Space-based Gravitational Wave Research Articles

Heterodyne detection enhanced by quantum correlation

Heterodyne detectors as phase-insensitive (PI) devices have found important applications in precision measurements such as space-based gravitational-wave (GW) observation. However, the output signal of a PI heterodyne detector is supposed to suffer from signal-to-noise ratio (SNR) degradation due to image band vacuum and imperfect quantum efficiency. Here we show that the SNR degradation can be overcome when the image band vacuum is quantum correlated with the input signal. We calculate the noise figure of the detector and prove the feasibility of heterodyne detection with enhanced noise performance through quantum correlation. This work should be of great interest to ongoing space-borne GW signal searching experiments.

Unveiling the Architecture of a Pulsar–Binary Black Hole Triple System with Pulsar Arrival Time Analysis

Abstract A large number of binary black holes (BBHs) with longer orbital periods are supposed to exist as progenitors of BBH mergers recently discovered with gravitational wave (GW) detectors. In our previous papers, we proposed to search for such BBHs in triple systems through the radial velocity modulation of the tertiary orbiting star. If the tertiary is a pulsar, high-precision and high-cadence observations of its arrival time enable an unambiguous characterization of the pulsar–BBH triples located at several kiloparsecs, which are inaccessible with the radial velocity of stars. The present paper shows that such inner BBHs can be identified through the short-term Rømer delay modulation, on the order of 10 ms for our fiducial case, a triple consisting of a 20 M ⊙ BBH and 1.4 M ⊙ pulsar with P in = 10 days and P out = 100 days. If the relativistic time delays are measured as well, one can determine basically all the orbital parameters of the triple. For instance, this method is applicable to inner BBHs of down to ∼1 hr orbital periods if the orbital period of the tertiary pulsar is around several days. Inner BBHs with ≲1 hr orbital period emit the GW detectable by future space-based GW missions, including LISA, DECIGO, and BBO, and very short inner BBHs with subsecond orbital period can be even probed by the existing ground-based GW detectors. Therefore, our proposed methodology provides a complementary technique to search for inner BBHs in triples, if they exist at all, in the near future.

Orbit insertion error analysis for a space-based gravitational wave observatory

Constellation is required to be highly stable over several years for a space-based gravitational wave observatory. However, the stability of the constellation can be affected by orbit insertion errors. The effects of orbit insertion errors on the constellation are mainly studied in this paper. Firstly, Monte-Carlo, Unscented Transformation Covariance Analysis Method (UTCAM) and Spherical Simplex Unscented Transformation Covariance Analysis Method (SSUTCAM) are used for simulation. The results indicate that UTCAM and SSUTCAM are highly efficient in calculating, with a relative error of less than 6%. Therefore, it is concluded that because of their accuracy and high efficiency, UTCAM and SSUTCAM can be adequately used in orbit insertion error analysis for a space-based gravitational wave observatory. Secondly, SSUTCAM is used to study the effects of position and velocity errors on the constellation. For the case in this paper, when the position error does not exceed 300 km, and the velocity error does not exceed 4 cm/s, the constellation remains stable.

Time-delay interferometry for space-based gravitational wave detection

The predecessor of China Optics was China Optics and Applied Optics Digest, which was founded in 1985. At that time, it was the only retrieval journal in the field of optics in China. At the end of 2008, China Optics and Applied Optics Digest was renamed

TianQin Space-Based Gravitational Wave Detector: Key Technologies and Current State of Implementation

TianQin is a project of a space-based gravitational wave detector for detecting GW events in the millihertz frequency range. The space-based detector must be implemented on three identical drag-free spacecraft orbiting around the Earth. The key technologies that form the principles of operation of the space-based GW detector are, first, an ultrastable transponder laser interferometer and, second, a system for compensating nongravitational disturbances. This work discusses the basic principles of operation and the current state of the key technologies developed in the PRC. At the current level of technological readiness, it is expected that TianQin will be launched in the second half of the next decade and will serve as a space observatory for a wide class of astrophysical sources of gravitational waves.

The Pairing Probability of Massive Black Holes in Merger Galaxies in the Presence of Radiative Feedback

Abstract Dynamical friction (DF) against stars and gas is thought to be an important mechanism for orbital evolution of massive black holes (MBHs) in merger remnant galaxies. Recent theoretical investigations, however, show that DF does not always lead to MBH inspiral. For MBHs evolving in gas-rich backgrounds, the ionizing radiation that emerges from the innermost parts of their accretion flow can affect the surrounding gas in such a way to cause the MBHs to accelerate and gain orbital energy. This effect was dubbed “negative DF.” We use a semianalytic model to study the impact of negative DF on pairs of MBHs in merger remnant galaxies evolving under the combined influence of stellar and gaseous DF. Our results show that for a wide range of merger galaxy and MBH properties negative DF reduces the MBH pairing probability by ∼46%. The suppression of MBH pairing is most severe in galaxies with one or more of these properties: (1) a gas fraction of f g ≥ 0.1; (2) a galactic gas disk rotating close to the circular velocity; (3) MBH pairs in prograde, low eccentricity orbits; and (4) MBH pairs with mass <108 M ⊙. The last point is of importance because MBH pairs in this mass range are direct progenitors of merging binaries targeted by the future space-based gravitational wave observatory the Laser Interferometer Space Antenna (LISA).

The eccentricity enhancement effect of intermediate-mass-ratio-inspirals: dark matter and black hole mass * *Supported by National Natural Science Foundation of China (11503078, 11573060, 11673060, 11661161010)

It was found that dark matter (DM) in an intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of a stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors, including LISA, Taiji, and Tianqin in future observations. In this paper, we study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: (1) in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; (2) in the presence of a DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BH's mass; and (3) considering the change in the eccentricity in the presence and absence of a DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at a scale of approximately .

Sparsity-based recovery of Galactic-binary gravitational waves

The detection of galactic binaries as sources of gravitational waves promises an unprecedented wealth of information about these systems, but also raises several challenges in signal processing. In particular the large number of expected sources and the risk of misidentification call for the development of robust methods. We describe here an original non-parametric reconstruction of the imprint of galactic binaries in measurements affected by instrumental noise typical of the space-based gravitational wave observatory LISA. We assess the impact of various approaches based on sparse signal modelling and focus on adaptive structured block sparsity. We carefully show that a sparse representation gives a reliable access to the physical content of the interferometric measurement. In particular we check the successful fast extraction of the gravitational wave signal on a simple yet realistic example involving verification galactic binaries recently proposed in LISA data challenges.

The LISA DFACS: A nonlinear model for the spacecraft dynamics

In the last few years, the observation of gravitational waves by means of LIGO and Virgo interferometers and the success of LISA Pathfinder, gave a significant boost to the development of space-based gravitational wave observatories. The European Space Agency confirmed LISA as the third large class mission of the Cosmic Vision program. The present work is part of the Drag Free and Attitude Control System (DFACS) preliminary prototyping study, which aims at the development of mathematical models and advanced controllers for the science phases of the LISA mission. Nonlinear modelling is a fundamental step for the derivation of linearized and decoupled models as well as for the development of suitable linear and nonlinear controllers. In this paper, an analytical nonlinear model is derived, which describes all the relevant dynamics of a LISA spacecraft, representing an effective compromise between accuracy and complexity. The model is extensively validated through linearization analysis and Monte Carlo simulations.

3 m × 3 m heterolithic passive resonant gyroscope with cavity length stabilization

Large-scale high sensitivity laser gyroscopes have important applications for ground-based and space-based gravitational wave detection. We report on the development of a 3 m × 3 m heterolithic passive resonant gyroscope (HUST-1) which is installed on the ground of a cave laboratory. We operate the HUST-1 on different longitudinal cavity modes and the rotation sensitivity reaches 1.6 × 10−9 rad s−1 Hz−1/2 above 1 Hz. The drift of the cavity length is one of the major sensitivity limits for our gyroscope in the low frequency regime. By locking cavity length to an ultra-stable reference laser, we achieve a cavity length stability of 5.6 × 10−9 m Hz−1/2 at 0.1 mHz, a four orders of magnitude improvement over the unconstrained cavity in the low frequency regime. We stabilize the cavity length of a large-scale heterolithic passive resonant gyroscope through active feedback and realize long-term operation. The rotation sensitivity reaches 1.7 × 10−7 rad s−1 Hz−1/2 at 0.1 mHz, a three orders of magnitude improvement over the unconstrained cavity, which is no longer limited by the cavity length drift in this frequency range.

Testing the Kerr nature of supermassive and intermediate-mass black hole binaries using spin-induced multipole moment measurements

The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects []. Here, we apply the idea proposed in reference [] to binary systems composed of supermassive and intermediate-mass black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be ⩽0.1 for almost 3% of the total supermassive binary black hole population which is detectable by LISA whereas it is ∼46% for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity. We find that errors on both the quadrupole and octupole moment parameters can be estimated to be ⩽1 for ∼2% and ∼50% of the population respectively for LISA and DECIGO detectors. Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10% precision.

Science with the TianQin Observatory: Preliminary results on Galactic double white dwarf binaries

We explore the prospects of detecting of Galactic double white dwarf (DWD) binaries with the space-based gravitational wave (GW) observatory TianQin. In this work, we analyze both a sample of currently known DWDs and a realistic synthetic population of DWDs to assess the number of guaranteed detections and the full capacity of the mission. We find that TianQin can detect 12 out of $\sim100$ known DWDs; GW signals of these binaries can be modeled in detail ahead of the mission launch, and therefore they can be used as verification sources. Besides we estimate that TianQin has potential to detect as many as $10^4$ DWDs in the Milky Way. TianQin is expected to measure their orbital periods and amplitudes with accuracies of $\sim10^{-7}$ and $\sim0.2$, respectively, and to localize on the sky a large fraction (39%) of the detected population to better than 1 deg$^2$. We conclude that TianQin has the potential to significantly advance our knowledge on Galactic DWDs by increasing the sample up to 2 orders of magnitude, and will allow their multi-messenger studies in combination with electromagnetic telescopes. We also test the possibilities of different configurations of TianQin: (1) the same mission with a different orientation, (2) two perpendicular constellations combined into a network, and (3) the combination of the network with the ESA-led Laser Interferometer Space Antenna. We find that the network of detectors boosts the accuracy on the measurement of source parameters by 1-2 orders of magnitude, with the improvement on sky localization being the most significant.

Will gravitational waves discover the first extra-galactic planetary system?

Gravitational waves have opened a new observational window through which some of the most exotic objects in the universe, as well as some of the secrets of gravitation itself, can now be revealed. Among all these new discoveries, we recently demonstrated15 that space-based gravitational wave observations will have the potential to detect a new population of massive circumbinary exoplanets everywhere inside our Galaxy. In this paper, we argue that these circumbinary planetary systems can also be detected outside the Milky Way, in particular within its satellite galaxies. Space-based gravitational wave observations might thus constitute the mean to detect the first extra-galactic planetary system, a target beyond the reach of standard electromagnetic searches.

Analyses of residual accelerations for TianQin based on the global MHD simulation

TianQin is a proposed space-based gravitational wave observatory. It is designed to detect the gravitational wave signals in the frequency range of 0.1 mHz–1 Hz. At a geocentric distance of 105 km, the plasma in the Earth magnetosphere will contribute as the main source of environmental noises. Here, we analyze the acceleration noises that are caused by the magnetic field of space plasma for the test mass of TianQin. The real solar wind data observed by the Advanced Composition Explorer are taken as the input of the magnetohydrodynamic simulation. The Space Weather Modeling Framework is used to simulate the global magnetosphere of the Earth, from which we obtain the plasma and magnetic field parameters on the detector’s orbits at φs = 0°, 30°, 60° and 90°, where φs is the acute angle between the line that joins the Sun and the Earth and the projection of the normal of the detector’s plane on the ecliptic plane. We calculate the time series of the residual accelerations and the corresponding amplitude spectral densities on these orbit configurations. We find that the residual acceleration produced by the interaction between the TM’s magnetic moment induced by the space magnetic field and the spacecraft magnetic field (aM1) is the dominant term, which can approach 10−15 m s–2 Hz–1/2 at f ≈ 0.2 mHz for the nominal values of the magnetic susceptibility (χm = 10−5) and the magnetic shielding factor (ξm = 10) of the test mass. The ratios between the amplitude spectral density of the acceleration noise caused by the space magnetic field and the preliminary goal of the inertial sensor are 0.38 and 0.08 at 1 mHz and 10 mHz, respectively. We discuss the further reduction of this acceleration noise by decreasing χm and/or increasing ξm in the future instrumentation development for TianQin.

Tilt-to-length noise coupled by wavefront errors in the interfering beams for the space measurement of gravitational waves.

The space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna (LISA) or the Taiji program, aim to detect gravitational waves in space with a triangular constellation of three spacecraft. The unavoidable jitters of the spacecraft and the pointing will couple with the misalignment of the interfering beams into the longitudinal path length readout. This effect is called tilt-to-length (TTL) coupling, which is one of the keys to achieving the required measuring accuracy of 1pm/Hz. In terms of two phase definitions (the LISA Pathfinder (LPF) signal and the Average Phase (AP) signal), we implement the comprehensive theoretical analysis concerning the effect of aberrations on TTL coupling noise. In addition, we analytically derive that the proper lateral shift of the interfering beams relative to the detector can partly cancel out the TTL noise coupled with aberrations, especially coma and trefoil aberrations for the AP signal. Based on the above results, the meaningful guidance can be provided for the design and construction of the optical system in LISA or Taiji.

The gravitational wave background signal from tidal disruption events

ABSTRACT In this paper, we derive the gravitational wave stochastic background from tidal disruption events (TDEs). We focus on both the signal emitted by main-sequence stars disrupted by supermassive black holes (SMBHs) in galaxy nuclei and on that from disruptions of white dwarfs by intermediate-mass black holes (IMBHs) located in globular clusters. We show that the characteristic strain hc’s dependence on frequency is shaped by the pericenter distribution of events within the tidal radius and under standard assumptions hc∝f−1/2. This is because, the TDE signal is a burst of gravitational waves at the orbital frequency of the closest approach. In addition, we compare the background characteristic strains with the sensitivity curves of the upcoming generation of space-based gravitational wave interferometers: the Laser Interferometer Space Antenna (LISA), TianQin, ALIA, the DECI-hertz inteferometer Gravitational wave Observatory (DECIGO), and the Big Bang Observer (BBO). We find that the background produced by main-sequence stars might be just detected by BBO in its lowest frequency coverage, but it is too weak for all the other instruments. On the other hand, the background signal from TDEs with white dwarfs will be within reach of ALIA, and especially of DECIGO and BBO, while it is below the LISA and TianQin sensitive curves. This background signal detection will not only provide evidence for the existence of IMBHs up to redshift z ∼ 3, but it will also inform us on the number of globular clusters per galaxy and on the occupation fraction of IMBHs in these environments.

The TianQin project: Current progress on science and technology

Abstract TianQin is a planned space-based gravitational wave (GW) observatory consisting of three Earth-orbiting satellites with an orbital radius of about $10^5 \, {\rm km}$. The satellites will form an equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4} \, {\rm Hz}$ and $1 \, {\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe and exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new-generation $17 \, {\rm cm}$ single-body hollow corner-cube retro-reflector which was launched with the QueQiao satellite on 21 May 2018; a new laser-ranging station equipped with a $1.2 \, {\rm m}$ telescope has been constructed and the station has successfully ranged to all five retro-reflectors on the Moon; and the TianQin-1 experimental satellite was launched on 20 December 2019—the first-round result shows that the satellite has exceeded all of its mission requirements.

Merging compact binaries near a rotating supermassive black hole: Eccentricity excitation due to apsidal precession resonance

We study the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration. We include various general relativistic effects that couple the inner orbit, the outer orbit and the spin of the SMBH. During the orbital decay due to gravitational radiation, the inner binary can encounter an "apsidal precession resonance" and experience eccentricity excitation. This resonance occurs when the apsidal precession rate of the inner binary matches that of the outer binary, with the precessions driven by both Newtonian interactions and various post-Newtonian effects. The eccentricity excitation requires the outer orbit to have a finite eccentricity, and is most effective for triples with small mutual inclinations, in contrast to the well-studied Lidov-Kozai effect. The resonance and the associated eccentricity growth may occur while the binary emits gravitational waves in the low-frequency band, and may be detectable by future space-based gravitational wave detectors.

Non-linear dynamical tides in white dwarf binaries

ABSTRACT Compact white dwarf (WD) binaries are important sources for space-based gravitational-wave (GW) observatories, and an increasing number of them are being identified by surveys like Extremely Low Mass (ELM) and Zwicky Transient Facility (ZTF). We study the effects of non-linear dynamical tides in such binaries. We focus on the global three-mode parametric instability and show that it has a much lower threshold energy than the local wave-breaking condition studied previously. By integrating networks of coupled modes, we calculate the tidal dissipation rate as a function of orbital period. We construct phenomenological models that match these numerical results and use them to evaluate the spin and luminosity evolution of a WD binary. While in linear theory the WD’s spin frequency can lock to the orbital frequency, we find that such a lock cannot be maintained when non-linear effects are taken into account. Instead, as the orbit decays, the spin and orbit go in and out of synchronization. Each time they go out of synchronization, there is a brief but significant dip in the tidal heating rate. While most WDs in compact binaries should have luminosities that are similar to previous traveling-wave estimates, a few per cent should be about 10 times dimmer because they reside in heating rate dips. This offers a potential explanation for the low luminosity of the CO WD in J0651. Lastly, we consider the impact of tides on the GW signal and show that the Laser Interferometer Space Antenna (LISA) and TianGO can constrain the WD’s moment of inertia to better than $1{{\ \rm per\ cent}}$ for centi-Hz systems.

Full analytical formulas for frequency response of space-based gravitational wave detectors

The discovery of gravitational waves, which are ripples of space-time itself, opened a new window to test general relativity, because it predicts that there are only plus and cross polarizations for gravitational waves. For alternative theories of gravity, there may be up to six polarizations. The measurement of the polarization is one of the major scientific goals for future gravitational wave detectors. To evaluate the capability of the detector, we need to use the frequency dependent response functions averaged over the source direction and polarization angle. We derive the full analytical formulas of the averaged response functions for all six possible polarizations and present their asymptotic behaviors based on these analytical formulas. Compared with the numerical simulation, the full analytical formulas are more efficient and valid for any equal-arm interferometric gravitational wave detector without optical cavities in the arms and for a time-delay-interferometry Michelson combination.