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Extreme-mass-ratio inspirals (EMRIs), consisting of a massive black hole and a stellar compact object, are one of the most important sources for space-borne gravitational wave detectors like TianQin. Their population study can be used to constrain astrophysical models that interpret the EMRI formation mechanisms. In this paper, as a first step, we employ a parametrization method to describe the EMRI population model in the loss cone formation channel. This approach, however, can be extended to other models such as the accretion disc driven formation channel. We present the phenomenological characteristic of the MBH mass, spin, and redshift distributions. Then, we investigate the posterior distribution of the hyper-parameters that describe this population model. Our results show that TianQin could recover almost all the posterior of the hyper-parameters within $1\sigma$ confidence interval. With one hundred detectable EMRI events, the hyper-parameters $\alpha_1, \alpha_2, b$, which describe the MBH mass distribution, could be measured with an accuracy of $37\%$, $24\%$, and $3\%$, respectively. The hyper-parameters $\mu_z$, and $\sigma_z$, which describe the redshift distribution, have $\mu_z$ above the detectable range of TianQin, and $\sigma_z$ measured with an accuracy of $14.5\%$. With this estimation accuracy, the EMRI population characteristics can be effectively demonstrated, potentially serving as evidence for EMRI formation in the future studies. Furthermore, with an increasing number of detectable events, the parameter estimation for the hyper-parameters will improve and the confidence intervals will be narrowed., Comment: 11 pages, 5 figures

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

Extreme-mass-ratio inspirals (EMRIs) could be detected by space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA), TianQin and Taiji. Localizing EMRIs by GW detectors can help us select candidate host galaxies, which can be used to infer the cosmic expansion history. In this paper, we demonstrate that the localization information can also be used to infer the formation channel of EMRIs, and hence allow us to extract more precisely the redshift probability distributions. By conducting mock observations of the EMRIs which can be detected by TianQin and LISA, as well as the galaxies which can be provided by the future Chinese Space Station Telescope, we find that TianQin can constrain the Hubble-Lema\^itre constant $H_0$ to a precision of $\sim3\%-8\%$ and the dark energy equation of state parameter $w_0$ to $\sim10\%-40\%$. The TianQin+LISA network, by increasing the localization accuracy, can improve the precisions of $H_0$ and $w_0$ to $\sim0.4\%-7\%$ and $\sim4\%-20\%$, respectively. Then, considering an illustrative case in which all EMRIs originate in AGNs, and combining the mock EMRI observation with a mock AGN catalog, we show that TianQin can recognize the EMRI-AGN correlation with $\sim 1300$ detections. The TianQin+LISA network can reduce this required number to $\sim 30$. Additionally, we propose a statistical method to directly estimate the fraction of EMRIs produced in AGNs, $f_{\rm agn}$, and show that observationally deriving this value could significantly improve the constraints on the cosmological parameters. These results demonstrate the potentials of using EMRIs as well as galaxy and AGN surveys to improve the constraints on cosmological parameters and the formation channel of EMRIs., Comment: 21 pages, 10 figures, and 1 table; accepted for publication in ApJS

The Einstein-dilaton-Gauss-Bonnet (EdGB) theory is a modified theory which include a scalar field to couple with the higher order curvature terms. It has already been constrained with various observations include the gravitational wave (GW) with LIGO, Virgo and KAGRA (LVK) Collaboration. In this work, we study the problem of using the GW of Extreme Mass-Ratio Inspiral (EMRI) to constrain the EdGB theory. We use the "numerical kludge (NK)" method to construct the waveform of EMRI in the EdGB theory, focusing on the case when the central black hole is spinless. We then study how a future space-borne gravitational wave detector, TianQin, for example, can place constraints on the EdGB theory through the detection of EMRIs. With the analysis using mismatch and Fisher Information Matrix (FM), we find that the EdGB parameter $\sqrt{\alpha}$ is expected to be constrained to the level of $\sim\mathcal{O}(0.1)$ km., Comment: 9 page, 3 figures

Space-based gravitational wave detectors like TianQin or LISA could observe extreme-mass-ratio-inspirals (EMRIs) at millihertz frequencies. The accurate identification of these EMRI signals from the data plays a crucial role in enabling in-depth study of astronomy and physics. We aim at the identification stage of the data analysis, with the aim to extract key features of the signal from the data, such as the evolution of the orbital frequency, as well as to pinpoint the parameter range that can fit the data well for the subsequent parameter inference stage. In this manuscript, we demonstrated the identification of EMRI signals without any additional prior information on physical parameters. High-precision measurements of EMRI signals have been achieved, using a hierarchical search. It combines the search for physical parameters that guide the subsequent parameter inference, and a semi-coherent search with phenomenological waveforms that reaches precision levels down to $10^{-4}$ for the phenomenological waveform parameters $\omega_{0}$, $\dot{\omega}_{0}$, and $\ddot{\omega}_{0}$. As a result, we obtain measurement relative errors of less than 4% for the mass of the massive black hole, while keeping the relative errors of the other parameters within as small as 0.5%., Comment: 16 pages, 7 figures, comments welcom

The millihertz gravitational wave band is expected to be opened by space-borne detectors like TianQin. Various mechanisms can produce short outbursts of gravitational waves, whose actual waveform can be hard to model. In order to identify such gravitational wave bursts and not to misclassify them as noise transients, we proposed a proof-of-principle energy excess method, that utilized the signal-insensitive channel to veto noise transients. We perform a test on simulated data, and for bursts with a signal-to-noise ratio of 20, even with the contamination of noise transient, our methods can reach a detection efficiency of 97.4% under a false alarm rate of once per year. However, more frequent occurrences of noise transients would lower the detection efficiency., Comment: 13 pages, 9 figures, comments welcome

Recently discovered regular X-ray bursts known as quasi-periodic eruptions have a proposed model that suggests a tidal stripping white dwarf inspiralling into the galaxy's central black hole on an eccentric orbit. According to this model, the interaction of the stripping white dwarf with the central black hole would emit gravitational wave signals as well, their detection can help explore the formation mechanism of quasi-periodic eruptions and facilitate multi-messenger observations. In this paper, we aim to perform a preliminary study of the gravitation wave observation of TianQin on this stripping white dwarf model. We investigated the horizon distance of TianQin on this type of gravitation wave signal and found it can be set to 200Mpc. We also find that those stripping white dwarf model sources with central black hole mass within $10^4\sim10^{5.5}M_\odot$ are more likely to be detected by TianQin. We assessed the parameter estimation precision of TianQin on those stripping white dwarf model sources. Our result shows that, even in the worst case, TianQin can determine the central black hole mass, the white dwarf mass, the central black hole spin, and the orbital initial eccentricity with a precision of $10^{-2}$. In the optimistic case, TianQin can determine the central black hole mass and the white dwarf mass with a precision of $10^{-7}$, determine the central black hole spin with a precision of $10^{-5}$, and determine the orbital initial eccentricity with a precision of $10^{-8}$. Moreover, TianQin can determine the luminosity distance with a precision of $10^{-1}$ and determine the sky localization with a precision of $10^{-2}\sim10$ $\rm deg^2$., Comment: 9 pages, 4 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.

Constituted with a massive black hole and a stellar mass compact object, Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study of massive black holes, such as by measuring and checking the relations among the mass, spin and quadrupole moment of a massive black hole, putting the no-hair theorem to test. TianQin is a planned space-based gravitational wave observatory and EMRI is one of its main types of sources. It is important to estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In this work, we use the analytic kludge waveform with quadrupole moment corrections and study how the quadrupole moment can be constrained with TianQin. We find that TianQin can measure the dimensionless quadrupole moment parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The choice of the waveform cutoff is found to have significant effect on the result: if the Schwarzschild cutoff is used, the accuracy depends strongly on the mass of the massive black hole, while the spin has negligible impact; if the Kerr cutoff is used, however, the dependence on the spin is more significant. We have also analyzed the cases when TianQin is observing simultaneously with other detectors such as LISA., Comment: 10 pages, 9 figures, matches the published version

Systems consisting of a massive black hole and a stellar-origin compact object (CO), known as extreme-mass-ratio inspirals (EMRIs), are of great significance for space-based gravitational-wave detectors, as they will allow for testing gravitational theories in the strong field regime, and for checking the validity of the black hole no-hair theorem. In this work, we present a calculation of the EMRI rate and parameter estimation capabilities of the TianQin observatory, for various astrophysical models for these sources. We find that TianQin can observe EMRIs involving COs with mass of 10$M_\odot$ up to redshift $\sim2$. We also find that detections could reach tens or hundreds per year in the most optimistic astrophysical scenarios. Intrinsic parameters are expected to be recovered to within fractional errors of $\sim 10^{-6}$, while typical errors on the luminosity distance and sky localization are 10% and 10 deg$^2$, respectively. TianQin observation of EMRIs can also constrain possible deviations from the Kerr quadrupole moment to within fractional errors $\lesssim10^{-4}$. We also find that a network of multiple detectors would allow for improvements in both detection rates (by a factor $\sim 1.5$ -$3$) and in parameter estimation precision (20-fold improvement for the sky localization and fivefold improvement for the other parameters)., Comment: 13 pages, 5 figures

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