Space-borne Gravitational Wave Detectors Research Articles

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.

Resistive-Based Micro-Kelvin Temperature Resolution for Ultra-Stable Space Experiments.

High precision temperature measurements are a transversal need in a wide area of physical experiments. Space-borne gravitational wave detectors are a particularly challenging case, requiring both high precision and high stability in temperature measurement. In this contribution, we present a design able to reach 1 μK/Hz in most of the measuring band down to 1 mHz, and reaching 20 μK/Hz at 0.1 mHz. The scheme is based on resistive sensors in a Wheatstone bridge configuration which is AC modulated to minimize the 1/f noise. As a part of our study, we include the design of a test bench able to guarantee the high stability environment required for measurements. We show experimental results characterising both the test bench and the read-out, and discuss potential noise sources that may limit our measurement.

Time delay interferometry with a transfer oscillator.

In this work, we experimentally perform time delay interferometry by using a transfer oscillator, which is capable of reducing the laser frequency noise and the clock noise simultaneously in the post processing. The iodine frequency reference is coherently downconverted to the microwave frequency using a laser frequency comb. The residual noise of the downconversion network is 5 × 10-6Hz/Hz1/2 at 0.7 mHz, and 4 × 10-6Hz/Hz1/2 at 0.1 Hz, indicating high homology between the optical frequency and the microwave frequency. We carry out time delay interferometry with the aid of the electrical delay module, which can introduce large time delays. The results show that the laser frequency noise and the clock noise can be reduced simultaneously by ten and three orders of magnitude, respectively, in the frequency band from 0.1 mHz to 0.1 Hz. The performance of the noise reduction can reach 6 × 10-8Hz/Hz1/2 at 0.1 mHz, and 7 × 10-7Hz/Hz1/2 at 1 mHz, meeting the requirements of the space-borne gravitational wave detection. Our work will be able to offer an alternative method for the frequency comb-based time delay interferometry in the future space-borne gravitational wave detectors.

Resolving Galactic binaries using a network of space-borne gravitational wave detectors

Extracting gravitational wave (GW) signals from individual Galactic binaries (GBs) against their self-generated confusion noise is a key data analysis challenge for space-borne detectors operating in the $\ensuremath{\approx}0.1$ to $\ensuremath{\approx}10\text{ }\text{ }\mathrm{mHz}$ range. Given the likely prospect that there will be multiple such detectors, namely Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin, with overlapping operational periods in the next decade, it is important to examine the extent to which the joint analysis of their data can benefit GB resolution and parameter estimation. To investigate this, we use realistic simulated LISA and Taiji data containing the set of $30\ifmmode\times\else\texttimes\fi{}{10}^{6}$ GBs used in the first LISA data challenge (Radler) and an iterative source extraction method called GBSIEVER introduced in an earlier work. We find that a coherent network analysis of LISA-Taiji data boosts the number of confirmed sources by $\ensuremath{\approx}75%$ over that from a single detector. The residual after subtracting out the reported sources from the data of any one of the detectors is much closer to the confusion noise expected from an ideal, but infeasible, multisource resolution method that perfectly removes all sources above a given signal-to-noise ratio threshold. While parameter estimation for sources common to both the single detector and network improves broadly in line with the enhanced signal-to-noise ratio of GW sources in the latter, deviation from the scaling of error variance predicted by Fisher information analysis is observed for a subset of the parameters.

Decentralized X-ray pulsar-based navigation system for space-borne gravitational wave detector

In this paper, the inter-satellite link (ISL) aided X-ray pulsar-based navigation (XPNAV) system is studied to improve the survivability of space-borne gravitational wave detector. An unscented transform (UT) based distributed Kalman estimator is proposed for state estimation within less computational and communication costs. Three different navigation scenarios are designed based on a typical large-scale distributed heliocentric orbital space-borne gravitational wave detector, Laser Interferometer Space Antenna (LISA). Simulation results show that the positioning root-mean-square error (RMSE) reduces ̃28% after introducing the ISL to XPNAV. Moreover, the proposed distributed Kalman estimator and the classical Kalman estimator shows similar performance in XPNAV/ISL integrated navigation system with the positioning RMSE of ̃528m and ̃520m, respectively. Compared with the classical method, both analytical and simulating analyses demonstrate that the proposed algorithm efficiently reduces the computational costs to 1/N2 for a team with N agents and avoids additional communication needs simultaneously. The efficient distributed Kalman estimator-based XPNAV/ISL integrated navigation provides a high-performance autonomous navigation solution for interplanetary spacecraft formation flying missions.

Weak-Light Phase-Locking Time Delay Interferometry with Optical Frequency Combs.

In the future space-borne gravitational wave (GW) detector, the optical transponder scheme, i.e., the phase-locking scheme, will be utilized so as to maintain the signal-to-noise ratio (SNR). In this case, the whole constellation will share one common laser equivalently, which enables the considerable simplification of time delay interferometry (TDI) combinations. Recently, and remarkably, the unique combination of TDI and optical frequency comb (OFC) has shown a bright prospect for the future space-borne missions. When the laser frequency noise and the clock noise are synchronized using OFC as the bridge, the data streams will be reasonably simplified. However, in the optical transponder scheme, the weak-light phase-locking (WLPL) loops could bring additional noises. In this work, we analyze the phase-locking scheme with OFC and transfer characteristics of the noises including the WLPL noise. We show that the WLPL noise can be efficiently reduced by using the specific TDI combination, and the cooperation of phase-locking and frequency combs can greatly simplify the post-processing.

Thermal environment analysis for TianQin: II. Solar irradiance disparity across constellation

Space-borne gravitational wave (GW) detectors aim to detect GWs in low and middle frequency ranges, as a complement to the terrestrial detectors like LIGO and VIRGO. As the detectors are extremely sensitive to temperature fluctuation, great efforts have been taken to perform thermal analyses on the satellite platforms. Our previous work analysed the external thermal environment of an individual satellite for the TianQin mission. This paper raises the issue of thermal disparity across the triangular constellation. Based on optimized orbits of the TianQin, the LISA, the eLISA/NGO, and the ASTROD-GW, we evaluate the solar irradiance differences between adjacent satellites and make comparisons of the results among the missions. We subsequently introduce a universal relation to describe how orbit type and arm lengths may affect the maximum disparity. For the geocentric orbits of TianQin, we further extend the discussion on the science observation windows.

Geometric approach for the modified second generation time delay interferometry

The time delay interferometry (TDI) is an algorithm proposed to suppress the laser frequency noise in space-borne gravitational wave detectors. As a post-processing technique, it is implemented by constructing a virtual equal arm interferometer through an appropriate combination of the time-shifted data streams. Such an approach is tailored to the intrinsic feature of the space-based gravitational wave detection, namely, the distances between spacecraft are governed by the orbit dynamics and thus can not be held constant. Among different implementations, the geometric TDI was introduced as a method of exhaustion to evaluate the second-generation TDI combinations. The applications of the algebraic approach based on computational algebraic geometry, on the other hand, are mostly restricted to the first and the modified first-generation TDI. Besides, geometric TDI furnishes an intuitive physical interpretation about the synthesis of the virtual optical paths. In this paper, the geometric TDI is utilized to investigate the modified second-generation TDI combinations in conjunction with a ternary search algorithm. The distinction between the second-generation and modified second-generation TDI solutions is elaborated regarding the rate of change of the arm lengths with respect to the opposite cyclic directions. For the sixteen-link combinations, forty second-generation TDI solutions are recovered, among which nine of them are identified as the modified second-generation ones.

Drag-free control design and in-orbit validation of TianQin-1 satellite

Drag-free control (DFC) is one of the key technologies for space-borne gravitational wave detectors. For the TianQin (TQ) project, non-gravitational disturbances on the spacecraft must be suppressed by DFC. TianQin-1 (TQ-1) is the first satellite for technology verification, whose main goal is to verify the disturbances reduction technologies. In this paper, the DFC requirement and preliminary analysis for the TQ project are introduced, and then the design and the experimental validation with the TQ-1 satellite is presented. In-orbit results show a successful validation of DFC and the residual acceleration of TQ-1 satellite has been suppressed to at 10 mHz versus thruster noise.

Confronting the primordial black hole scenario with the gravitational-wave events detected by LIGO-Virgo

Adopting a binned method, we model-independently reconstruct the mass function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH mass function can be explained by a broad red-tilted power spectrum of curvature perturbations if all the events (or the small effective spin events) have a primordial origin. Even though GW190521 with component masses in upper mass gap (m>65M⊙) can be naturally interpreted in the PBH scenario, the events (including GW190814, GW190425, GW200105, and GW200115) with component masses in the light mass range (m<3M⊙) are quite unlikely to be explained by binary PBHs although there are no electromagnetic counterparts because the corresponding PBH merger rates are much smaller than those given by LIGO-Virgo. Furthermore, we predict that both the gravitational-wave (GW) background generated by the binary PBHs and the scalar-induced GWs accompanying the formation of PBHs should be detected by the ground-based and space-borne GW detectors and pulsar timing arrays in the future.

Constraining the cosmological parameters using gravitational wave observations of massive black hole binaries and statistical redshift information

Space-borne gravitational wave detectors like TianQin are expected to detect GW signals emitted by the mergers of massive black hole binaries. Luminosity distance information can be obtained from GW observations, and one can perform cosmological inference if redshift information can also be extracted, which would be straightforward if an electromagnetic counterpart exists. In this paper, we concentrate on the conservative scenario where the EM counterparts are not available, and comprehensively study if cosmological parameters can be inferred through a statistical approach, utilizing the non-uniform distribution of galaxies as well as the black hole mass-host galaxy bulge luminosity relationship. By adopting different massive black hole binary merger models, and assuming different detector configurations, we conclude that the statistical inference of cosmological parameters is indeed possible. TianQin is expected to constrain the Hubble constant to a relative error of about 4%-7%, depending on the underlying model. The multidetector network of TianQin and LISA can significantly improve the precision of cosmological parameters. In the most favorable model, it is possible to achieve a level of 1.7% with a network of TianQin and LISA. We find that without EM counterparts, constraints on all other parameters need a larger number of events or more precise sky localization of GW sources, which can be achieved by the multidetector network or under a favorable model for massive black hole mergers. However, in the optimistic case, where EM counterparts are available, one can obtain useful constraints on all cosmological parameters in the Lambda-CDM cosmology, regardless of the population model. Moreover, we can also constrain the equation of state of the dark energy without the EM counterparts, and it is even possible to study the evolution of EoS of the DE when the EM counterparts are observed.

Constraining the Hubble constant to a precision of about 1% using multi-band dark standard siren detections

Gravitational wave signal from the inspirai of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspirai covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly 30% through detections of 10 gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of <10%, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within 5% precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about 1%. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P-P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant.

Arm locking using laser frequency comb

The space-borne gravitational wave (GW) detectors, e.g., LISA, TaiJi, and TianQin, will open the window in the low-frequency regime (0.1 mHz to 1 Hz) to study the highly energetic cosmic events, such as coalescences and mergers of binary black holes and neutron stars. For the sake of successful observatory of GWs, the required strain sensitivity of the detector is approximately 10-21/Hz1/2 in the science band, 7 orders of magnitude better than the state of the art of the ultra-stable laser. Arm locking is therefore proposed to reduce the laser phase noise by a few orders of magnitude to relax the burden of time delay interferometry. During the past two decades, various schemes have been demonstrated by using single or dual arms between the spacecraft, with consideration of the gain, the nulls in the science band, and the frequency pulling characteristics, etc. In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. When the laser source is pre-stabilized to a Fabry-Perot cavity or a Mach-Zehnder interferometer, the noise can reach the floor determined by the clock noise, the spacecraft motion, and the shot noise. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only does our method allow the suppression of the peaks, the high gain, and low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We then discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Finally, the time-series simulations in Simulink have been carried out, and the results indicate a good agreement with the theory, showing that the presented method is reasonable and feasible. Our work could provide a back-up strategy for the arm locking in the future space-borne GW detectors.

Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories

Stellar-mass binary black holes (BBHs) may merge in the vicinity of a supermassive black hole (SMBH). It is suggested that the gravitational-wave (GW) emitted by a BBH has a high probability to be lensed by the SMBH if the BBH's orbit around the SMBH (i.e., the outer orbit) has a period of less than a year and is less than the duration of observation of the BBH by a space-borne GW observatory. For such a BBH + SMBH triple system, the de Sitter precession of the BBH's orbital plane is also significant. In this work, we thus study GW waveforms emitted by the BBH and then modulated by the SMBH due to effects including Doppler shift, de Sitter precession, and gravitational lensing. We show specifically that for an outer orbital period of 0.1 yr and an SMBH mass of $10^7 M_\odot$, there is a 3\%-10\% chance for the standard, strong lensing signatures to be detectable by space-borne GW detectors such as LISA and/or TianGO. For more massive lenses ($\gtrsim 10^8 M_\odot$) and more compact outer orbits with periods <0.1 yr, retro-lensing of the SMBH might also have a 1%-level chance of detection. Furthermore, by combining the lensing effects and the dynamics of the outer orbit, we find the mass of the central SMBH can be accurately determined with a fraction error of $\sim 10^{-4}$. This is much better than the case of static lensing because the degeneracy between the lens' mass and the source's angular position is lifted by the outer orbital motion. Including lensing effects also allows the de Sitter precession to be detectable at a precession period 3 times longer than the case without lensing. Lastly, we demonstrate that one can check the consistency between the SMBH's mass determined from the orbital dynamics and the one inferred from gravitational lensing, which serves as a test on theories behind both phenomena. The statistical error on the deviation can be constrained to a 1% level.

Wet extreme mass ratio inspirals may be more common for spaceborne gravitational wave detection

Extreme mass ratio inspirals (EMRIs) can be classified as dry EMRIs and wet EMRIs based on their formation mechanisms. Dry (or the ``loss-cone'') EMRIs, previously considered as the main EMRI sources for the Laser Interferometer Space Antenna, are primarily produced by multibody scattering in the nuclear star cluster and gravitational capture. In this work, we highlight an alternative EMRI formation channel: (wet) EMRI formation assisted by the accretion flow around accreting galactic-center massive black holes (MBHs). In this channel, the accretion disk captures stellar-mass black holes that are initially moving on inclined orbits and subsequently drives them to migrate towards the MBH---this process boosts the formation rate of EMRIs in such galaxies by orders of magnitude. Taking into account the fraction ($\mathcal{O}({10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}1})$) of active galactic nuclei where the MBHs are expected to be rapidly accreting, we forecast that wet EMRIs will contribute an important or even dominant fraction of all detectable EMRIs by spaceborne gravitational wave detectors.

Alternative LISA-TAIJI networks

The spaceborne gravitational wave (GW) detectors LISA and TAIJI are planned to be launched in the 2030s. The dual detectors with comparable sensitivities will form a network observing GWs with significant advantages. In this work, we investigate the three possible LISA-TAIJI networks for the different location and orientation compositions of the LISA orbit ($+60\ifmmode^\circ\else\textdegree\fi{}$ inclination and trailing the Earth by 20\ifmmode^\circ\else\textdegree\fi{}) and alternative TAIJI orbit configurations, including TAIJIp ($+60\ifmmode^\circ\else\textdegree\fi{}$ inclination and leading the Earth by 20\ifmmode^\circ\else\textdegree\fi{}), TAIJIc ($+60\ifmmode^\circ\else\textdegree\fi{}$ inclination and colocated with LISA), and TAIJIm ($\ensuremath{-}60\ifmmode^\circ\else\textdegree\fi{}$ inclination and leading the Earth by 20\ifmmode^\circ\else\textdegree\fi{}). Of the three LISA-TAIJI configurations, the LISA-TAIJIm network shows the best performance in the sky localization and polarization determination for massive binary systems due to its better complementary antenna pattern, and LISA-TAIJIc could achieve the best cross-correlation and observe the stochastic GW background with optimal sensitivity.

Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits

Extreme-mass-ratio inspirals (EMRIs) are among the most important sources for future spaceborne gravitational wave detectors. In this kind of system, compact objects usually orbit around central supermassive black holes on complicated trajectories. Usually, these trajectories are approximated as the geodesics of Kerr space-times, and orbital evolution is simulated with the help of the adiabatic approximation. However, this approach omits the influence of the compact object on its background. In this paper, using the effective one-body formalism, we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit (omitting the orbital inclination) and express the fundamental orbital frequencies in explicit forms. Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion. Furthermore, we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes. By calculating the gravitational waves using the Teukolsky equations, we quantitatively reveal the influence of the mass of the compact object on the data analysis. We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.

Formation rate of extreme mass ratio inspirals in active galactic nuclei

Extreme mass ratio inspirals (EMRIs) are important sources for space-borne gravitational wave detectors, such as the laser interferometer space antenna and TianQin. Previous EMRI rate studies have focused on the ``loss cone'' scenario, where stellar-mass black holes (sBHs) are scattered into highly eccentric orbits near the central massive black hole (MBH) via multibody interaction. In this work, we calculate the rate of EMRIs of an alternative formation channel: EMRI formation assisted by the accretion flow around accreting massive black holes. In this scenario, sBHs and stars on inclined orbits are captured by the accretion disk, and then subsequently migrate towards the MBH, under the influence of density wave generation and head wind. By solving the Fokker-Planck equation incorporating both sBH-sBH--sBH-star scatterings and sBH--star-disk interactions, we find that an accretion disk usually boosts the EMRI formation rate per individual MBH by $\mathcal{O}({10}^{1}--{10}^{3})$ compared with the canonical loss cone formation channel. Taking into account that the fraction of active Galactic nuclei (AGNs) is $\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}1})$, where the MBHs are expected to be rapidly accreting, we expect EMRI formation assisted by AGN disks to be an important channel for all EMRIs observed by space-borne gravitational wave detectors. These two channels also predict distinct distributions of EMRI eccentricities and orbit inclinations with respect to the MBH spin equatorial plane, which can be tested by future gravitational wave observations.

Relating black hole shadow to quasinormal modes for rotating black holes

In this work, we explore the connection between the critical curves ("shadows") and the quasinormal mode frequencies (in the eikonal limit) of Kerr black holes. This mapping has been previously established for non-rotating black holes. We show that, the shadow seen by an distant observer at a given inclination angle, can be mapped to a family of quasinormal modes with $m/(\ell+1/2)$ bounded within certain range, where $m$ is is azimuthal node number and $\ell$ is the angular node number. We discuss the possibility of testing such relation with space-borne gravitational wave detectors and the next-generation Event Horizon Telescope.