arXiv subjects

Xin-yi Lin

Publications and source records attributed to Xin-yi Lin.

6 recordsLinked to original sources

arXiv2026

Effects of formation channels and gravitational lensing on stochastic gravitational wave background

Two primary formation channels for black holes have been proposed: the astrophysical channel, driven by the collapse of massive stars, and the primordial channel, involving their direct formation from density fluctuations in the early Universe. The key distinction between astrophysical black holes (ABHs) and primordial black holes (PBHs) is that PBHs can form at very high redshifts, before any stars have formed, leading to different stochastic gravitational-wave backgrounds (SGWBs). These SGWBs arise from the superposition of unresolved gravitational-wave signals accumulated over all redshifts. In this work, we employ the Hierarchical Bayesian Inference (HBI) framework and the publicly available GWTC-4 data to infer the population hyperparameters of PBHs. We then compute the SGWBs from ABHs and PBHs separately, accounting for the lensing effect, which can modify the strain amplitude of the SGWBs. By comparing the resulting SGWBs with the power-law integrated (PI) sensitivity curves of ground-based gravitational-wave detectors -- LIGO and the Einstein Telescope (ET) -- we find that both detectors can distinguish between these two black hole formation models within specific frequency ranges. However, LIGO is limited to a single method for distinguishing these models, and the lensing effect alters the frequency range over which discrimination is possible. In contrast, ET is capable of distinguishing ABHs from PBHs across a broader parameter space.

gr-qc↗

arXiv2026

An Opacity-Free Test of the Cosmic Distance Duality Relation Using Strongly Lensed Gravitational Wave Signals with Space-Based Detector Networks

The cosmic distance duality relation (CDDR), expressed as $d_L(z) = (1+z)^2 D_A(z)$, is a fundamental relation in modern cosmology. In this work, we apply a method to test the CDDR using simulated strongly lensed gravitational-wave (SLGW) signals from massive binary black holes (MBBH) as observed by proposed space-based detector networks. Our analysis is conducted under the point-mass lens model, considering the strong lensing scenario that produces two images. We generate 90 days of simulated SLGW data for 10 events based on the Population III stellar formation model, with source redshifts in the range $z_s \in [2,6]$ and lens redshifts in $z_L \in [0.2,1]$. The deviation of CDDR is parameterized by $\eta_1(z) = 1 + \eta_0 z$ and $\eta_2(z) = 1 + \eta_0 z/(1+z)$, and we incorporate the deviation parameter $\eta_0$ directly into the waveform model. Parameter estimation is performed within a Bayesian statistical framework, combining simulated data from both Taiji and LISA. For a single lensed event, the joint Taiji+LISA analysis improves the measurement precision of $\eta_0$ by roughly a factor of two compared with Taiji-only observations. By combining 10 simulated events, the population-level constraints on $\eta_0$, quantified by the half width of the $95\%$ credible interval, reach approximately $2.61\times10^{-4}$ ($1.72\times10^{-4}$) for the $\eta_1(z)$ parameterization and $1.22\times10^{-3}$ ($6.86\times10^{-4}$) for $\eta_2(z)$ in the Taiji-only (Taiji+LISA) scenario, respectively. The inferred values of $\eta_0$ remain consistent with $\eta_0 = 0$ within the estimated uncertainties, with no statistically significant evidence for deviations from the CDDR at the achieved precision. These results demonstrate the significant advantage of joint space-based observations for high-precision tests of the CDDR.

astro-ph.CO↗

arXiv2025

Bayesian Analysis of Wave-Optics Gravitationally Lensed Massive Black Hole Binaries with Space-Based Gravitational Wave Detector

Within a Bayesian statistical framework, we jointly estimate the source and lens parameters and evaluate the relative evidence between the lensed and unlensed models. This work focuses on the wave optics effects induced by a point mass (PM) lens on gravitational waves (GW) from equal-mass massive binary black holes (MBHB), and assesses the capability of the space-based GW detector Taiji to detect such effects. Specifically, we investigate the impact of the redshifted lens mass MLz in the range [3e5, 3e7] solar masses, impact parameter y in [10, 50], source redshift zs in [4, 6], and total source mass Ms in [1e5, 1e7] solar masses on parameter estimation and model selection. Our results show that, for the cases we studied, larger MLz increases the waveform mismatch MM, which directly enhances the waveform difference and the corresponding signal-to-noise ratio (SNR), thereby improving the ability to discriminate between the lensed and unlensed models. In contrast, for y > 50, both MM and SNR are too small to allow effective model discrimination in these cases. Parameter estimation further indicates that for y < 50, the degeneracy between the luminosity distance and MLz can be effectively broken. Although the Bayes factor decreases as zs increases, lensing signatures remain identifiable up to zs = 6. The role of Ms depends on the overlap of the GW signal with the detector sensitive band. Overall, effective model discrimination requires MM greater than or equal to 1e-7 (corresponding to SNR greater than 5).

astro-ph.HE↗

arXiv2025

Bayesian model selection of Primordial Black Holes and Dressed Primordial Black Holes with lensed Gravitational Waves

If particle dark matter (DM) and primordial black holes (PBHs) coexist, PBHs will be surrounded by particle DM, forming celestial objects known as dressed PBHs (dPBHs). These structures suggest a scenario in which PBHs and DM can exist simultaneously. However, in the high-frequency regime, the gravitational lensing effect of bare PBHs is similar to that of dPBHs. Ground-based gravitational wave (GW) detectors are particularly sensitive to high-frequency GW signals. In this regime, the lensing effect of a point-mass lens with a mass in the range of $10^{-1} \sim 10^2 M_{\odot}$ becomes significant. In this work, we incorporate dPBH models with GW observations and employ Bayesian inference techniques to distinguish PBHs from dPBHs. Using the third-generation ground-based GW detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), as examples, we demonstrate that these detectors can effectively differentiate the lensing effects of dPBHs from those of PBHs across a broad frequency range. Furthermore, we find that with a larger black hole (BH) mass inside the surrounding particle DM, ET and CE can distinguish these two lensed models with even greater precision.

gr-qc↗

arXiv2024

An Opacity-Free Method of Testing the Cosmic Distance Duality Relation Using Strongly Lensed Gravitational Wave Signals

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.

astro-ph.CO↗

arXiv2023

Detecting Strong Gravitational Lensing of Gravitational Waves with TianQin

When gravitational waves (GWs) pass by a massive object on its way to Earth, a strong gravitational lensing effect will happen. Thus, the GW signal will be amplified, deflected, and delayed in time. Through analyzing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of mergers of massive black hole binaries (MBHBs) as far as z=15 and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHB signals.Three lens models are considered in this work: the point mass model, the singular isothermal sphere (SIS) model, and the Navarro-Frenk-White (NFW) model. The sensitive frequency band for space-borne GW detectors is around millihertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluating the diffraction integral at low frequencies. Through a Fisher analysis, we analyze the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10^-3 for the mass of point mass and SIS lens and to the level of 10^-5 for the density of the NFW lens. We also assess the impact on the accuracy of estimating the source parameters and find that the improvement of the accuracy is dominated by the increasing of signal-to-noise ratio.

gr-qc↗