arXiv subjects

Shichao Wu

Publications and source records attributed to Shichao Wu.

At least 19 recordsLinked to original sources

arXiv2025

Multiband parameter estimation with phase coherence and extrinsic marginalization: Extracting more information from low-SNR CBC signals in LISA data

This paper presents a novel coherent multiband analysis framework for characterizing stellar- and intermediate-mass binary black holes using LISA and next-generation ground-based detectors (ET and CE), leveraging the latest developments in the \texttt{PyCBC} pipeline. Given the population parameters inferred from LVK results and LISA's sensitivity limits at high frequencies, most stellar-mass binary black holes would likely have SNRs below 5 in LISA, but the most state-of-the-art multiband parameter estimation methods, such as those using ET and CE posteriors as priors for LISA, typically struggle to analyze sources with a LISA SNR less than 5. We present a novel coherent multiband parameter estimation method that directly calculates a joint likelihood, which is highly efficient; this efficiency is enabled by multiband marginalization of the extrinsic parameter space, implemented using importance sampling, which can work robustly even when the LISA SNR is as low as 3. Having an SNR of $\sim 3$ allows LISA to contribute nearly double the number of multiband sources. Even if LISA only observes for one year, most of the multiband detector-frame chirp mass's 90\% credible interval (less than $10^{-4} \mathrm{M}_\odot$) is still better than that of the most accurately measured events for ET+2CE network in 7.5 years of observation, by at least one order of magnitude. For the first time, we show efficient multiband Bayesian parameter estimation results on the population scale, which paves the way for large-scale astrophysical tests using multibanding.

gr-qc↗

arXiv2025

General relaxation model for a homogeneous plasma with spherically symmetric velocity space

A kinetic moment-closed model (KMCM), derived from the Vlasov-Fokker-Planck (VFP) equation with spherically symmetric velocity space, is introduced as a general relaxation model for homogeneous plasmas. The closed form of this model is presented by introducing a set new functions called $R$ function and $R$ integration. This nonlinear model, based on the finitely distinguishable independent features (FDIF) hypothesis, enables the capture of the nature of the equilibrium state. From this relaxation model, a general temperature relaxation model is derived when velocity space exhibits spherical symmetry, and the general characteristic frequency of temperature relaxation is presented.

physics.plasm-ph↗

arXiv2024

Efficient Stochastic Template Bank using Inner Product Inequalities

Gravitational wave searches are crucial for studying compact sources like neutron stars and black holes. Many sensitive modeled searches use matched filtering to compare gravitational strain data to a set of waveform models known as template banks. We introduce a new stochastic placement method for constructing template banks, offering efficiency and flexibility to handle arbitrary parameter spaces, including orbital eccentricity, tidal deformability, and other extrinsic parameters. This method can be computationally limited by the ability to compare proposal templates with the accepted templates in the bank. To alleviate this computational load, we introduce the use of inner product inequalities to reduce the number of required comparisons. We also introduce a novel application of Gaussian Kernel Density Estimation to enhance waveform coverage in sparser regions. Our approach has been employed to search for eccentric binary neutron stars, low-mass neutron stars, primordial black holes, supermassive black hole binaries. We demonstrate that our method produces self-consistent banks that recover the required minimum fraction of signals. For common parameter spaces, our method shows comparable computational performance and similar template bank sizes to geometric placement methods and stochastic methods, while easily extending to higher-dimensional problems. The time to run a search exceeds the time to generate the bank by a factor of $\mathcal{O}(10^5)$ for dedicated template banks, such as geometric, mass-only stochastic, and aligned spin cases, $\mathcal{O}(10^4)$ for eccentric and $\mathcal{O}(10^3)$ for the tidal deformable bank. With the advent of efficient template bank generation, the primary area for improvement is developing more efficient search methodologies.

astro-ph.HE↗

arXiv2024

The Heavier the Faster: A Sub-population of Heavy, Rapidly Spinning and Quickly Evolving Binary Black Holes

The spins of binary black holes (BBHs) measured from gravitational waves carry notable information of the formation pathways. Here we propose a quantity "dimensionless net spin" ($χ_{\rm N}$), which is related to the sum of angular momentum of component black holes in the system, to provide a novel perspective to study the origin(s) of BBHs. By performing hierarchical Bayesian inference on $χ_{\rm N}$, we find strong evidence that the marginal distribution of this quantity can be better fitted by two Gaussian components rather than one: there is a narrow peak at $χ_{\rm N} \sim 0.15$ and another extended peak at $χ_{\rm N} \sim 0.47$. We also find that the rapidly spinning systems likely dominate the high-mass end of the population and they evolve with redshift much quicker. These findings bring new challenges to the field binary scenario, and suggest that dynamical process should plays a key role in forming high total mass BBHs.

astro-ph.HE↗

arXiv2024

Formation of Lower Mass-gap Black Hole--Neutron Star Binary Mergers through Super-Eddington Stable Mass Transfer

Super-Eddington accretion of neutron stars (NSs) has been suggested both observationally and theoretically. In this paper, we propose that NSs in close-orbit binary systems with companions of helium (He) stars, most of which systems form after the common-envelope phase, could experience super-Eddington stable Case BB/BC mass transfer (MT), and can sometimes occur accretion-induced collapses (AICs) to form lower mass-gap black holes (mgBHs). Our detailed binary evolution simulations reveal that AIC events tend to happen if the primaries NS have an initial mass $\gtrsim1.7\,M_\odot$ with an accretion rate of $\gtrsim300$ times the Eddington limit. These mgBHs would have a mass nearly equal to or slightly higher than the NS maximum mass. The remnant mgBH--NS binaries after the core collapses of He stars are potential progenitors of gravitational-wave (GW) source. Multimessenger observation between GW and kilonova signals from a population of high-mass binary NS and mgBH--NS mergers formed through super-Eddington stable MT are helpful in constraining the maximum mass and equation of state of NSs. S230529ay, a mgBH--NS merger candidate recently detected in the fourth observing run of the LIGO-Virgo-KAGRA Collaboration, could possibly originate from this formation scenario.

astro-ph.HE↗

arXiv2023

Adapting the PyCBC pipeline to find and infer the properties of gravitational waves from massive black hole binaries in LISA

The Laser Interferometer Space Antenna (LISA), due for launch in the mid 2030s, is expected to observe gravitational waves (GW)s from merging massive black hole binaries (MBHB)s. These signals can last from days to months, depending on the masses of the black holes, and are expected to be observed with high signal to noise ratios (SNR)s out to high redshifts. We have adapted the PyCBC software package to enable a template bank search and inference of GWs from MBHBs. The pipeline is tested on the LISA data challenge (LDC)'s Challenge 2a (\enquote{Sangria}), which contains MBHBs and thousands of galactic binaries (GBs) in simulated instrumental LISA noise. Our search identifies all 6 MBHB signals with more than $92\%$ of the optimal SNR. The subsequent parameter inference step recovers the masses and spins within their $90\%$ confidence interval. Sky position parameters have 8 high likelihood modes which are recovered but often our posteriors favour the incorrect sky mode. We observe that the addition of GBs biases the parameter recovery of masses and spins away from the injected values, reinforcing the need for a global fit pipeline which will simultaneously fit the parameters of the GB signals before estimating the parameters of MBHBs.

astro-ph.IM↗

arXiv2023

Mock data study for next-generation ground-based detectors: The performance loss of matched filtering due to correlated confusion noise

The next-generation (3G/XG) ground-based gravitational-wave (GW) detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE) will begin observing in the next decade. Due to the extremely high sensitivity of these detectors, the majority of stellar-mass compact-binary mergers in the entire Universe will be observed. It is also expected that 3G detectors will have significant sensitivity down to 2-7 Hz; the observed duration of binary neutron star signals could increase to several hours or days. The abundance and duration of signals will cause them to overlap in time, which may form a confusion noise that could affect the detection of individual GW sources when using naive matched filtering; matched filtering is only optimal for stationary Gaussian noise. We create mock data for CE and ET using the latest population models informed by the GWTC-3 catalog and investigate the performance loss of matched filtering due to overlapping signals. We find the performance loss mainly comes from a deviation in the noise's measured amplitude spectral density. The redshift reach of CE (ET) can be reduced by 15%-38% (8%-21%) depending on the merger rate estimate. The direct contribution of confusion noise to the total signal-to-noise ratio (SNR) is generally negligible compared to the contribution from instrumental noise. We also find that correlated confusion noise has a negligible effect on the quadrature summation rule of network SNR for ET, but might reduce the network SNR of high detector-frame mass signals for detector networks including CE if no mitigation is applied. For ET, the null stream can mitigate the astrophysical foreground. For CE, we demonstrate that a computationally efficient, straightforward single-detector signal subtraction method suppresses the total noise to almost the instrument noise level; this will allow for near-optimal searches.

astro-ph.IM↗

arXiv2022

Searching for candidates of coalescing binary black holes formed through chemically homogeneous evolution in GWTC-3

The LIGO, Virgo, and KAGRA (LVK) collaboration has announced 90 coalescing binary black holes (BBHs) with $p_{\rm astro} > 50\%$ to date, however, the origin of their formation channels is still an open scientific question. Given various properties of BBHs (BH component masses and individual spins) inferred using the default priors by the LVK, independent groups have been trying to explain the formation of the BBHs with different formation channels. Of all formation scenarios, the chemically homogeneous evolution (CHE) channel has stood out with distinguishing features, namely, nearly-equal component masses and preferentially high individual spins aligned with the orbital angular momentum. We perform Bayesian inference on the BBH events officially reported in GWTC-3 with astrophysically-predicted priors representing different formation channels of the isolated binary evolution (CEE: common-envelope evolution channel; CHE; SMT: stable mass transfer). Given assumed models, we report strong evidence for GW190517\_055101 being most likely to have formed through the CHE channel. Assuming the BBH events in the subsample are all formed through one of the isolated binary evolution channels, we obtain the lower limits on the local merger rate density of these channels at $11.45 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CEE), $0.18 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CHE), and $0.63 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (SMT) at $90\%$ credible level.

astro-ph.HE↗

arXiv2022

Kilonova and Optical Afterglow from Binary Neutron Star Mergers. II. Optimal Search Strategy for Serendipitous Observations and Target-of-opportunity Observations of Gravitational-wave Triggers

In the second work of this series, we explore the optimal search strategy for serendipitous and gravitational-wave-triggered target-of-opportunity (ToO) observations of kilonovae and optical short-duration gamma-ray burst (sGRB) afterglows from binary neutron star (BNS) mergers, assuming that cosmological kilonovae are AT2017gfo-like (but with viewing-angle dependence) and that the properties of afterglows are consistent with those of cosmological sGRB afterglows. A one-day cadence serendipitous search strategy with an exposure time of $\sim30\,$s can always achieve an optimal search strategy of kilonovae and afterglows for various survey projects. We show that the optimal detection rates of the kilonovae (afterglows) are $\sim0.3/0.6/1/20\,$yr$^{-1}$ ($\sim50/60/100/800\,$yr$^{-1}$) for ZTF/Mephisto/WFST/LSST, respectively A better search strategy for SiTian than the current design is to increase the exposure time. In principle, a fully built SiTian can detect $\sim7({2000})\,$yr$^{-1}$ kilonovae (afterglows). Population properties of electromagnetic (EM) signals detected via the serendipitous observations are studied in detail. For ToO observations, we predict that one can detect $\sim11\,{\rm{yr}}^{-1}$ BNS gravitational wave (GW) events during the fourth observing run (O4) by considering an exact duty cycle of the third observing run. The median GW sky localization area is expected to be $\sim10\,{\rm{deg}}^2$ for detectable BNS GW events. In O4, we predict that ZTF/Mephisto/WFST/LSST can detect $\sim5/4/3/3$ kilonovae ($\sim1/1/1/1$ afterglows) per year, respectively. The GW detection rates, GW population properties, GW sky localizations, and optimistic ToO detection rates of detectable EM counterparts for BNS GW events at the Advanced Plus, LIGO Voyager and ET\&CE eras are detailedly simulated in this paper.

astro-ph.HE↗

arXiv2022

MLGWSC-1: The first Machine Learning Gravitational-Wave Search Mock Data Challenge

We present the results of the first Machine Learning Gravitational-Wave Search Mock Data Challenge (MLGWSC-1). For this challenge, participating groups had to identify gravitational-wave signals from binary black hole mergers of increasing complexity and duration embedded in progressively more realistic noise. The final of the 4 provided datasets contained real noise from the O3a observing run and signals up to a duration of 20 seconds with the inclusion of precession effects and higher order modes. We present the average sensitivity distance and runtime for the 6 entered algorithms derived from 1 month of test data unknown to the participants prior to submission. Of these, 4 are machine learning algorithms. We find that the best machine learning based algorithms are able to achieve up to 95% of the sensitive distance of matched-filtering based production analyses for simulated Gaussian noise at a false-alarm rate (FAR) of one per month. In contrast, for real noise, the leading machine learning search achieved 70%. For higher FARs the differences in sensitive distance shrink to the point where select machine learning submissions outperform traditional search algorithms at FARs $\geq 200$ per month on some datasets. Our results show that current machine learning search algorithms may already be sensitive enough in limited parameter regions to be useful for some production settings. To improve the state-of-the-art, machine learning algorithms need to reduce the false-alarm rates at which they are capable of detecting signals and extend their validity to regions of parameter space where modeled searches are computationally expensive to run. Based on our findings we compile a list of research areas that we believe are the most important to elevate machine learning searches to an invaluable tool in gravitational-wave signal detection.

astro-ph.IM↗

arXiv2022

4-OGC: Catalog of gravitational waves from compact-binary mergers

We present the fourth Open Gravitational-wave Catalog (4-OGC) of binary neutron star (BNS), binary black hole (BBH) and neutron star-black hole (NSBH) mergers. The catalog includes observations from 2015-2020 covering the first through third observing runs (O1, O2, O3a, O3b) of Advanced LIGO and Advanced Virgo. The updated catalog includes 7 BBH mergers which were not previously reported with high significance during O3b for a total of 94 observations: 90 BBHs, 2 NSBHs, and 2 BNSs. The most confident new detection, GW200318_191337, has component masses $49.1^{+16.4}_{-12.0}\textrm{M}_\odot$ and $31.6^{+12.0}_{-11.6}\textrm{M}_\odot$; its redshift of $0.84^{+0.4}_{-0.35}$ ($90\%$ credible interval) may make it the most distant merger so far. We estimate the merger rate of BBH sources, assuming a powerlaw mass distribution containing an additive Gaussian peak, to be $16.5_{-6.2}^{+10.4} (25.0_{-8.0}^{+12.6})$ Gpc$^{-3}$ yr$^{-1}$ at a redshift of $z=0$ ($0.2$). For BNS and NSBH sources, we estimate a merger rate of $200^{+309}_{-148}$ Gpc$^{-3}$ yr$^{-1}$ and $19^{+30}_{-14}$ Gpc$^{-3}$ yr$^{-1}$, respectively, assuming the known sources are representative of the total population. We provide reference parameter estimates for each of these sources using an up-to-date model accounting for instrumental calibration uncertainty. The corresponding data release also includes our full set of sub-threshold candidates.

astro-ph.HE↗

arXiv2022

Long-duration Gamma-ray Burst and Associated Kilonova Emission from Fast-spinning Black Hole--Neutron Star Mergers

Here we collect three unique bursts, GRBs\,060614, 211211A and 211227A, all characterized by a long-duration main emission (ME) phase and a rebrightening extended emission (EE) phase, to study their observed properties and the potential origin as neutron star-black hole (NSBH) mergers. NS-first-born (BH-first-born) NSBH mergers tend to contain fast-spinning (non-spinning) BHs that more easily (hardly) allow tidal disruption to happen with (without) forming electromagnetic signals. We find that NS-first-born NSBH mergers can well interpret the origins of these three GRBs, supported by that: (1) Their X-ray MEs and EEs show unambiguous fall-back accretion signatures, decreasing as $\propto{t}^{-5/3}$, which might account for their long duration. The EEs can result from the fall-back accretion of $r$-process heating materials, predicted to occur after NSBH mergers. (2) The beaming-corrected local event rate density for this type of merger-origin long-duration GRBs is $\mathcal{R}_0\sim2.4^{+2.3}_{-1.3}\,{\rm{Gpc}}^{-3}\,{\rm{yr}}^{-1}$, consistent with that of NS-first-born NSBH mergers. (3) Our detailed analysis on the EE, afterglow and kilonova of the recently high-impact event GRB\,211211A reveals it could be a merger between a $\sim1.23^{+0.06}_{-0.07}\,M_\odot$ NS and a $\sim8.21^{+0.77}_{-0.75}\,M_\odot$ BH with an aligned-spin of $χ_{\rm{BH}}\sim0.62^{+0.06}_{-0.07}$, supporting an NS-first-born NSBH formation channel. Long-duration burst with rebrightening fall-back accretion signature after ME, and bright kilonova might be commonly observed features for on-axis NSBHs. We estimate the multimessenger detection rate between gravitational waves, GRBs and kilonovae from NSBH mergers in O4 (O5) is $\sim0.1\,{\rm{yr}}^{-1}$ ($\sim1\,{\rm{yr}}^{-1}$).

astro-ph.HE↗

arXiv2022

Population Properties of Gravitational-Wave Neutron Star--Black Hole Mergers

Over the course of the third observing run of LIGO-Virgo-KAGRA Collaboration, several gravitational-wave (GW) neutron star--black hole (NSBH) candidates have been announced. By assuming these candidates are real signals and of astrophysical origins, we analyze the population properties of the mass and spin distributions for GW NSBH mergers. We find that the primary BH mass distribution of NSBH systems, whose shape is consistent with that inferred from the GW binary BH (BBH) primaries, can be well described as a power-law with an index of $α= 4.8^{+4.5}_{-2.8}$ plus a high-mass Gaussian component peaking at $\sim33^{+14}_{-9}\,M_\odot$. The NS mass spectrum could be shaped as a near flat distribution between $\sim1.0-2.1\,M_\odot$. The constrained NS maximum mass agrees with that inferred from NSs in our Galaxy. If GW190814 and GW200210 are NSBH mergers, the posterior results of the NS maximum mass would be always larger than $\sim2.5\,M_\odot$ and significantly deviate from that inferred in the Galactic NSs. The effective inspiral spin and effective precession spin of GW NSBH mergers are measured to potentially have near-zero distributions. The negligible spins for GW NSBH mergers imply that most events in the universe should be plunging events, which supports the standard isolated formation channel of NSBH binaries. More NSBH mergers to be discovered in the fourth observing run would help to more precisely model the population properties of cosmological NSBH mergers.

astro-ph.HE↗

arXiv2021

Event rate predictions of strongly lensed gravitational waves with detector networks and more realistic templates

Strong lensing of gravitational waves (GWs) is attracting growing attention of the community. The event rates of lensed GWs by galaxies were predicted in numerous papers, which used some approximations to evaluate the GW strains detectable by a single detector. The joint-detection of GW signals by a network of instruments will increase the detecting ability of fainter and farther GW signals, which could increase the detection rate of the lensed GWs, especially for the 3rd generation detectors, e.g., Einstein Telescope (ET) and Cosmic Explorer (CE). Moreover, realistic GW templates will improve the accuracy of the prediction. In this work, we consider the detection of galaxy-scale lensed GW events under the 2nd, 2.5th, and 3rd generation detectors with the network scenarios and adopt the realistic templates to simulate GW signals. Our forecast is based on the Monte Carlo technique which enables us to take Earth's rotation into consideration. We find that the overall detection rate is improved, especially for the 3rd generation detector scenarios. More precisely, it increases by ~37% adopting realistic templates, and under network detection strategy, further increases by ~58% comparing with adoption of the realistic templates, and we estimate that the 3rd generation GW detectors will detect hundreds lensed events per year. The effect from the Earth's rotation is weakened in the detector network strategy.

astro-ph.GA↗

arXiv2021

Probing the large-scale structure of the universe through gravitational-wave observations

The improvements in the sensitivity of the gravitational wave (GW) network enable the detection of several large redshift GW sources by third-generation GW detectors. These advancements provide an independent method to probe the large-scale structure of the universe by using the clustering of the binary black holes. The black hole catalogs are complementary to the galaxy catalogs because of large redshifts of GW events, which may imply that binary black holes (BBHs) are a better choice than galaxies to probe the large-scale structure of the universe and cosmic evolution over a large redshift range. To probe the large-scale structure, we used the sky position of the binary black holes observed by third-generation GW detectors to calculate the angular correlation function (ACF) and the bias factor of the population of binary black holes. This method is also statistically significant as 5000 BBHs are simulated. Moreover, for the third-generation GW detectors, we found that the bias factor can be recovered to within 33$\%$ with an observational time of ten years. This method only depends on the GW source-location posteriors; hence, it can be an independent method to reveal the formation mechanisms and origin of the BBH mergers compared to the electromagnetic method.

astro-ph.CO↗

arXiv2021

No Detectable Kilonova Counterpart is Expected for O3 Neutron Star-Black Hole Candidates

We analyse the tidal disruption probability of potential neutron star--black hole (NSBH) merger gravitational wave (GW) events, including GW190426_152155, GW190814, GW200105_162426 and GW200115_042309, detected during the third observing run of the LIGO/Virgo Collaboration, and the detectability of kilonova emission in connection with these events. The posterior distributions of GW190814 and GW200105_162426 show that they must be plunging events and hence no kilonova signal is expected from these events. With the stiffest NS equation of state allowed by the constraint of GW170817 taken into account, the probability that GW190426_152155 and GW200115_042309 can make tidal disruption is $\sim24\%$ and $\sim3\%$, respectively. However, the predicted kilonova brightness is too faint to be detected for present follow-up search campaigns, which explains the lack of electromagnetic (EM) counterpart detection after triggers of these GW events. Based on the best constrained population synthesis simulation results, we find that disrupted events account for only $\lesssim20\%$ of cosmological NSBH mergers since most of the primary BHs could have low spins. The associated kilonovae for those disrupted events are still difficult to be discovered by LSST after GW triggers in the future, because of their low brightness and larger distances. For future GW-triggered multi-messenger observations, potential short-duration gamma-ray bursts and afterglows are more probable EM counterparts of NSBH GW events.

astro-ph.HE↗

arXiv2021

Kilonova Emission From Black Hole-Neutron Star Mergers. II. Luminosity Function and Implications for Target-of-opportunity Observations of Gravitational-wave Triggers and Blind Searches

We present detailed simulations of black hole-neutron star (BH-NS) mergers kilonova and gamma-ray burst (GRB) afterglow and kilonova luminosity function, and discuss the detectability of electromagnetic (EM) counterpart in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity observations, and time-domain blind searches. The predicted absolute magnitude of the BH-NS kilonovae at $0.5\,{\rm days}$ after the merger falls in $[-10,-15.5]$. The simulated luminosity function contains the potential viewing-angle distribution information of the anisotropic kilonova emission. We simulate the GW detection rates, detectable distances and signal duration, for the future networks of 2nd/2.5th/3rd-generation GW detectors. BH-NSs tend to produce brighter kilonovae and afterglows if the BH has a higher aligned-spin, and a less massive NS with a stiffer EoS. The detectability of kilonova is especially sensitive to the BH spin. If BHs typically have low spins, the BH-NS EM counterparts are hard to discover. For the 2nd generation GW detector networks, a limiting magnitude of $m_{\rm limit}\sim23-24\,{\rm mag}$ is required to detect the kilonovae even if BH high spin is assumed. Thus, a plausible explanation for the lack of BH-NS associated kilonova detection during LIGO/Virgo O3 is that either there is no EM counterpart (plunging events), or the current follow-ups are too shallow. These observations still have the chance to detect the on-axis jet afterglow associated with an sGRB or an orphan afterglow. Follow-up observations can detect possible associated sGRB afterglows, from which kilonova signatures may be studied. For time-domain observations, a high-cadence search in redder filters is recommended to detect more BH-NS associated kilonovae and afterglows.

astro-ph.HE↗

arXiv2020

Measuring eccentricity of binary black holes in GWTC-1 by using inspiral-only waveform

In this paper, we estimate the eccentricity of the 10 BBHs in GWTC-1 by using the inspiral-only BBH waveform template EccentricFD. Firstly, we test our method with simulated eccentric BBHs. Afterwards we apply the method to the real BBH gravitational wave data. We find that the BBHs in GWTC-1 except GW151226, GW170608 and GW170729 admit very small eccentricity. Their upper limits on eccentricity range from 0.033 to 0.084 with 90% credible interval at the reference frequency 10 Hz. For GW151226, GW170608 and GW170729, the upper limits are higher than 0.1. The relatively large eccentricity of GW151226 and GW170729 is probably due to ignoring the effective spin and low signal-to-noise ratio, and GW170608 is worthy of follow-up research. We also point out the limitations of the inspiral-only non-spinning waveform template in eccentricity measurement. The measurement of BBH eccentricity helps to understand its formation mechanism. With the increase in the number of BBH gravitational wave events and the more complete eccentric BBH waveform template, this will become a viable method in the near future.

astro-ph.IM↗