Space-based Gravitational Wave Detectors Research Articles

Suppression of clock-jitter noise and laser phase noise in arm locking

Abstract Arm-locking technique has been a focus of attention as one of the means to suppress the laser phase noise in space-based gravitational wave detector. The main idea of the arm-locking technique is to transfer the stability of the detector arm length to laser frequency by introducing a feedback control loop. Generally, laser phase noise will be suppressed by an amount similar to the magnitude of the controller gain. However, on the one hand, clock-jitter noise and optical bench motion noise, as the noise floor of the arm-locking technique, need to be suppressed. On the other hand, limited by the Doppler frequency pulling, the gain of the controller generally cannot be too large. It means that even if we do not consider clock-jitter noise and optical bench motion noise, it is difficult to suppress laser phase noise below the noise floor only by arm-locking technique. In this work, we combine self-referenced optical frequency combs and arm-locking technique to generate clock signals that are coherently referenced to the closed-loop laser beams, so that the clock-jitter noise is also suppressed by about the level of controller gain. We conduct a simulation on the above configuration, and the results show that the performance of the arm-locking is no longer limited by clock-jitter noise in the low-frequency band. To address the issue of insufficient laser phase noise suppression by the arm-locking technique, we further investigate time-delay interferometry (TDI) combinations under outputs of arbitrary arm-locking configurations. We obtain the equations for eliminating laser phase noise. To ensure that the TDI combinations can directly operate in the time domain, we derive a restricted solution space by assuming a specific form for the solutions.

Probing stochastic ultralight dark matter with space-based gravitational-wave interferometers

Ultralight particles are theoretically well-motivated dark matter candidates. In the vicinity of the Solar System, these ultralight particles can be described as a superposition of plane waves, resulting in a stochastic field with sizable amplitude fluctuations on scales determined by the velocity dispersion of dark matter. In this work, we systematically investigate the sensitivity of space-based gravitational-wave interferometers to the stochastic ultralight dark matter field within the frequentist framework. We derive the projected sensitivity of a single detector using the time-delay interferometry. Our results show that space-based gravitational-wave interferometers have the potential to probe unconstrained regions in parameter space and improve the current limit on coupling strengths. Furthermore, we explore the sensitivity of a detector network and investigate the optimal configuration for ultralight dark matter detection. We introduce the overlap reduction function for ultralight dark matter, which quantifies the degree of correlation between the signals observed by different detectors. We find that the configuration, where the signals observed by two detectors are uncorrelated, is the optimal choice for ultralight dark matter detection due to a smaller chance of missing signals. This contrasts with the detection of stochastic gravitational-wave background, where the correlated configuration is preferred. Our results may provide useful insights for potential joint observations involving space-based gravitational-wave detectors like LISA and Taiji, as well as other ultralight dark matter detection networks operating in the coherence limit. Published by the American Physical Society 2024

Evaluating the gravitational wave detectability of globular clusters and the Magellanic Clouds for LISA

We used the stellar evolution code bpass and the gravitational wave (GW) simulation code legwork to simulate populations of compact binaries that may be detected by the future space-based GW detector LISA. Specifically, we simulate the Magellanic Clouds and binary populations mimicking several globular clusters, neglecting dynamical effects. We find that a handful of sources should be detectable in each of the Magellanic Clouds, but for globular clusters the amount of detectable sources will likely be less than one each. We compared our results to earlier research and find that our predicted numbers are several dozen times lower than both the results from calculations that used the stellar evolution code bse and take dynamical effects into account, and results from calculations that used the stellar evolution code SeBa for the Magellanic Clouds. Earlier research that compared bpass models for GW sources in the Galactic disk with bse models found a similarly sized discrepancy. We determine that this discrepancy is caused by differences between the stellar evolution codes, particularly in the treatment of mass transfer and common-envelope events in binaries: in bpass mass transfer is more likely to be stable and tends to lead to less orbital shrinkage in the common-envelope phase than in other codes. This difference results in fewer compact binaries with periods short enough to be detected by LISA existing in the bpass population. For globular clusters, we conclude that the impact of dynamical effects is uncertain based on the literature, but the differences in stellar evolution have an effect of a factor of 20 to 40 on the number of detectable binaries.

Black hole spectroscopy with ground-based atom interferometer and space-based laser interferometer gravitational wave detectors

Gravitational wave (GW) detection allows us to test general relativity in entirely new regimes. A prominent role takes the detection of quasi-normal modes (QNMs), which are emitted after the merger of a binary black hole (BBH) when the highly distorted remnant emits GWs to become a regular Kerr black hole (BH). The BH uniqueness theorems of Kerr black hole solutions in general relativity imply that the frequencies and damping times of QNMs are determined solely by the mass and spin of the remnant BH. Therefore, detecting QNMs offers a unique way to probe the nature of the remnant BH and to test general relativity. We study the detection of a merging BBH in the intermediate-mass range, where the inspiral–merger phase is detected by space-based laser interferometer detectors TianQin and LISA, while the ringdown is detected by the ground-based atom interferometer (AI) observatory AION. The analysis of the ringdown is done using the regular broadband mode of AI detectors as well as the resonant mode optimizing it to the frequencies of the QNMs predicted from the inspiral–merger phase. We find that the regular broadband mode allows constraining the parameters of the BBH with relative errors of the order 10−1 and below from the ringdown. Moreover, for a variety of systems considered, the frequencies and the damping times of the QNMs can be determined with relative errors below 0.1 and 0.2, respectively. We further find that using the resonant mode can improve the parameter estimation for the BBH from the ringdown by a factor of up to three. Utilizing the resonant mode significantly limits the detection of the frequency of the QNMs but improves the detection error of the damping times by around two orders of magnitude.

Uncertainty of the white dwarf astrophysical gravitational wave background

The astrophysical gravitational wave background (AGWB) is a stochastic gravitational wave (GW) signal emitted by different populations of in-spiralling binary systems containing compact objects throughout the Universe . In the frequency range between 10$^ $ and 10$^ $ hertz (Hz), it will be detected by future space-based gravitational wave detectors, such as Laser Interferometer Space Antenna (LISA). In a recent work, we concluded that the white dwarf (WD) contribution to the AGWB dominates that of black holes (BHs) and neutron stars (NSs) We aim to investigate the uncertainties of the WD AGWB that arise from the use of different stellar metallicities, star formation rate density (SFRD) models, and binary evolution models. We used the code we previously developed to determine the WD component of the AGWB. We used a metallicity-dependent SFRD based on an earlier work to construct five different SFRD models. We used four different population models based on a range of common-envelope treatments and six different metallicities for each model. For all possible combinations, the WD component of the AGWB is dominant over other populations of compact objects. The effects of metallicity and population model are less significant than the effect of a (metallicity dependent) SFRD model. We find a range of about a factor of 5 in the level of the WD AGWB around a value of $ WD $ at 1 mHz and a shape that is weakly dependent on the model. We find the uncertainty for the WD component of the AGWB to be about a factor of 5. We note that there are other uncertainties that have an effect on this signal as well. We discuss whether the turnover of the WD AGWB at 10 mHz will be detectable by LISA and find it to be likely. We confirm our previous findings asserting that the WD component of the AGWB dominates over other populations, in particular, BHs.

Time-delay interferometry with onboard optical delays

Time-delay interferometry (TDI) is a data processing technique for space-based gravitational-wave detectors to create laser-noise-free equal-optical-path-length interferometers virtually on the ground. It relies on the interspacecraft signal propagation delays, which are delivered by intersatellite ranging monitors. Also, onboard signal propagation and processing delays have a non-negligible impact on the TDI combinations. However, these onboard delays were only partially considered in previous TDI-related research; onboard optical path lengths have been neglected. In this paper, we study onboard optical path lengths in TDI. We derive analytical models for their coupling to the second-generation TDI Michelson combinations and verify these models numerically. Furthermore, we derive a compensation scheme for onboard optical path lengths in TDI and validate its performance via numerical simulations. Published by the American Physical Society 2024

Sky localization of space-based detectors with time-delay interferometry

The accurate sky localization of gravitational wave (GW) sources is an important scientific goal for space-based GW detectors. The main differences between future space-based GW detectors, such as Laser Interferometer Space Antenna (LISA), Taiji, and TianQin, include the time-changing orientation of the detector plane, the arm length, the orbital period of the spacecraft and the noise curve. Because of the effects of gravity on three spacecraft, it is impossible to maintain the equality of the arm length, so the time-delay interferometry (TDI) method is needed to cancel out the laser frequency noise for space-based GW detectors. Extending previous work based on equal-arm Michelson interferometer, we explore the impacts of different first-generation TDI combinations and detector's constellations on the sky localization for monochromatic sources. We find that the sky localization power is almost unaffected by the inclusion of the TDI Michelson (X, Y, Z) combination in the analysis. We also find that the variation in the sky localization power for different TDI combinations is entirely driven by the variation in the sensitivities of these combinations. For the six particular TDI combinations studied, the Michelson (X, Y, Z) combination is the best for source localization.

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.

Continuous gravitational waves: A new window to look for heavy nonannihilating dark matter

Sunlike stars can transmute into comparable mass black holes by steadily accumulating heavy nonannihilating dark matter particles over the course of their lives. If such stars form in binary systems, they could give rise to quasi-monochromatic, persistent gravitational waves, commonly known as continuous gravitational waves, as they inspiral toward one another. We demonstrate that next-generation space-based detectors, e.g., Laser Interferometer Space Antenna (LISA) and Big Bang Observer (BBO), can provide novel constraints on dark matter parameters (dark matter mass and its interaction cross-section with the nucleons) by probing gravitational waves from transmuted sunlike stars that are in close binaries. Our projected constraints depend on several astrophysical uncertainties and nevertheless are competitive with the existing constraints obtained from cosmological measurements as well as terrestrial direct searches, demonstrating a notable science case for these space-based gravitational wave detectors as probes of particle dark matter. Published by the American Physical Society 2024

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.

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

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.

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.

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.

Detectability of stochastic gravitational wave background from weakly hyperbolic encounters

We compute the stochastic gravitational wave (GW) background generated by black hole–black hole (BH–BH) hyperbolic encounters with eccentricities close to one and compare them with the respective sensitivity curves of planned GW detectors. We use the Keplerian potential to model the orbits of the encounters and the quadrupole formula to compute the emitted GWs. We take into account hyperbolic encounters that take place in clusters up to redshift 5 and with BH masses spanning from 5 M⊙ to 55 M⊙. We assume the clusters to be virialized and study several cluster models with different mass and virial velocity, and finally obtain an accumulative result, displaying the background as an average. Using the maxima and minima of our accumulative result for each frequency, we provide analytical expressions for both optimistic and pessimistic scenarios. Our results suggest that the background from these encounters is likely to be detected by the third-generation detectors Cosmic explorer and Einstein telescope, while the tail section at lower frequencies intersects with DECIGO, making it a potential target source for both ground- and space-based future GW detectors.

Gravitational waves with dark matter minispikes: Fourier-domain waveforms of eccentric intermediate-mass-ratio-inspirals

Abstract An intermediate mass black hole (IMBH) may have a dark matter (DM) minihalo around it and develop a spiky structure called DM minispike. Gravitational waves (GWs) can be produced if a stellar compact object, such as a black hole (BH) or neutron star, inspirals into the IMBH. This kind of systems are known as itermediate-mass-ratio-inspirals (IMRIs) and may be observed by space-based gravitational wave detectors including LISA, Taiji and Tianqin. In this paper, we lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waves produced by eccentric IMRIs with DM minispikes in a post-circular or small-eccentricity approximation (e < 0.4). We take the effect of dynamical friction from the DM as a perturbation, and decompose the dynamical equations into perturbed part and unperturbed part. The equations are solved in a series expansion form about zero initial eccentricity to eighth order. The time-dependent, “plus” and “cross” polarizations are expanded in Bessel functions, which are then self-consistently reexpanded in a power series about zero initial eccentricity. The stationary-phase approximation is then employed to obtain the explicit DM-modified analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering a typical IMRI with a DM minispike and find the GW detectability strongly depends on the radial profile of the DM distribution. When the density of DM is large enough, the signal to noise ratio (SNR) will be degraded significantly and a detection loss may occur if we use a template without the effect of DM to treat a signal including the DM effect. With the Fourier-domain gravitational waveforms we also estimate the accuracy of the measurement of the DM minispike parameters in our reference model. Our framework hold the promise to construct a “ready-to-use” Fourier-domain waveforms for data analysis of eccentric IMRIs with DM minispikes.

Prospects for Taiji to detect a gravitational-wave background from cosmic strings

Recently, multiple pulsar timing array collaborations have presented compelling evidence for a stochastic signal at nanohertz frequencies, potentially originating from cosmic strings. Cosmic strings are linear topological defects that can arise during phase transitions in the early Universe or as fundamental strings in superstring theory. This paper focuses on investigating the detection capabilities of Taiji, a planned space-based gravitational wave detector, for the gravitational wave background generated by cosmic strings. By analyzing simulated Taiji data and utilizing comprehensive Bayesian parameter estimation techniques, we demonstrate a significant improvement in precision compared to the NANOGrav 15-year data set, surpassing it by an order of magnitude. This highlights the enhanced measurement capabilities of Taiji. Consequently, Taiji can serve as a valuable complementary tool to pulsar timing arrays in validating and exploring the physics of cosmic strings in the early Universe.

Low Frequency Hierarchical Cooperative Impulse Control for Gravitational Wave Detector Formation Keeping

Configuration stability is crucial for the detection accuracy of space-based gravitational wave (GW) detectors. This paper proposes a low-frequency hierarchical cooperative impulse control strategy and a high-fidelity orbit optimization method to achieve a formation of GW detectors with high detection performance. The control strategy employs a hierarchical structure to divide the configuration control into position and shape layers. In the upper layer, the position layer, a state transition tensor method is employed to analyze the sensitivity and feasible range of the formation center position on the configuration stability. In the lower layer, the shape layer, a novel consistency protocol cooperatively uses the states of all individuals in the formation to determine the control expectations. The constraint on formation position is relaxed to reduce the number of impulses, achieving a low-frequency impulse control. The optimization method, characterized by a careful selection of the optimization variables and a design of adaptive model continuation from a low-fidelity model to a high-fidelity model, is proposed to reduce the problem-solving difficulty. The proposed strategy and method are applied to the Laser Interferometer Space Antenna (LISA) mission, and the results demonstrate that the configuration stability is effectively enhanced with several low-frequency impulses.

Deep learning forecasts of cosmic acceleration parameters from DECi-hertz Interferometer Gravitational-wave Observatory

Context. Validating the accelerating expansion of the universe is an important aspect in improving our understanding of the evolution of the universe. By constraining the cosmic acceleration parameter XH, we can discriminate between the cosmological constant plus cold dark matter (ΛCDM) model and the Lemaître–Tolman–Bondi (LTB) model. Aims. In this paper, we explore the possibility of constraining the cosmic acceleration parameter with the inspiral gravitational waveform of neutron star binaries (NSBs) in the frequency range of 0.1 Hz–10 Hz, which can be detected by the second-generation space-based gravitational wave detector DECIGO. Methods. We used a convolutional neural network (CNN) and a long short-term memory (LSTM) network combined with a gated recurrent unit (GRU), along with a Fisher information matrix to derive constraints on the cosmic acceleration parameter, XH. Results. We assumed that our networks estimate the cosmic acceleration parameter without biases (the expected value of the estimation is equal to the true value). Under this assumption, based on the simulated gravitational wave data with a time duration of one month, we conclude that CNN can limit the relative error to 15.71%, while LSTM network combined with GRU can limit the relative error to 14.14%. Additionally, using a Fisher information matrix for gravitational wave data with a five-year observation can limit the relative error to 32.94%. Conclusions. Under the assumption of an unbiased estimation, the neural networks can offer a high-precision estimation of the cosmic acceleration parameter at different redshifts. Therefore, DECIGO is expected to provide direct measurements of the acceleration of the universe by observing the chirp signals of coalescing binary neutron stars.