Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional $N$ bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for the \emph{strong} gravitational fields, such as binary pulsars and some gravitational wave sources. The result's application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find the possible tests for the alternative gravitational theories, such as a possible determination for the post-Newtonian parameter $γ$ in the level of some scalar-tensor theories of gravity.
This talk adds more detail to the proposed TianQin mission \cite{TQ}. The response of TianQin to a binary source is an important problem for the experiment. Here we present the detail of the response function of an equal-arm Michelson interferometer to the gravitation waves of a binary source with a circular orbit.
TianQin is a proposed space gravitational-wave detection mission using circular high Earth orbits. The geocentric concept has raised questions about the disturbing effect of the nearby gravity field of the Earth-Moon system on the highly-sensitive intersatellite ranging measurements. Here we examine the issue through high precision numerical orbit simulation with detailed gravity-field models. By evaluating range accelerations between distant free-falling test masses, the study shows that the majority of the Earth-Moon's gravity disturbances are not in TianQin's detection frequency band above …
The capture of compact objects by massive black holes in galaxies or dwarf galaxies will generate short gravitational wave signals, called extreme-mass-ratio bursts (EMRBs), before evolving into extreme-mass-ratio inspirals. Their detection will provide an investigation of the black hole properties and shed light on astronomy and astrophysics. In this work, we investigate the detection number of the TianQin observatory on EMRBs. Our result shows that TianQin can detect tens of EMRBs events during its mission lifetime. For those detected events, we use the Fisher information matrix to quantify …
In future geocentric space-based gravitational-wave observatory missions, eclipses due to passing through the Moon's and Earth's shadows can negatively impact the sciencecraft's thermal stability and steady power supply. The occurrence should be reduced as much as possible in orbit design. In regard to TianQin's circular high orbits, we tackle the combined challenges of avoiding eclipses and stabilizing the nearly equilateral-triangle constellation. Two strategies are proposed, including initial phase selection and orbit resizing to 1:8 synodic resonance with the Moon, where the latter involve…
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 detec…
TianQin is a geocentric space-based gravitational-wave observatory mission consisting of three drag-free controlled satellites in an equilateral triangle with an orbital radius of $ 10^{5}$ km. The constellation faces the white-dwarf binary RX J0806.3+1527 located slightly below the ecliptic plane, and is subject to gravitational perturbations that can distort the formation. In this study, we present combined methods to optimize the TianQin orbits so that a set of 5-year stability requirements can be met. Moreover, we discuss slow long-term drift of the detector pointing due to orbital precess…
TianQin is a proposed space-based gravitational-wave observatory mission to be deployed in high circular Earth orbits. The equilateral-triangle constellation, with a nearly fixed orientation, can be distorted primarily under the lunisolar perturbations. To accommodate science payload requirements, one must optimize the orbits to stabilize the configuration in terms of arm-length, relative velocity, and breathing angle variations. In this work, we present an efficient optimization method and investigate how changing the two main design factors, i.e., the orbital orientation and radius, impacts …
TianQin is a proposed geocentric space-based gravitational wave observatory mission, which requires time-delay interferometry (TDI) to cancel laser frequency noise. With high demands for precision, solar-wind plasma environment at $\sim 10^5$ km above the Earth may constitute a non-negligible noise source to laser interferometric measurements between satellites, as charged particles perturb the refractivity along light paths. In this paper, we first assess the plasma noises along single links from space-weather models and numerical orbits, and analyze the time and frequency domain characterist…
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 …
TianQin is a proposed space-borne gravitational wave (GW) observatory composed of three identical satellites orbiting around the geocenter with a radius of $10^5$ km. It aims at detecting GWs in the frequency range of 0.1 mHz -- 1 Hz. The detection of GW relies on the high precision measurement of optical path length at $10^{-12}$~m level. The dispersion of space plasma can lead to the optical path difference (OPD, $Δl$) along the propagation of laser beams between any pair of satellites. Here, we study the OPD noises for TianQin. The Space Weather Modeling Framework is used to simulate the in…
TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz -- 1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately $1.7 \times 10^{5} ~\rm{km}$. The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit an…
We investigate the prospects of detecting gravitational waves from coalescing massive black hole binaries in the Universe with the TianQin observatory, a space-based gravitational wave interferometer proposed to be launched in the 2030s. To frame the scientific scope of the mission, in this paper, we carry out a preliminary estimation of the signal-to-noise ratio, detection rate and parameter estimation precision of massive black hole binaries detectable by TianQin. In order to make our results as robust as possible, we consider several models of the growth history of massive black holes, expl…
Detectability of Nearby Binary Neutron Stars with Future sub-mHz Gravitational Wave Missions
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文学院）；Institute for Gravitational Wave Astronomy, Henan Academy of Sciences（河南省科学院引力波天文研究院）
School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus)（中山大学（珠海校区）物理与天文学院）；School of Electronic and Electrical Engineering, Zhaoqing University（肇庆学院电子与电气工程学院）；Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；Department of Physics, The University of Hong Kong（香港大学物理系）；The Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学卡尔·萨根宇宙粒子与暗物质研究所）
The relativistic theories of light propagation are generalized by introducing two new parameters $ς$ and $η$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $γ$ and $β$. This new 2PN parameterized (2PPN) formalism includes the non-stationary gravitational fields and the influences of all kinds of relativistic effects. The multipolar components of gravitating bodies are taken into account as well at the first post-Newtonian order. The equations of motion and their solutions of this 2PPN light propagation problem are obtained. Started from the…
We study the stellar binary black holes (BBHs) inspiralling/merging in galactic nuclei based on our numerical method GNC. We find that $3-40\%$ of all new born BBHs will finally merge due to various dynamical effects. In a five year's mission, up to $10^4$, $10^5$, $\sim100$ of BBHs inspiralling/merging in galactic nuclei can be detected with SNR$>8$ in aLIGO, Einstein/DECIGO, TianQin/LISA/TaiJi, respectively. About tens are detectable in both LISA/TaiJi/TianQin and aLIGO. These BBHs have two unique characteristics: (1) Significant eccentricities. $1-3\%$, $2-7\%$, or $30-90\%$ of them is with…
Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission
研究了光的相对论引力偏转对未来空间干涉测量任务精度的影响。本文计算了太阳系中一些天体的引力场的四极、八极和四极分量所引起的偏转角。我们观察到，在许多情况下，相应的影响的大小是显着大于1 uas的精度预期SIM。这一事实表明，有必要为该飞行任务开发一个相对论观测模型，以说明重力对光传播的静态和时变效应的影响。这里介绍的结果是不同的，从其他地方获得的事实，我们特别占未来SIM天体测量的差分性质。我们还估计了通过SIM全球天体测量活动可能确定爱丁顿参数γ的精度;我们得出结论，通过测量太阳引力引起的光偏转，可以实现~7 x 10^{-6}的精度。
Detectability of Gravitational Waves from Extreme-Mass-Ratio Inspirals on Periodic Orbits around Bardeen Black Holes
School of Physics and Electronic Information, Yunnan Normal University（云南师范大学物理与电子信息学院）；School of Mathematics and Physics, Shangrao Normal University（上饶师范学院数学与物理学院）
Observational data from the ESA astrometric mission Gaia determining the positions of celestial objects within an accuracy of few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to significantly improve such precision in the next years. The data reduction process needs high-precision general relativistic models, allowing one to solve the inverse ray-tracing problem in the gravitational field of the Solar System up to the requested level of accuracy and leading then to the estimate of astrometric parameters. Besides a satisfactory descrip…
High-Precision Ground Characterization of Test-Mass Magnetic Properties for the Taiji Gravitational Wave Mission via a Physics-Informed Neural Framework
National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）；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国家实验室引力波实验中心）；University of Chinese Academy of Sciences（中国科学院大学）；Lanzhou Center of Theoretical Physics, Lanzhou University（兰州大学理论物理中心）；Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences（中国科学院长春光学精密机械与物理研究所）；Key Laboratory of Gravitational Wave Precision Measurement of Zhejiang Province（浙江省引力波精密测量重点实验室）
We study the effects of ultralight vector field (ULVF) dark matter on gravitational-wave propagation. We find that the coherent oscillations of the vector field induce an anisotropic suppression of the gravitational-wave amplitude as compared to the $Λ$CDM prediction. The effect is enhanced for smaller vector field masses and peaks for modes around $k=H_0/\sqrt{a(H=m)}$. The suppression is negligible for astrophysically generated gravitational waves but could be sizeable for primordial gravity waves. We discuss the possibility of detecting such an effect on the tensor power spectrum with futur…
Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the Time Transfer Functions formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the Time Transfer Functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a…
We develop a high-precision model for laser ranging interferometric (LRI) observables of the GRACE Follow-On (GRACE-FO) mission. For this, we study the propagation of an electromagnetic wave in the gravitational field in the vicinity of an extended body, in the post-Newtonian approximation of the general theory of relativity. We present a general relativistic model for the phase of a plane wave that accounts for contributions of all the multipoles of the gravitating body, its angular momentum, as well as the contribution of tidal fields produced by external sources. We develop a new approach t…
The propagation speed of gravitational waves, $c_T$, has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent $c_T$. Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of $c_T$ from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for $c_T(f)$, and study their impact upon the gravitational waveforms …
Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the ticks of local clocks to reconstruct the orbital path of the satellite to high accuracy, and to implicitly measure general relativistic effects. In particular, Schwarzschild space curvature (static) and frame-dragging (stationary) due to the planet's spin affect the satellite's orbit. The dominant relativistic effect on the path of the signal photons is Shap…
