=2,3,4,5$$\\end{document}, the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} bounds on the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} have the same order of magnitude: α∼107\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\alpha }\\sim 10^7$$\\end{document} m.