Search

Massive black hole binaries are one of the important sources for the TianQin project. Our research has revealed that, for TianQin, the signal-to-noise ratio squared during the inspiral phase of massive black hole binaries exhibits a direct proportionality to the ratio of the observation duration to the time remaining until coalescence. This finding is expected to greatly simplify the estimation of detection capabilities for massive black hole binaries. In this paper, we demonstrated this relationship under both all-sky average and non-average conditions. The latter introduces only an additional term, which we refer to as the response factor. Although this term is not easily calculated analytically, we provide a simple estimation method with an error margin of within 2%., Comment: 12 pages, 5 figures, comments welcome

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

As a space-borne gravitational wave observatory, TianQin can observe a large variety of gravitational wave sources. The rich signals can be composed by different types of astronomical systems, like Galactic compact binaries, inspiral of stellar mass black holes, merger of massive black holes, and extreme mass ratio inspirals. The incoherent summation of these signals can also form a stochastic gravitational wave background. Using the future TianQin observation, it is possible to put stringent constraints on fundamental science, like the expansion history of our universe. In this work, we provide a brief review of these topics that contributes to the 7th International Workshop on the TianQin Science Mission., Comment: Prepared for the proceeding of the 7th International Workshop on the TianQin Science Mission. 12 pages, 2 figures

In the milli-Hertz frequency band, stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one-year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to $l=4$. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Thirdly, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). Finally, we find that since the different data channel combinations correspond to different singularities, certain combinations might have an advantage in stochastic background map-making. We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational-wave detectors aiming to decipher anisotropies in the stochastic background., Comment: 12 pages, 6 figures

Space-borne detectors, including TianQin and Laser Interferometry Space Antenna (LISA), are tasked with the simultaneous observation of Galactic foreground, astrophysical and cosmological stochastic gravitational-wave backgrounds (SGWBs). For the first time, we employ a space-borne detector network to identify the multi-component SGWB. Specifically, we develop a tailored likelihood for cross-correlation detection with such networks. Combined with the likelihood, we use the simulated datasets of the TianQin + LISA network to conduct model selection and parameter estimation. Our results indicate that, after 4 years of operation, the network could detect a single SGWB from either astrophysical or cosmological origins, with an energy density $\Omega_{\rm ast/cos}$ (10 mHz) on the order of $10^{-12}$, despite the presence of a Galactic foreground. Furthermore, to distinguish the cosmological background from both a Galactic foreground and the expected astrophysical background, the energy density $\Omega_{\rm cos}$ should reach around $2\times 10^{-11}$., Comment: 17 pages, 9 figures

The early inspiral from stellar-mass binary black holes can emit milli-Hertz gravitational wave signals, making them detectable sources for space-borne gravitational wave missions like TianQin. However, the traditional matched filtering technique poses a significant challenge for analyzing this kind of signals, as it requires an impractically high number of templates ranging from $10^{31}$ to $10^{40}$. We propose a search strategy that involves two main parts: initially, we reduce the dimensionality of the simulated signals using incremental principal component analysis (IPCA). Subsequently we train the convolutional neural networks (CNNs) based on the compressed TianQin data obtained from IPCA, aiming to develop both a detection model and a point parameter estimation model. The compression efficiency for the trained IPCA model achieves a cumulative variance ratio of 95.6% when applied to $10^6$ simulated signals. To evaluate the performance of CNN we generate the receiver operating characteristic curve for the detection model which is applied to the test data with varying signal-to-noise ratios. At a false alarm probability of 5% the corresponding true alarm probability for signals with a signal-to-noise ratio of 50 is 86.5%. Subsequently, we introduce the point estimation model to evaluate the value of the chirp mass of corresponding sBBH signals with an error. For signals with a signal-to-noise ratio of 50, the trained point estimation CNN model can estimate the chirp mass of most test events, with a standard deviation error of 2.48 $M_{\odot}$ and a relative error precision of 0.12., Comment: 12 pages, 10 figures

Silicon strip detectors have been widely utilized in space experiments for gamma-ray and cosmic-ray detections thanks to their high spatial resolution and stable performance. For a silicon micro-strip detector, the Monte Carlo simulation is recognized as a practical and cost-effective approach to verify the detector performance. In this study, a technique for the simulation of the silicon micro-strip detector with the $\rm Allpix^{2}$ framework is developed. By incorporating the electric field into the particle transport simulation based on Geant4, this framework could precisely emulate the carrier drift in the silicon micro-strip detector. The simulation results are validated using the beam test data as well as the flight data of the DAMPE experiment, which suggests that the $\rm Allpix^{2}$ framework is a powerful tool to obtain the performance of the silicon micro-strip detector.

Space-borne gravitational wave detectors like TianQin might encounter data gaps due to factors like micro-meteoroid collisions or hardware failures. Such glitches will cause discontinuity in the data and have been observed in the LISA Pathfinder. The existence of such data gaps presents challenges to the data analysis for TianQin, especially for massive black hole binary mergers, since its signal-to-noise ratio (SNR) accumulates in a non-linear way, a gap near the merger could lead to significant loss of SNR. It could introduce bias in the estimate of noise properties, and furthermore the results of the parameter estimation. In this work, using simulated TianQin data with injected a massive black hole binary merger, we study the window function method, and for the first time, the inpainting method to cope with the data gap, and an iterative estimate scheme is designed to properly estimate the noise spectrum. We find that both methods can properly estimate noise and signal parameters. The easy-to-implement window function method can already perform well, except that it will sacrifice some SNR due to the adoption of the window. The inpainting method is slower, but it can minimize the impact of the data gap., Comment: 12 pages, 5 figures, comments welcome

Weak-signal limit is often used in estimating stochastic gravitational-wave background (SGWB) intensities. This approximation fails and the signal-to-noise ratio (SNR) can be much weaker when background signals are loud compared to the detector noise. In this work, we highlight this limitation for the SGWB detection using space-borne detector networks. For the TianQin + LISA network, the SNR estimated under the weak-signal limit might be off by as large as an order of magnitude. Contour plots of SNR over the parameter spaces are also presented to indicate regions susceptible to this discrepancy. Our results suggest that DA and DB type extragalactic double white dwarfs may yield an SGWB with SNR surpassing 100 after 1 year of operation in the weak-signal-limit scenario, with a redshift-independent merger rate of about $500\,\,{\rm Mpc^{-3}\,Myr^{-1}}$. In fact, this value falls significantly below the necessary threshold. Similar influences arise for first-order phase transitions, yet pinning down parameter regions remains formidable due to model uncertainties., Comment: 11 pages, 7 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 cosmic distance duality relation (CDDR), expressed as DL(z) = (1 + z)2DA(z), plays an important role in modern cosmology. In this paper, we propose a new method of testing CDDR using strongly lensed gravitational wave (SLGW) signals. Under the geometric optics approximation, we calculate the gravitational lens effects of two lens models, the point mass and singular isothermal sphere. We use functions of {\eta}1(z) = 1 + {\eta}0z and {\eta}2(z) = 1 + {\eta}0z=(1 + z) to parameterize the deviation of CDDR. By reparameterizing the SLGW waveform with CDDR and the distance-redshift relation, we include the deviation parameters {\eta}0 of CDDR as waveform parameters. We evaluate the ability of this method by calculating the parameter estimation of simulated SLGW signals from massive binary black holes. We apply the Fisher information matrix and Markov Chain Monte Carlo methods to calculate parameter estimation. We find that with only one SLGW signal, the measurement precision of {\eta}0 can reach a considerable level of 0.5-1.3% for {\eta}1(z) and 1.1-2.6% for {\eta}2(z), depending on the lens model and parameters., Comment: 15 pages, 7 figures

The Silicon Charge Detector (SCD) is a subdetector of the High Energy Cosmic Radiation Detection payload. The dynamic range of the silicon microstrip detector can be extended by the capacitive coupling effect, which is related to the interstrip capacitance and the coupling capacitance. A detector prototype with several sets of parameters was designed and tested in the ion beams at the CERN Super Proton Synchrotron. The capacitive coupling fractions with readout strip and floating strip incidences were studied using the beam test data and SPICE simulation.

This paper analyses the impact of various parameter changes on the estimation of parameters for massive black hole binary (MBHB) systems using a Bayesian inference technique. Several designed MBHB systems were chosen for comparison with a fiducial system to explore the influence of parameters such as sky location, inclination angle, anti-spin, large mass ratio and light mass. And the two reported MBHB candidates named OJ287 and Tick-Tock are also considered. The study found that the network of TianQin and LISA can break certain degeneracies among different parameters, improving the estimation of parameters, particularly for extrinsic parameters. Meanwhile, the degeneracies between different intrinsic parameters are highly sensitive to the value of the parameters. Additionally, the small inclination angles and limited detection of the inspiral phase can introduce significant bias in the estimation of parameters. The presence of instrument noise will also introduce bias and worsen the precision. The paper concludes that the network of TianQin and LISA can significantly improve the estimation of extrinsic parameters by about one order of magnitude while yielding slight improvements in the intrinsic parameters. Moreover, parameter estimation can still be subject to biases even with a sufficiently high signal-to-noise ratio if the detected signal does not encompass all stages of the inspiral, merger, and ringdown., Comment: 17 pages, 10 figures

Theoretical predictions suggest that very massive stars have the potential to form through multiple collisions and eventually evolve into intermediate-mass black holes (IMBHs) within Population III star clusters embedded in mini dark matter haloes. In this study, we investigate the long-term evolution of Population III star clusters, including models with a primordial binary fraction of $f_{\rm b}=0$ and 1, using the $N$-body simulation code PETAR. We comprehensively examine the phenomenon of hierarchical triple black holes in the clusters, specifically focusing on their merging inner binary black holes (BBHs), with post-Newtonian correction, by using the TSUNAMI code. Our findings suggest a high likelihood of the inner BBHs containing IMBHs with masses on the order of $\mathcal{O}(100)M_{\odot}$, and as a result, their merger rate could be up to $0.1{\rm Gpc}^{-3}{\rm yr}^{-3}$. The orbital eccentricities of some merging inner BBHs oscillate over time periodically, known as the Kozai-Lidov oscillation, due to dynamical perturbations. Detectable merging inner BBHs for mHz GW detectors LISA/TianQin/Taiji concentrate within $z<3$. More distant sources would be detectable for CE/ET/LIGO/KAGRA/DECIGO, which are sensitive from $\mathcal{O}(0.1)$Hz to $\mathcal{O}(100)$Hz. Furthermore, compared with merging isolated BBHs, merging inner BBHs affected by dynamical perturbations from tertiary BHs tend to have higher eccentricities, with a significant fraction of sources with eccentricities closing to 1 at mHz bands. GW observations would help constrain formation channels of merging BBHs, whether through isolated evolution or dynamical interaction, by examining eccentricities., Comment: 19 pages, 22 figures, and 3 tables, accepted by MNRAS

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

Space-borne gravitational wave (GW) detectors can detect the merger of massive black holes. The early warning and localization of GW events before merging can be used to inform electromagnetic telescopes and conduct multimessenger observations. However, this requires real-time data transmission and analysis capabilities. The geocentric orbit of the space-borne GW detector TianQin makes it possible to conduct real-time data transmission. In this study, we develop a search and localization pipeline for massive black hole binaries (MBHBs) with TianQin under both regular and real-time data transmission modes. We demonstrate that, with real-time data transmission, MBHBs can be accurately localized on the fly. With the approaching merger, each analysis can be finished in only 40 min. For an MBHB system at a distance of 1 Gpc, if we receive data every hour, then we can pinpoint its location to within less than 1 deg$^2$ on the final day before the merger.

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

TianQin and LISA are space-based laser interferometer gravitational wave (GW) detectors planned to be launched in the mid-2030s. Both detectors will detect low-frequency GWs around $10^{-2}\,{\rm Hz}$, however, TianQin is more sensitive to frequencies above this common sweet-spot while LISA is more sensitive to frequencies below $10^{-2}\,{\rm Hz}$. Therefore, TianQin and LISA will be able to detect the same sources but with different accuracy depending on the source and its parameters. We consider some of the most important astrophysical sources -- massive black hole binaries, stellar-mass black hole binaries, double white dwarfs, extreme mass ratio inspirals, light and heavy intermediate mass ratio inspirals, as well as the stochastic gravitational background of astrophysical origin -- that TianQin and LISA will be able to detect. For each of these sources, we analyze how far they can be detected (detection distance) and how well their parameters can be measured (detection accuracy) using a Fisher Matrix analysis. We compare the results obtained by the three detection scenarios (TianQin alone, LISA alone, and joint detection by LISA and TianQin) highlighting the gains from joint detection as well as the contribution of TianQin and LISA to a combined study of astrophysical sources. In particular, we consider the different orientations, lifetimes, and duty cycles of the two detectors to explore how they can give a more complete picture when working together., Comment: 49 pages, 63 figures

We present a Bayesian parameter estimation progress to infer the stellar mass binary black hole properties by TianQin, LISA, and TianQin+LISA.Two typical stellar mass black hole binary systems, GW150914 and GW190521 are chosen as the fiducial sources. In this work, we establish the ability of TianQin to infer the parameters of those systems and first apply the full frequency response in TianQin's data analysis. We obtain the parameter estimation results and explain the correlation between them. We also find the TianQin+LISA could marginally increase the parameter estimation precision and narrow the $1\sigma$ area compared with TianQin and LISA individual observations. We finally demonstrate the importance of considering the effect of spin when the binaries have a nonzero component spin and great deviation will appear especially on mass, coalescence time and sky location., Comment: 17 pages, 6 figures

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

Single gravitational-wave detectors face inherent limitations in detecting the anisotropy of the stochastic background. In this work, we explore the sensitivity to anisotropic backgrounds with a network of space-borne detectors. We find that the separation between detectors plays an important role in determining the sensitivity. For the first time, we observe as large as three orders of magnitude enhancement in detection sensitivity for the multipoles with $l=5$ and 6, compared to coinciding detectors. Coordinating and optimizing the separation between two space-borne detectors can significantly enhance the network's sensitivity to the multipole components of the stochastic background. For the TianQin + LISA network, benefiting from detector separation, it is possible to achieve sensitivity levels of 2-3 orders of magnitude better than using TianQin or LISA detector alone. These findings pave the way to uncover the underlying physics of anisotropy through gravitational-wave detections., Comment: 19 pages, 13 figures

The measurement of the Hubble constant $H_0$ plays an important role in the study of cosmology. In this letter, we propose a new method to constrain the Hubble constant using the strongly lensed gravitational wave (GW) signals. By reparameterizing the waveform, we find that the lensed waveform is sensitive to the $H_0$. Assuming the scenario that no electromagnetic counterpart of the GW source can be identified, our method can still give meaningful constraints on the $H_0$ with the information of the lens redshift. We then apply Fisher information matrix and Markov Chain Monte Carlo to evaluate the potential of this method. For the space-based GW detector, TianQin, the $H_0$ can be constrained within a relative error of $\sim$ 0.3-2\%, using a single strongly lensed GW event. Precision varies according to different levels of electromagnetic information., Comment: 8 pages, 4 figures

The measurement of eccentricity would provide strong constraints on the formation channel of stellar-mass binary black holes. However, current ground-based gravitational wave detectors will, in most cases, not be able to measure eccentricity due to orbital circularization. Space-based observatories, in contrast, can determine binary eccentricity at 0.01Hz to $e_{0.01}\gtrsim\mathcal{O}(10^{-4}) $. Directly observing stellar-mass binary black holes with space-based observatories remains a challenging problem. However, observing such systems with ground-based detectors allows the possibility to identify the same signal in archival data from space-based observatories in the years previous. Since ground-based detectors provide little constraints on eccentricity, including eccentricity in the archival search will increase the required number of filter waveforms for the archival search by 5 orders of magnitudes [from $\sim \mathcal{O}(10^3)$ to $\sim \mathcal{O}(10^8)$], and will correspondingly need $ \sim8\times10^5 $ core hours (and $ \sim 10^5$ GB of memory), even for a mild upper limit on eccentricity of $0.1$. In this work, we have constructed the first template bank for an archival search of space-based gravitational wave detectors, including eccentricity. We have demonstrated that even though the inclusion of eccentricity brings extra computational burden, an archival search including eccentricity will be feasible in the time frame of planned space-based observatories, and will provide strong constraints on the eccentricities of stellar-mass binary black holes., Comment: 8 pages, 4 figures, comments welcome

In this paper, we revisit the problem of using gravitational wave data to test the Einstein-dilation-Gauss-Bonnet theory, by using nine selected gravitational wave events from GWTC-3. Compared with existing work, we are taking into account the higher harmonics more properly and we also study the contribution of the merger-ringdown data. Using the inspiral data alone, we find that the best result is from GW200115, giving $\sqrt{|\alpha|} < 1.1$ km, which is about 17\% tighter than the previous best result. We also notice the possible existence of a simple unexpected relation among the constraints from different events. Several combinations of the selected events give $\sqrt{|\alpha|} \leq 1.0$ km. The result is further improved when the merger-ringdown data is also included, using two phenomenological schemes, giving $\sqrt{|\alpha|} < 0.87$ km for GW200115 in the best case scenario.

Galactic short-period close white dwarf binaries (CWDBs) are important objects for space-borne gravitational-wave (GW) detectors in the millihertz frequency bands. Due to the intrinsically low luminosity, only about 25 identified CWDBs are detectable by the Laser Interferometer Space Antenna (LISA), which are also known as verification binaries (VBs). The Gaia Early Data Release 3 (EDR3) provids a catalog containing a large number of CWDB candidates, which also includes parallax and photometry measurements. We crossmatch the Gaia EDR3 and Zwicky Transient Facility public data release 8, and apply period-finding algorithms to obtain a sample of periodic variables. The phase-folded light curves are inspected, and finally we obtain a binary sample containing 429 CWDB candidates. We further classify the samples into eclipsing binaries (including 58 HW Vir-type binaries, 65 EA-type binaries, 56 EB-type binaries, and 41 EW-type binaries) and ellipsoidal variations (209 ELL-type binaries). We discovered four ultrashort period binary candidates with unique light-curve shapes. We estimate the GW amplitude of all of our binary candidates, and calculate the corresponding signal-to-noise ratio (S/N) for TianQin and LISA. We find two (six) potential GW candidates with S/Ns greater than 5 in the nominal mission time of TianQin (LISA), which increases the total number of candidate VBs for TianQin (LISA) to 18 (31)., Comment: 40 pages, 20 figures

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., Comment: 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

The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (DWDs) in our galaxy. This offers an excellent chance for testing the existence of extra polarization modes. In this article, we analyze the capability of detecting the extra polarization modes with DWDs. For the extra modes, we consider both the leading order dipole radiation and the subleading quadrupole radiation. We find that the capability of TianQin has very strong dependency on the source orientation. We also analyze all the verification binaries with determined position and frequency, and find that ZTF J1539 can give the best constraint on the extra polarization modes. We have also considered the case of TianQin twin constellation, and the joint observation with LISA., Comment: 13 pages, 18 figures, 5 tables, matches the published version

Quantitative and analytical analysis of modulation process of the collimator is a great challenge, and is also of great value to the design and development of Fourier transform imaging telescopes. The Hard X-ray Imager (HXI), as one of the three payloads onboard the Advanced Space-based Solar Observatory(ASO-S) mission, adopts modulating Fourier-Transformation imaging technique and will be used to explore mechanism of energy release and transmission in solar flare activities. As an important step to reconstruct the images of solar flares, accurate modulation functions of HXI are needed. In this paper, a mathematical model is developed to analyze the modulation function under a simplified condition first. Then its behavior under six degrees of freedom is calculated after adding the rotation matrix and translation change to the model. In addition, unparalleled light and extended sources also are considered so that our model can be used to analyze the X-ray beam experiment. Next, applied to the practical HXI conditions, the model has been confirmed not only by Geant4 simulations but also by some verification experiments. Furthermore, how this model helps to improve the image reconstruction process after the launch of ASO-S is also presented.

Gravitational waves (GWs) originated from mergers of stellar-mass binary black holes (SBBHs) are considered as dark sirens in cosmology since they usually do not have electromagnetic counterparts. In order to study cosmos with these events, we not only need the luminosity distances extracted from GW signals, but also require the redshift information of sources via, say, matching GW sky localization with galaxy catalogs. Based on such a methodology, we explore how well decihertz GW detectors, DO-Optimal and DECIGO, can constrain cosmological parameters. Using Monte-Carlo simulated dark sirens, we find that DO-Optimal can constrain the Hubble parameter to ${\sigma_{H_0}} / {H_0}\, \lesssim 0.23\%$ when estimating $H_0$ alone, while DECIGO performs better by a factor of 5 with ${\sigma_{H_0}} / {H_0}\lesssim 0.043\%$. Such a good precision of $H_0$ will shed light on the $H_0$ tension. For multiple-parameter estimation, DECIGO can still reach a level of relative uncertainty smaller than $7\%$. The reason why decihertz detectors perform well is explained by their large numbers of SBBH GW events with good distance and angular resolution., Comment: 14 pages, 8 figures, update to match published version

The space-borne gravitational wave detectors will observe a large population of double white dwarf binaries in the Milky Way. However, the search for double white dwarfs in the gravitational wave data will be time-consuming due to the large number of templates involved and antenna response calculation. In this paper, we implement an iterative combinatorial algorithm to search for double white dwarfs in MLDC-3.1 data. To quickly determine the rough parameters of the target sources, the following algorithms are adopted in a coarse search process: (1) using the downsampling method to reduce the number of original data points; (2) using the undersampling method to speed up the generation of a single waveform template; (3) using the stochastic template bank method to quickly construct the waveform template bank while achieving high coverage of the parameter space; (4) Combining the FFT acceleration algorithm with the stochastic template bank to reduce the calculation time of a single template. A fine search process is applied to further determine the parameters of the signals based on the coarse search, for which we adopt the particle swarm optimization. Finally, we detected $\mathcal{O}(10^4)$ double white dwarf signals, validating the feasibility of our method., Comment: 16 pages, 15 figures

Extreme mass ratio inspirals (EMRIs) are among the most interesting gravitational wave (GW) sources for space-borne GW detectors. However, successful GW data analysis remains challenging due to many issues, ranging from the difficulty of modeling accurate waveforms, to the impractically large template bank required by the traditional matched filtering search method. In this work, we introduce a proof-of-principle approach for EMRI detection based on convolutional neural networks (CNNs). We demonstrate the performance with simulated EMRI signals buried in Gaussian noise. We show that over a wide range of physical parameters, the network is effective for EMRI systems with a signal-to-noise ratio larger than 50, and the performance is most strongly related to the signal-to-noise ratio. The method also shows good generalization ability towards different waveform models. Our study reveals the potential applicability of machine learning technology like CNNs towards more realistic EMRI data analysis., Comment: 12 pages, 4 figures

The DArk Matter Particle Explorer (DAMPE) is well suitable for searching for monochromatic and sharp $\gamma$-ray structures in the GeV$-$TeV range thanks to its unprecedented high energy resolution. In this work, we search for $\gamma$-ray line structures using five years of DAMPE data. To improve the sensitivity, we develop two types of dedicated data sets (including the BgoOnly data which is the first time to be used in the data analysis for the calorimeter-based gamma-ray observatories) and adopt the signal-to-noise ratio optimized regions of interest (ROIs) for different DM density profiles. No line signals or candidates are found between 10 and 300 GeV in the Galaxy. The constraints on the velocity-averaged cross section for $\chi\chi \to \gamma\gamma$ and the decay lifetime for $\chi \to \gamma\nu$, both at 95% confidence level, have been calculated and the systematic uncertainties have been taken into account. Comparing to the previous Fermi-LAT results, though DAMPE has an acceptance smaller by a factor of $\sim 10$, similar constraints on the DM parameters are achieved and below 100 GeV the lower limits on the decay lifetime are even stronger by a factor of a few. Our results demonstrate the potential of high-energy-resolution observations on dark matter detection., Comment: 14 pages, 8 figures. Update the content to keep up with the published version

The detection of GW190521 gains huge attention because it is the most massive binary that LIGO and Virgo ever confidently detected until the release of GWTC-3 (GW190426_190642 is more massive), and it is the first black hole merger whose remnant is believed to be an intermediate mass black hole. Furthermore, the primary black hole mass falls in the black hole mass gap, where the pair-instability supernova prevents the formation of astrophysical black holes in this range. In this paper, we systematically explore the prospect of TianQin on detecting GW190521-like sources. For sources with small orbital eccentricities, (i) TianQin could resolve up to a dozen of sources with signal-to-noise ratio (SNR) larger than 8. Even if the signal-to-noise ratio threshold increases to 12, TianQin could still detect GW190521-like binaries. (ii) The parameters of sources merging within several years would be precisely recovered. The precision of coalescence time and sky localization closes to $1\ {\rm s}$ and $1\ {\rm deg^{2}}$ respectively. This indicates that TianQin could provide early warnings for ground-based gravitational waves detectors and electromagnetic telescopes for these sources. Furthermore, TianQin could distinguish the formation channels of these sources by measuring the orbital eccentricities with a relative precision of $10^{-4}$. (iii) TianQin could constrain the Hubble constant with a $10\%$ precision with GW190521-like sources. Finally, for very eccentric GW190521-like sources, although their gravitational wave signal might be too weak for TianQin to detect, even the null detection of TianQin could still present a significant contribution to the understanding of the underlying science., Comment: 15 pages, 9 figures, published in Phys. Rev. D

Gravitational wave signal from the inspiral of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspiral covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly $30\%$ through detections of $10$ gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of $< 10 \%$, assuming TianQin I+II. In the optimistic case, the multi-detector network of TianQin and LISA is capable of constraining the Hubble constant to within $5\%$ precision. It is worth highlighting that the multi-band network of TianQin and Einstein Telescope is capable of constraining the Hubble constant to a precision of about $1\%$. We conclude that inferring the Hubble constant without bias from photo-z galaxy catalog is achievable, and we also demonstrate self-consistency using the P$-$P plot. On the other hand, high-quality spectroscopic redshift information is crucial for improving the estimation precision of Hubble constant., Comment: 29 pages, 14 figures, update to match published version

The ringdown data of both GW150914 and GW190521\_074359 (GW190521r) show evidence supporting the presence of overtone. Previous studies all adopt a fundamental assumption, which were motivated more by convenience than by first principles, that the first overtone and the fundamental mode share a same onset. In this work, for the first time we relax such assumption, and we aim to probe the possible chromatic onsets of these two components within the GW150914 and GW190521r ringdown data. For both events, we bound the onset lags to be $\Delta t_0\geq 5M_f$ at probabilities of $\geq 94.7\%$, where $M_f$ is the mass of the remnant black hole formed in the merger. This result moderately favours the non-simultaneous excitation between the fundamental mode and the first overtone in the ringdown., Comment: 6 pages, 3 figures, 1 table, accepted by PRD

Primordial black holes (PBHs) have been proposed to explain at least a portion of dark matter. Observations have put strong constraints on PBHs in terms of the fraction of dark matter which they can represent, $f_{\rm PBH}$, across a wide mass range -- apart from the stellar-mass range of $20M_\odot\lesssim M_{\rm PBH}\lesssim 100M_\odot$. In this paper, we explore the possibility that such PBHs could serve as point-mass lenses capable of altering the gravitational-wave (GW) signals observed from binary black hole (BBH) mergers along their line-of-sight. We find that careful GW data analysis could verify the existence of such PBHs based on the $fitting~factor$ and odds ratio analyses. When such a lensed GW signal is detected, we expect to be able to measure the redshifted mass of the lens with a relative error $\Delta M_{\rm PBH}/M_{\rm PBH}\lesssim0.3$. If no such lensed GW events were detected despite the operation of sensitive GW detectors accumulating large numbers of BBH mergers, it would translate into a stringent constraint of $f_{\rm PBH}\lesssim 10^{-2}-10^{-5}$ for PBHs with a mass larger than $\sim10M_\odot$ by the Einstein Telescope after one year of running, and $f_{\rm PBH}\lesssim 0.2$ for PBHs with mass greater than $\sim 50M_\odot$ for advanced LIGO after ten years of running., Comment: 10 pages, 4 figures, accepted by Phys. Rev. D

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

Space-borne gravitational wave detectors like TianQin are expected to detect GW signals emitted by the mergers of massive black hole binaries. Luminosity distance information can be obtained from GW observations, and one can perform cosmological inference if redshift information can also be extracted, which would be straightforward if an electromagnetic counterpart exists. In this paper, we concentrate on the conservative scenario where the EM counterparts are not available, and comprehensively study if cosmological parameters can be inferred through a statistical approach, utilizing the non-uniform distribution of galaxies as well as the black hole mass-host galaxy bulge luminosity relationship. By adopting different massive black hole binary merger models, and assuming different detector configurations, we conclude that the statistical inference of cosmological parameters is indeed possible. TianQin is expected to constrain the Hubble constant to a relative error of about 4%-7%, depending on the underlying model. The multidetector network of TianQin and LISA can significantly improve the precision of cosmological parameters. In the most favorable model, it is possible to achieve a level of 1.7% with a network of TianQin and LISA. We find that without EM counterparts, constraints on all other parameters need a larger number of events or more precise sky localization of GW sources, which can be achieved by the multidetector network or under a favorable model for massive black hole mergers. However, in the optimistic case, where EM counterparts are available, one can obtain useful constraints on all cosmological parameters in the Lambda-CDM cosmology, regardless of the population model. Moreover, we can also constrain the equation of state of the dark energy without the EM counterparts, and it is even possible to study the evolution of EoS of the DE when the EM counterparts are observed., Comment: 34 pages, 17 figures, update to match published version

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