Space-borne Gravitational Wave Detectors Research Articles

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity f NL and g NL. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by C̃ ℓ ∝ [ℓ(ℓ + 1)]-1, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

Study on TPD Phasemeter to Suppress Low-Frequency Amplitude Fluctuation and Improve Fast-Acquiring Range for GW Detection.

A phasemeter as a readout system for the inter-satellite laser interferometer in a space-borne gravitational wave detector requires not only high accuracy but also insensitivity to amplitude fluctuations and a large fast-acquiring range. The traditional sinusoidal characteristic phase detector (SPD) phasemeter has the advantages of a simple structure and easy realization. However, the output of an SPD is coupled to the amplitude of the input signal and has only a limited phase-detection range due to the boundedness of the sinusoidal function. This leads to the performance deterioration of amplitude noise suppression, fast-acquiring range, and loop stability. To overcome the above shortcomings, we propose a phasemeter based on a tangent phase detector (TPD). The characteristics of the SPD and TPD phasemeters are theoretically analyzed, and a fixed-point simulation is further carried out for verification. The simulation results show that the TPD phasemeter tracks the phase information well and, at the same time, suppresses the amplitude fluctuation to the noise floor of 1 μrad/Hz1/2, which meets the requirements of GW detection. In addition, the maximum lockable step frequency of the TPD phasemeter is almost three times larger than the SPD phasemeter, indicating a greater fast-acquiring range.

Distinguishing ΛCDM from Evolving Dark Energy with Om Two-point Statistics: Implications from the Space-borne Gravitational-wave Detector

The Omh 2(z i , z j ) two-point diagnostics was proposed as a litmus test of the ΛCDM model, and measurements of the cosmic expansion rate H(z) have been extensively used to perform this test. The results obtained so far suggested a tension between observations and predictions of the ΛCDM model. However, the data set of H(z) direct measurements from cosmic chronometers and baryon acoustic oscillations was quite limited. This motivated us to study the performance of this test on a larger sample obtained in an alternative way. In this paper, we propose that gravitational-wave (GW) standard sirens could provide large samples of H(z) measurements in the redshift range of 0 < z < 5, based on the measurements of the dipole anisotropy of luminosity distance arising from the matter inhomogeneities of the large-scale structure and the local motion of the observer. We discuss the effectiveness of our method in the context of the space-borne DECi-herz Interferometer Gravitational-wave Observatory, based on a comprehensive H(z) simulated data set from binary neutron star merger systems. Our results indicate that in the GW domain, the Omh 2(z i , z j ) two-point diagnostics could effectively distinguish whether ΛCDM is the best description of our Universe. We also discuss the potential of our methodology in determining possible evidence for dark energy evolution, focusing on its performance on the constant and redshift-dependent dark energy equation of state.

The evaluation for plasma noise in arbitrary time-delay interferometry combinations

The laser interferometer space antenna (LISA) uses laser interferometry to measure gravitational wave-induced distance changes between freely falling test masses on separate spacecraft. In practice, the space-borne gravitational wave detector operates in a plasma medium, and subsequently, the variations in electron density affect the refractive index and add displacement noise to measurements. Geometric time-delay interferometry (TDI) is the TDI combinations searched by geometric method, which is employed to mitigate overwhelming laser phase noise. This study explores all forty-five second-generation geometric TDI combinations up to sixteen links, analyzing plasma noise effects via power spectral density and cross-spectral density calculations for different optical links. Our findings reveal that plasma noise can exceed the noise floor, which comprises optical metrology system and test mass acceleration noise, in certain low-frequency regions due to different noise transfer behaviors. Further, we establish electron density requirements for various TDI combinations, showing that densities below 100cm−3/Hz @ 10mHz satisfy LISA’s criteria across all forty-five combinations. This allows for optimized TDI selection based on specific plasma densities.

Search for Extreme Mass Ratio Inspirals Using Particle Swarm Optimization and Reduced Dimensionality Likelihoods

Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes (MBHs) with a mass range of approximately 104∼107M⊙. EMRIs are estimated to produce long-lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the high-dimensional and large-volume parameter space, make the fully coherent search challenging. In our previous work, we proposed a 10-dimensional search using Particle Swarm Optimization (PSO) with local maximization over the three initial angles. In this study, we extend the search to an 8-dimensional PSO with local maximization over both the three initial angles and the angles of spin direction of the MBH, where the latter contribute a time-independent amplitude to the waveforms. Additionally, we propose a 7-dimensional PSO search by using a fiducial value for the initial orbital frequency and shifting the corresponding 8-dimensional Time Delay Interferometry responses until a certain lag returns the corresponding 8-dimensional log-likelihood ratio’s maximum. The reduced dimensionality likelihoods enable us to successfully search for EMRI signals with a duration of 0.5 years and signal-to-noise ratio of 50 within a wider search range than our previous study. However, the ranges used by both the LISA Data Challenge (LDC) and Mock LISA Data Challenge (MLDC) to generate their simulated signals are still wider than the those we currently employ in our direct searches. Consequently, we discuss further developments, such as using a hierarchical search to narrow down the search ranges of certain parameters and applying Graphics Processing Units to speed up the code. These advances aim to improve the efficiency, accuracy, and generality of the EMRI search algorithm.

Absolute Ranging with Time Delay Interferometry for Space-Borne Gravitational Wave Detection.

In future space-borne gravitational wave (GW) detectors, time delay interferometry (TDI) will be utilized to reduce the overwhelming noise, including the laser frequency noise and the clock noise etc., by time shifting and recombining the data streams in post-processing. The successful operation of TDI relies on absolute inter-satellite ranging with meter-level precision. In this work, we numerically and experimentally demonstrate a strategy for inter-satellite distance measurement. The distances can be coarsely determined using the technique of arm-locking ranging with a large non-ambiguity range, and subsequently TDI can be used for precise distance measurement (TDI ranging) by finding the minimum value of the power of the residual noises. The measurement principle is introduced. We carry out the numerical simulations, and the results show millimeter-level precision. Further, we perform the experimental verifications based on the fiber link, and the distances can be measured with better than 0.05 m uncertainty, which can well satisfy the requirement of time delay interferometry.

MEMS miniaturized low-noise magnetic field sensor for the observation of sub-millihertz magnetic fluctuations in space exploration

The objective of this paper is to show that, using magnetic field modulation with a MEMS resonator, it is possible to reduce the noise floor of a commercial Tunneling Magnetic Resistance by one order of magnitude, in the ultra-low frequency range. Low noise at this frequency range is a strong requirement in planetary or space exploration missions like LISA (Laser Interferometer Space Antenna), where the observed gravitational waves will be in the 0.1 mHz to 0.1 Hz range. It will be shown that the noise spectral amplitude after demodulation from 0.1 mHz to 100 mHz is well below the 100 nT/Hz requirement for the future space-borne gravitational wave detector LISA – that we take as reference – being at 20 nT/Hz at 0.1 mHz, and reaching an average 1.5nT/Hz at higher frequencies, from 100 mHz to 1 Hz.

Transponder-type laser interferometer prototype for spaceborne gravitational wave detectors.

Transponder-type laser interferometry is essential in spaceborne gravitational wave detection missions. This paper presents a transponder-type laser interferometer prototype for potential noise calibration of spaceborne gravitational wave detectors. Using a digital optical phase-locked loop, we successfully locked the phase of the slave laser to the master laser (∼200p W). Once the link between the master laser and the slave laser is established, the two satellites (essentially two lasers) form a transponder-type laser interferometer. We carefully analyze the measurement stability and noise characteristics of the interferometer, and the results show that the Allan deviation of the zero drift can reach 243.2pm at t=0.429s, while the noise spectral density has a typical 1/f line shape with a floor of 21p m/H z 1/2 at 1Hz. The coherence analysis shows that the temperature drift is an important factor limiting the performance of the interferometer below 2mHz, while the frequency noise of the master laser is not dominant in the experiment. Transponder-type laser interferometers have a wide range of applications in intersatellite communication and measurement. Our design can serve as a valuable reference for gravitational wave detection missions such as LISA.

An energy-based approach to the nonlinear modelling and drag-free control system design of space-borne gravitational wave detectors

An energy-based approach to the nonlinear modelling and drag-free control system design of space-borne gravitational wave detectors

Primordial non-Gaussianity f NL and anisotropies in scalar-induced gravitational waves

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity f NL, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., Cℓ (ν) ∝ [ℓ(ℓ+1)]-1 with ν being a frequency and ℓ referring to the ℓ-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter f NL measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.

Magnetic field recovery technique based on distance weighting multipole expansion method

A space-borne gravitational wave detector requires the test mass (TM) to be in an ultra-low disturbance state. However, magnetic field fluctuations will disturb the TM and produce acceleration noise. To assess the influence of the magnetic field on the TM, it is necessary to monitor and reconstruct the magnetic field near the TM in real time. In this paper, a distance weighting multipole expansion (DWME) method was proposed, and its magnetic field reconstruction accuracy was analyzed. The results demonstrated that the proposed DWME method significantly improved the reconstruction precision compared to traditional methods. It reduced the average reconstruction error of the sensitive axial magnetic field from 1.2% to 0.8% and the maximum error from 16% to 8%. In the in-orbit situation, the DWME method also outperforms traditional methods.

Suppression of laser phase noise by using updated common arm locking

The space-borne gravitational wave (GW) detectors, e.g., LISA, TianQin, TaiJi, are designed to measure the GW in the low-frequency regime (0.1 mHz to 1 Hz). The arm length mismatches in the flying constellation prevent exact laser phase noise cancellation. For a typical Michelson interferometric design such as LISA, the two arms will differ by a few percent and the uncanceled fluctuation from the ultra-stable laser is about 5 orders larger than the sensitivity goal in the science band (0.1 mHz to 1 Hz). In this work, we try to resolve this discrepancy in real time by using an arm locking technique. Unlike the analysis in previous literatures, we use the subtraction of one closed loop phase meter output from another one at the main spacecraft to cancel the laser phase noise further. We find that, with a careful design of the arm locking controller, the laser phase noise can be suppressed below the level of secondary noises in most parts of the science band. We point out that since the nulls always exist in the presence the GW transfer function of Michelson interferometer, there is no need to move the nulls to outside the science band by using a complicated arm locking sensor. Then, a study on the Doppler frequency pulling for the system has been carried out, and the result suggests that the pulling rate can meet the requirement. Finally, a good agreement between the time-series simulation in Simulink and theoretical result indicates the feasibility of this scheme. Therefore, the suppression of laser phase noise can possibly be realized in real time with prestabilization and updated common arm locking techniques. Our work can provide a back-up strategy for the implementation of arm locking in future space-borne GW detectors.

Multimessenger observations of double neutron stars in the Galactic disk with gravitational and radio waves

We evaluate the prospects for radio follow-up of the double neutron stars (DNSs) in the Galactic disk that could be detected through future space-borne gravitational wave (GW) detectors. We first simulate the DNS population in the Galactic disk that is accessible to space-borne GW detectors according to the merger rate from recent LIGO results. Using the inspiraling waveform for the eccentric binary, the average number of the DNSs detectable by TianQin (TQ), LISA, and $\mathrm{TQ}+\mathrm{LISA}$ are 217, 368, and 429, respectively. For the joint GW detection of $\mathrm{TQ}+\mathrm{LISA}$, the forecasted parameter estimation accuracies, based on the Fisher information matrix, for the detectable sources can reach the levels of $\mathrm{\ensuremath{\Delta}}{P}_{\mathrm{b}}/{P}_{\mathrm{b}}\ensuremath{\lesssim}{10}^{\ensuremath{-}6}$, $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Omega}}\ensuremath{\lesssim}100\text{ }\text{ }{\mathrm{deg}}^{2}$, $\mathrm{\ensuremath{\Delta}}e/e\ensuremath{\lesssim}0.3$, and $\mathrm{\ensuremath{\Delta}}{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{P}}_{\mathrm{b}}/{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{P}}_{\mathrm{b}}\ensuremath{\lesssim}0.02$. These estimation accuracies are fitted in the form of power-law function of signal-to-noise ratio. Next, we simulate the radio pulse emission from the possible pulsars in these DNSs according to pulsar beam geometry and the empirical distributions of spin period and luminosity. For the DNSs detectable by $\mathrm{TQ}+\mathrm{LISA}$, the average number of DNSs detectable by the follow-up pulsar searches using the Parkes, FAST, SKA1, and SKA are 8, 10, 43, and 87, respectively. Depending on the radio telescope, the average distances of these GW-detectable pulsar binaries vary from 1 to 7 kpc. Considering the dominant radiometer noise and phase jitter noise, the timing accuracy of these GW-detectable pulsars can be as low as 70 ns while the most probable value is about $100\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}$.

Impact of combinations of time-delay interferometry channels on stochastic gravitational wave background detection

The method of time-delay interferometry (TDI) is proposed to cancel the laser noise in space-borne gravitational-wave detectors. Among all different TDI combinations, the most commonly used ones are the orthogonal channels A, E, and T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile, for the detection of stochastic gravitational-wave background, one needs to introduce the overlap reduction function to characterize the correlation between channels. For the calculation of overlap reduction function, it is often convenient to work in the low-frequency approximation, and assuming the equal-arm Michelson channels. However, if one wishes to work on the overlap reduction function of $\mathrm{A}/\mathrm{E}$ channels, then the low-frequency approximation fails. We derive the exact form of overlap reduction function for $\mathrm{A}/\mathrm{E}$ channels. Based on the overlap reduction function, we calculate the sensitivity curves of TianQin, TianQin $\mathrm{I}+\mathrm{II}$, and $\mathrm{TianQin}+\text{LISA}$. We conclude that the detection sensitivity calculated with $\mathrm{A}/\mathrm{E}$ channels is mostly consistent with that obtained from the equal-arm Michelson channels.

Constraining the evolution of Newton’s constant with slow inspirals observed from spaceborne gravitational-wave detectors

Spaceborne gravitational-wave (GW) detectors observing at milli-Hz and deci-Hz frequencies are expected to detect large numbers of quasi-monochromatic signals. The first and second time-derivative of the GW frequency ($\dot f_0$ and $\ddot f_0$) can be measured for the most favourable sources and used to look for negative post-Newtonian corrections, which can be induced by the source's environment or modifications of general relativity. We present an analytical, Fisher-matrix-based approach to estimate how precisely such corrections can be constrained. We use this method to estimate the bounds attainable on the time evolution of the gravitational constant $G(t)$ with different classes of quasi-monochromatic sources observable with LISA and DECIGO, two representative spaceborne detectors for milli-Hz and deci-Hz GW frequencies. We find that the most constraining source among a simulated population of LISA galactic binaries could yield $\dot G/G_0 \lesssim 10^{-6}\text{yr}^{-1}$, while the best currently known verification binary will reach $\dot G/G_0 \lesssim 10^{-4}\text{yr}^{-1}$. We also perform Monte-Carlo simulations using quasi-monochromatic waveforms to check the validity of our Fisher-matrix approach, as well as inspiralling waveforms to analyse binaries that do not satisfy the quasi-monochromatic assumption. We find that our analytical Fisher matrix produces good order-of-magnitude constraints even for sources well beyond its regime of validity. Monte-Carlo investigations also show that chirping stellar-mass compact binaries detected by DECIGO-like detectors at cosmological distances of tens of Mpc can yield constraints as tight as $\dot G/G_0 \lesssim 10^{-11}\text{yr}^{-1}$.

Oscillations and tidal deformations of crystallized white dwarfs

ABSTRACTLong predicted more than 50 years ago, strong evidence for the existence of crystalline cores inside white dwarfs has recently been obtained by the Gaia space telescope. It is thus important to investigate how a crystalline core may affect the properties and dynamics of white dwarfs. In this paper, we first study the dependence of the frequencies of the fundamental (f), interfacial (i), and shear (s) oscillation modes on the size of the crystalline core. We find that the frequencies of the i and s modes depend sensitively on the size of the core, while the frequency of the f mode is affected only slightly by at most a few percent for our chosen white dwarf models. We next consider the tidal deformability of crystallized white dwarfs and find that the effect of crystallization becomes significant only when the radius of the core is larger than about 70 per cent of the stellar radius. The tidal deformability can change by a few to about 10 per cent when a white dwarf becomes fully crystallized. We also show that there exist approximate equation-of-state insensitive relations connecting the mass, moment of inertia, tidal deformability, and f-mode frequency for pure fluid white dwarfs. Depending on the stellar mass and composition, however, these relations can be affected by a few percent when the white dwarf is crystallized. These changes could leave an imprint on the gravitational waves emitted from the late inspiral or merger of white dwarf binaries, which may be detectable by future space-borne gravitational wave detectors.

Black Hole Ultracompact X-Ray Binaries: Galactic Low-frequency Gravitational Wave Sources

In the Galaxy, close binaries with compact objects are important low-frequency gravitational wave (GW) sources. As potential low-frequency GW sources, neutron star/white dwarf (WD) ultracompact X-ray binaries (UCXBs) have been investigated extensively. Using the Modules for Experiments in Stellar Astrophysics code, we systematically explored the evolution of black hole (BH)-main-sequence star (MS) binaries to determine whether their descendants can be detected by space-borne GW detectors. Our simulations showed that BH-MS binaries with an initial orbital period less than the bifurcation period can evolve into BH UCXBs that can be detected by LISA. Such an evolutionary channel would form compact mass-transferring BH-WD systems rather than detached BH-WD systems. The calculated X-ray luminosities of BH UCXBs that can be detected by LISA at a distance d = 1 kpc are ∼1033–1035 erg s−1 (∼1034–1035 erg s−1 for d = 10 kpc); hence, it is possible to detect their electromagnetic counterparts. It is worth emphasizing that only some BH-MS systems with an initial orbital period very close to the bifurcation period can evolve toward low-frequency GW sources whose chirp masses can be measured. The maximum GW frequency of BH UCXBs forming via the BH-MS pathway is about 3 mHz, which is smaller than the minimum GW frequency (6.4 mHz) of mass-transferring BH-WDs originating from a dynamic process. Furthermore, we obtain an initial parameter space (donor-star masses and orbital periods) of progenitors of BH UCXB-GW sources, which can be applied to future population synthesis simulations. By a rough estimation, we predict that LISA would only be able to detect a few BH UCXB-GW sources formed by the BH-MS channel.

Study on picometer-level laser interferometer readout system in TianQin project

As a central payload of TianQin space-borne gravitational wave detector, inter satellite laser interferometer allows to measure distance variance with extremely high precision. The readout system, or phasemeter, is often based on all digital phase locked loop in an FPGA. However, sampling jitter is one of the main inevitable noise sources during digitization. Here we use the pilot tone correction to suppress sampling jitter noise. To obtain accurate correction coefficient rather than preset values by normal pilot tone (NPT) correction, a least squares method (LSM) is presented. The experimental results show that the noise floor after pilot tone correction reaches 5 µrad/Hz1/2, which meets the TianQin project displacement noise requirement of 1 pm/Hz1/2. Besides, the correlation between the signal corrected before and after by LSM method is less than half of that by NPT method.

Bayesian analysis of the stochastic gravitational-wave background with alternative polarizations for space-borne detectors

Future space gravitational-wave detectors will detect gravitational waves with high sensitivity in the mHz frequency band. One possible source is the stochastic gravitational-wave background (SGWB), possibly from astronomy and cosmology. Detecting SGWB could provide an opportunity to directly examine the polarization of gravitational waves. While general relativity predicts only two tensor modes for gravitational-wave polarization, general metric theories of gravity allow up to four additional modes, including two vector and two scalar modes. Observing other polarization modes of gravitational waves would directly indicate that general relativity needs to be modified. However, the application of polarization identification methods developed for ground-borne detectors to space-borne detectors will require improvement. In this paper, we design a new statistic for the characteristics of space-borne detectors and perform Bayesian analysis. We analyze the performance of the new statistics, including the signal-to-noise ratio, ability to identify SGWB, and parameter estimation. The results show that the Bayesian method with new statistics is good enough to meet the needs of space detectors to identify polarized SGWB. In particular, space-borne gravitational-wave detectors will have the ability to distinguish the scalar-breathing mode and the scalar-longitudinal mode with this Bayesian method, which ground-based detectors cannot.

An Implementation of Galactic White Dwarf Binary Data Analysis for MLDC-3.1

The space-borne gravitational wave detectors will observe a large population of double white dwarf binaries in the Milky Way. However, the search for double white dwarfs in the gravitational wave data will be time-consuming due to the large number of templates involved and antenna response calculation. In this paper, we implement an iterative combinatorial algorithm to search for double white dwarfs in MLDC-3.1 data. To quickly determine the rough parameters of the target sources, the following algorithms are adopted in a coarse search process: (1) using the downsampling method to reduce the number of original data points; (2) using the undersampling method to speed up the generation of a single waveform template; (3) using the stochastic template bank method to quickly construct the waveform template bank while achieving high coverage of the parameter space; (4) combining the FFT acceleration algorithm with the stochastic template bank to reduce the calculation time of a single template. A fine search process is applied to further determine the parameters of the signals based on the coarse search, for which we adopt the particle swarm optimization. Finally, we detect double white dwarf signals, validating the feasibility of our method.