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The method of time delay interferometry (TDI) is proposed to cancel the laser noise in space-borne gravitational-wave detectors. Among all different TDI combinations, the most commonly used ones are the orthogonal channels A, E and T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile, for the detection of stochastic gravitational-wave background, one needs to introduce the overlap reduction function to characterize the correlation between channels. For the calculation of overlap reduction function, it is often convenient to work in the low-frequency approximation, and assuming the equal-arm Michelson channels. However, if one wishes to work on the overlap reduction function of $\rm A/E$ channels, then the low-frequency approximation fails. We derive the exact form of overlap reduction function for $\rm A/E$ channels. Based on the overlap reduction function, we calculate the sensitivity curves of TianQin, TianQin I+II and TianQin + LISA. We conclude that the detection sensitivity calculated with $\rm A/E$ channels is mostly consistent with that obtained from the equal-arm Michelson channels., 18 pages,10 figures

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 these uncertainties in the inference of their parameters. We consider the possible network of TianQin+LISA and study how a network can improve parameter estimation. The result shows that, for most sources, the CO mass, the MBH mass, and the MBH spin can be determined with an accuracy of the order $10^{-1}$ and the sky localization can be determined with an accuracy of 10 square degrees. We further explore the gravitational wave background generated by those unsolved EMRBs and conclude that it is about $10^6$ times weaker than TianQin's sensitivity and thus it can be ignored.

The detection of stochastic gravitational wave background (SGWB) is among the leading scientific goals of the space-borne gravitational wave observatory, which would have significant impact on astrophysics and fundamental physics. In this work, we developed a data analysis software, \texttt{TQSGWB}, which can extract isotropic SGWB using the Bayes analysis method based on the TianQin detector. We find that for the noise cross spectrum, there are imaginary components and they play an important role in breaking the degeneracy of the position noise in the common laser link. When the imaginary corrections are considered, the credible regions of the position noise parameters are reduced by two orders of magnitude. We demonstrate that the parameters of various signals and instrumental noise could be estimated directly in the absence of a Galactic confusion foreground through Markov chain Monte Carlo sampling. With only a three-month observation, we find that TianQin could be able to confidently detect SGWBs with energy density as low as $\Omega_{\rm PL} = 1.3 \times 10^{-12}$, $\Omega_{\rm Flat} = 6.0 \times 10^{-12}$, and $\Omega_{\rm SP} = 9.0 \times 10^{-12}$, for power-law, flat, and single-peak models respectively., Comment: 28 pages, 8 figures

In this work, we study the prospect of detecting the stochastic gravitational-wave background with the TianQin Observatory. We consider sources of both astrophysical-origin and cosmological-origin, including stellar-mass binary black holes, binary neutron stars, Galactic white dwarves, inflation, first-order phase transitions, and cosmic defects. For the detector configurations, we consider TianQin, TianQin I+II, and TianQin + LISA. We study the detectability of stochastic gravitational-wave backgrounds with both the cross correlation and null channel methods, and present the corresponding power-law integrated sensitivity curves. We introduce the definition of the "joint foreground" with a network of detectors. With the joint foreground, the number of resolved double white dwarves in the Galaxy will be increased by 5$-$22\% compared with a simple combination of individual detectors. The astrophysical background is expected to be detectable with a signal-to-noise ratio of 100 after 5 years of operation and dominated by the extragalactic double white dwarves. On the other hand, due to the uncertain nature of underlying models, we can only estimate the detection capability of the cosmological background for specific cases., Comment: 20 pages, 10 figures, update to match published version

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 a 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 or 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 has been 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 the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., 16 pages, 1 figure, invited article to a special section in PTEP

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., 21 pages, 7 figures, 6 tables, 5 appendices, to be published in Phys. Rev. D

We derive an ansatz for the five dimensional equal-rotation Kerr-Newman metric that contains two unknown functions. By solving for these functions through perturbation series, we find that the metric can be cast into the Kerr-Shild form in a background that is flat at the spatial infinity., Comment: 13 pages, fixing a loophole in the original version of the paper