Time-delay interferometry is put forward to improve the signal-to-noise ratio of space-borne gravitational wave detectors by canceling the large laser phase noise with different combinations of measured data. Based on the Michelson data combination, the sensitivity function of the detector can be obtained by averaging the all-sky wave source positions. At present, there are two main methods to encode gravitational wave signal into detector. One is to adapt gravitational wave polarization angle depending on the arm orientation in the gravitational wave frame, and the other is to divide the gravitational wave signal into plus and cross polarizations in the detector frame. Although there are some attempts using the first method to provide the analytical expression of sensitivity function, only a semianalytical one could be obtained. Here, starting with the second method, we demonstrate the equivalence of both methods. First time to obtain the full analytical expression of sensitivity function, which provides a fast and accurate mean to evaluate and compare the performance of different space-borne detectors, such as LISA and TianQin.
Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling…
The basic constituent of many space-borne gravitational missions, in particular for interferometric gravitational waves detectors, is the so-called link made out of a satellite sending an electromagnetic beam to a second satellite. We illustrate how, by measuring the time derivative of the frequency of the received beam, the link behaves as a differential, time-delayed dynamometer in which the effect of gravity is exactly equivalent to an effective differential force applied to the two satellites. We also show that this differential force gives an integrated measurement of curvature along the …
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 $\approx 0.1$ mHz to $\approx 10$ mHz range. Given the likely prospect that there will be multiple such detectors, namely 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 Ta…
Unlike ground-based interferometric gravitational wave detectors, large space-based systems will not be rigid structures. When the end-stations of the laser interferometer are freely flying spacecraft, the armlengths will change due to variations in the spacecraft positions along their orbital trajectories, so the precise equality of the arms that is required in a laboratory interferometer to cancel laser phase noise is not possible. However, using a method discovered by Tinto and Armstrong, a signal can be constructed in which laser phase noise exactly cancels out, even in an unequal arm inte…
Two recent papers\citep{xmri1, xmri2} revealed that in our Galaxy there are very extreme-mass-ratio inspirals composed by brown dwarfs and the supermassive black hole at the center of the Galaxy. The event rates estimated in these papers are very considerable for future space-borne detectors. In addition, there are plunge events during the formation of inspiraling orbits. In this work, we calculate the gravitational waves from compact objects (brown dwarf, primordial black hole and etc.) plunging into or being scattered by the central supermassive black hole. We find that for space-borne detec…
Space-borne interferometric gravitational-wave detectors, sensitive in the low-frequency (mHz) band, will fly in the next decade. In these detectors, the spacecraft-to-spacecraft light-travel times will necessarily be unequal and time-varying, and (because of aberration) will have different values on up- and down-links. In such unequal-armlength interferometers, laser phase noise will be canceled by taking linear combinations of the laser-phase observables measured between pairs of spacecraft, appropriately time-shifted by the light propagation times along the corresponding arms. This procedur…
The screened modified gravity (SMG) is a unified theoretical framework, which describes the scalar-tensor gravity with screening mechanism. Based on the gravitational-wave (GW) waveform derived in our previous work \citep{liu2018waveforms}, in this article we investigate the potential constraints on SMG theory through the GW observation of the future space-borne GW detectors, including LISA, TianQin and Taiji. We find that, for the EMRIs consisting of a massive black hole and a neutron star, if the EMRIs are at Virgo cluster, the GW signals can be detected by the detectors at quite high signif…
TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the …
Future space borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterisation of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most …
In preparation for future space-borne gravitational-wave (GW) detectors, should the modelling effort focus on high-precision vacuum templates or on the astrophysical environment of the sources? We perform a systematic comparison of the phase contributions caused by 1) known environmental effects in both gaseous and stellar matter backgrounds, or 2) high-order post-Newtonian {(PN)} terms in the evolution of mHz GW sources {during the inspiral stage of massive binaries}. We use the accuracy of currently available analytical waveform models as a benchmark {value, finding} the following trends: th…
pespace: A new tool of GPU-accelerated and auto-differentiable response generation and likelihood evaluation for space-borne gravitational wave detectors
In this paper, we investigate the sensitivity to additional gravitational wave polarization modes of future detectors. We first look at the upcoming Einstein Telescope and its combination with existing or planned Earth-based detectors in the case of a stochastic gravitational wave background. We then study its correlation with a possible future space-borne detector sensitive to high-frequencies, like DECIGO. Finally, we adapt those results for a single GW source and establish the sensitivity of the modes, as well as the localization on the sky.
Laser frequency stabilization is notably one of the major challenges on the way to a space-borne gravitational wave observatory. The proposed Laser Interferometer Space Antenna (LISA) is presently under development in an ESA, NASA collaboration. We present a novel method for active laser stabilization and phase noise suppression in such a gravitational wave detector. The proposed approach is a further evolution of the "arm locking" method, which in essence consists of using an interferometer arm as an optical cavity, exploiting the extreme long-run stability of the cavity size in the frequency…
By taking into account the contamination of foreground radiations, we employ the Fisher matrix to forecast the future sensitivity on the tilt of power spectrum of primordial tensor perturbations for several ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments of B-mode polarizations. For the fiducial model $n_t=0$, our results show that the satellite experiments give good sensitivity on the tensor tilt $n_t$ to the level $σ_{n_t}\lesssim0.1$ for $r\gtrsim2\times10^{-3}$, while the ground-based and ballo…
In this paper, we investigate the potential of dark sirens by the space-borne atom interferometric gravitational-wave detectors to probe the Hubble constant. In the mid-frequency band, the sources live a long time. The motion of a detector around the Sun as well as in Earth orbit would induce large Doppler and reorientation effects, providing a precise angular resolution. Such precise localization for the GW sources makes it possible to observe the dark sirens with only one potential host galaxy, which are dubbed "golden dark sirens". We construct the catalogs of golden dark sirens and estimat…
Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and LISA for monochromatic gravitational waves. With the long-wavelength approximation we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low frequency regime there exist different patterns in angular resolutions and estimation errors of sources' pa…
Clock Noise Cancellation in Heterodyne Links between Optical Cavities for Space-Borne Gravitational-Wave Telescopes
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency（宇宙科学研究所，日本宇宙航空研究开发机构）；Department of Physics, The University of Tokyo（东京大学物理学系）
DECIGO Pathfinder (DPF) has an ability to detect gravitational waves from galactic intermediate-mass black hole binaries. If the signal is detected, it would be possible to determine parameters of the binary components. Furthermore, by using future space-borne gravitational wave interferometers, it would be possible to test alternative theories of gravity in the strong field regime. In this review article, we first explain how the detectors like DPF and DECIGO/BBO work and discuss the expected event rates. Then, we review how the observed gravitational waveforms from precessing compact binarie…
We present a numerical analysis to simulate the response of a spherical resonant gravitational wave detector and to compute its sensitivity. Under the assump- tion of optimal filtering, we work out the sensitivity curve for a sphere first taking into account only a single transducer, and then using a coherent analysis of the whole set of transducers.
Self-supervised reconstruction of transients in data from space-borne gravitational-wave detectors
Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力实验室引力波实验中心）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS)（中国科学院大学太极引力波宇宙实验室（北京/杭州））
We present the performances and the strain sensitivity of the first spherical gravitational wave detector equipped with a capacitive transducer and read out by a low noise two-stage SQUID amplifier and operated at a temperature of 5 K. We characterized the detector performance in terms of thermal and electrical noise in the system output sygnal. We measured a peak strain sensitivity of $1.5\cdot 10^{-20} Hz^{-1/2}$ at 2942.9 Hz. A strain sensitivity of better than $5\cdot 10{-20}Hz{-1/2}$ has been obtained over a bandwidth of 30 Hz. We expect an improvement of more than one order of magnitude …
Recently, observational searches for gravitational wave background (GWB) have developed and given direct and indirect constraints on the energy density of GWB in a broad range of frequencies. These constraints have already rejected some theoretical models of large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though the indirect limit by He4 abundance due to big-bang nucleosynthesis exists. In this paper, we propose an experiment with laser interferometers searching GWB at 100 MHz. We considered three detector designs and evaluated the GW response fu…
Atom interferometers (AIs) as gravitational-wave (GW) detectors have been proposed a decade ago. Both ground and space-based projects will be in construction and preparation in the near future. In this paper, for the first time, we investigate the potential of the space-borne AIs on detecting GW standard sirens and hence the applications on cosmology. We consider AEDGE as our fiducial AI GW detector and estimate the number of bright sirens that would be obtained within a 5-years data-taking period of GW and with the follow-up observation of electromagnetic (EM) counterparts. We then construct …
The future laser interferometric gravitational-wave detectors sensitivity can be improved using squeezed light. In particular, recently a scheme which uses the optical field with frequency dependent squeeze factor, prepared by means of a relatively short (~30 m) amplitude filter cavity, was proposed \cite{Corbitt2004-3}. Here we consider an improved version of this scheme, which allows to further reduce the quantum noise by exploiting the quantum entanglement between the optical fields at the filter cavity two ports.
Proper tuning of the orbital characteristics of the three spacecrafts that constitute the usual triangular configuration of the space-borne gravitational-wave detector LISA, could minimize the breathing mode of its arm-lengths. Since the three spacecrafts form three pairs of interferometric arms, we have the freedom to minimize whichever combination of arm-length variations that might be useful in signal analysis. Thus for any kind of time delay interferometry (TDI), that is chosen to be used in analysing the data, the optimal orbital characteristics could be chosen accordingly, so as to enhan…
We summarize the sensitivity achieved by the LIGO and Virgo gravitational wave detectors for low-mass compact binary coalescence (CBC) searches during LIGO's sixth science run and Virgo's second and third science runs. We present strain noise power spectral densities (PSDs) which are representative of the typical performance achieved by the detectors in these science runs. The data presented here and in the accompanying web-accessible data files are intended to be released to the public as a summary of detector performance for low-mass CBC searches during S6 and VSR2-3.
We present a study of spectrum estimation of relic gravitational waves (RGWs) as a Gaussian stochastic background from output signals of future space-borne interferometers, like LISA and ASTROD. As the target of detection, the analytical spectrum of RGWs generated during inflation is described by three parameters: the tensor-scalar ratio, the spectral index and the running index. For RGW detection, we analyze the auto-correlated signals for a single interferometer, and the cross-correlated, integrated as well as un-integrated signals for a pair of interferometers, and give SNR for RGW, and obt…
We calculate the quantum noise limited displacement sensitivity of a Michelson-Fabry-Perot (MFP) with detuned cavities, followed by phase-sensitive homodyne detection. We show that the standard quantum limit can be surpassed even with resonant cavities and without any signal-recycling mirror nor additional cavities. Indeed, thanks to the homodyne detection, the output field quadrature can be chosen in such a way to cancel the effect of input amplitude fluctuations, i.e., eliminating the force noise. With detuned cavities, the modified opto-mechanical susceptivity allows to reach unlimited sens…
According to the common wisdom, between a fraction of the mHz and few Hz the spectral energy density of the inflationary gravitons can be safely disregarded even assuming the most optimistic sensitivities of the space-borne detectors. In this analysis we show that this conclusion is evaded if, prior to nucleosynthesis, the post-inflationary evolution includes a sequence of stages expanding either faster or slower than radiation. As a consequence, contrary to the conventional lore, it is shown that below a fraction of the Hz the spectral energy density of the relic gravitons may exceed (even by…
Eccentricity of the inspiraling compact binaries can greatly improve the distance inference and source localization of dark sirens. In this paper, we continue the research for the space-borne atom interferometric gravitational-wave detector AEDGE and investigate the effects of eccentricity on the dark sirens observed by AEDGE in the mid-band. We simulate five types of typical compact binaries with component mass ranging from $1-100~M_{\odot}$. The largest improvement for both distance inference and localization can be as much as 1.5--3 orders of magnitude. We then construct the catalogs of dar…
We analyze the sensitivity of gravitational-wave antenna with stable double optical spring created by two independent pumps. We investigate regime of three close eigen frequencies (roots of characteristic equation) which appears to provide more wide frequency band in which sensitivity of antenna can beat Standard Quantum Limit (SQL) than previously considered regime with two close eigen frequencies. We take into account optical losses and show that they do not degrade sensitivity significantly. We also demonstrate possible application of considered regime to Einstein Telescope.
We analyze the sensitivity of a network of interferometer gravitational-wave detectors to the gravitational-wave stochastic background, and derive the dependence of this sensitivity on the orientations of the detector arms. We build on and extend the recent work of Christensen, but our conclusion for the optimal choice of orientations of a pair of detectors differs from his. For a pair of detectors (such as LIGO) that subtends an angle at the center of the earth of $\,\alt 70^\circ$, we find that the optimal configuration is for each detector to have its arms make an angle of $45^\circ$ (modul…
Cracking Gravitational Wave Multiple Ringdown Modes in Space
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Sun Yat-sen University (Zhuhai Campus)（中山大学（珠海校区））；Dalian University of Technology（大连理工大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
We survey the prospective sensitivities of terrestrial and space-borne atom interferometers (AIs) to gravitational waves (GWs) generated by cosmological and astrophysical sources, and to ultralight dark matter. We discuss the backgrounds from gravitational gradient noise (GGN) in terrestrial detectors, and also binary pulsar and asteroid backgrounds in space-borne detectors. We compare the sensitivities of LIGO and LISA with those of the 100m and 1km stages of the AION terrestrial AI project, as well as two options for the proposed AEDGE AI space mission with cold atom clouds either inside or …
Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves ideal probes of fundamental physics. The promotion of Newton's constant to a time-function introduces modifications to the binary's binding energy and the gravitational wave luminosity, leading to corrections in the chirping frequency. Such corrections propagate into the response function and, given a gravitational wave observation, they allow for constraints…
