Estimating up-limits of eccentricities for the binary black holes in the LIGO-Virgo catalog GWTC-1

In the first Gravitational-Wave Transient Catalogue of LIGO and Virgo,all events are announced having zero eccentricity.In the present paper,we investigate the performance of SEOBNRE,which is a spin-aligned eccentric waveform model in time-domain.By comparing with all the eccentric waveforms in SXS library,we find that the SEOBNRE coincides perfectly with numerical relativity data.Employing the SEOBNRE,we re-estimate the eccentricities of all black hole merger events.We find that most of these events allow a possibility for existence of initial eccentricities at 10 Hz band,but are totally circularized at the observed frequency(≥20 Hz).The upcoming update of LIGO and the next generation detector like Einstein Telescope will observe the gravitational waves starting at 10 Hz or even lower.If the eccentricity exists at the lower frequency,then it may significantly support the dynamical formation mechanism taking place in globular clusters.

Possibility of measuring spin precession of the nearest supermassive black hole by using S stars

The supermassive black hole （SMBH） with a mass of 4 million M⊙ inside the radio source Sgr A＊ in our Galactic center is the nearest SMBH. Once S stars with a shorter period are observed, relativistic precessions especially the Lense-Thirring effect can be measured by astronomical observations at the 10 ~tas level in the future. An interesting but so far unaddressed problem is that the SMBH not only has spin but also spin precession like similar objects. We study the effect of such spin precession on the orbital precessions of orbiting stars. Our results show that the spin precession can produce a periodic oscillation in the precession of the star＇s orbital plane, but has no obvious effect on the periapse shift. For stars with an orbital period of O（0.1） yr or less, such visible oscillations occur when the SMBH＇s spin-precession period ranges from about a few tens of years to hundreds of years. The period of oscillation is the same as the one of the spin precession. In principle, the precession of this oscillating orbital plane can be observed and then the spin and spin precession of the nearest SMBH can be determined.

Numerical simulation of the Moon's rotation in a rigorous relativistic framework

This paper describes a numerical simulation of the rigid rotation of the Moon in a relativis- tic framework. Following a resolution passed by the International Astronomical Union （IAU） in 2000, we construct a kinematieally non-rotating reference system named the Selenocentric Celestial Reference System （SCRS） and give the time transformation between the Selenocentric Coordinate Time （TCS） and Barycentric Coordinate Time （TCB）. The post-Newtonian equations of the Moon＇s rotation are written in the SCRS, and they are integrated numerically. We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques as well as geodetic precession. We find two dominant periods associated with this correction： 18.6 yr and 80.1 yr. In addition, the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed, and we have found that the main periods of this precession are 27.3 d, 2.9 yr, 18.6 yr and 80.1 yr.

A long time span relativistic precession model of the Earth

A numerical solution to the Earth＇s precession in a relativistic framework for a long time span is presented here. We obtain the motion of the solar system in the Barycentric Celestial Reference System by numerical integration with a symplectic in- tegrator. Special Newtonian corrections accounting for tidal dissipation are included in the force model. The part representing Earth＇s rotation is calculated in the Geocentric Celestial Reference System by integrating the post-Newtonian equations of motion published by Klioner et al. All the main relativistic effects are included following Klioner et al. In particular, we consider several relativistic reference systems with cor- responding time scales, scaled constants and parameters. Approximate expressions for Earth＇s precession in the interval ~1 Myr around J2000.0 are provided. In the interval 4-2000 years around J2000.0, the difference compared to the P03 precession theory is only several arcseconds and the results are consistent with other long-term precession theories.

General formalism for dirty extreme-mass-ratio inspirals

Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals(EMRIs).There is still a challenge to efficiently describe various“dirty”impacts on the inspirals,such as dark matter,gas,dipole radiation,and electromagnetic interaction.In this study,we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky equation.On the basis of this property,we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and waveforms.With the new decoupling form,the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be conveniently calculated.This will help to resolve the environment(including gas,field,dark matter,electromagnetic interaction)around supermassive black holes and test general relativity.

Taiji data challenge for exploring gravitational wave universe

The direct observation of gravitational waves(GWs)opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe.GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena.Taiji is a proposed space-based gravitational wave(GW)detection mission that will be launched in the 2030s.Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background,posing various data analysis challenges.In order to empower potential scientific discoveries,the Mock Laser Interferometer Space Antenna(LISA)data challenge and the LISA data challenge(LDC)were developed.While LDC provides a baseline framework,the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji’s constellation.In this paper,we review the scientific objectives and the roadmap for Taiji,as well as the technical difficulties in data analysis and the data generation strategy,and present the associated data challenges.In contrast to LDC,we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques.Additionally,we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum,which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations.Furthermore,we present a comprehensive showcase of parameter estimation using a toy dataset.This showcase not only demonstrates the scientific potential of the Taiji data challenge(TDC)but also serves to validate the effectiveness of the pipeline.As the first data challenge for Taiji,we aim to build an open ground for data analysis related to Taiji sources and sciences.More details can be found on the official website(taiji-tdc.ictp-ap.org).

Exploring the nature of black hole and gravity with an imminent merging binary of supermassive black holes

A supermassive binary black-hole candidate SDSS J1430+2303 reported recently motivates us to investigate an imminent binary of supermassive black holes as potential gravitational wave source, and the radiated gravitational waves at the end of the merger are shown to be in the band of space-borne detectors. We provide a general analysis on the required detecting sensitivity needed for probing such type gravitational wave sources and make a full discussion by considering two typically designed configurations of space-borne antennas. If a source is so close, it is possible to be detected with Taiji pathfinder-plus which is proposed to be an extension for the planned Taiji pathfinder by just adding an additional satellite to the initial two satellites. The gravitational wave detection on such kind of source enables us to explore the properties of supermassive black holes and the nature of gravity.

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.