arXiv subjects

Kai Liao

Publications and source records attributed to Kai Liao.

At least 19 recordsLinked to original sources

arXiv2026

Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves

Strong lensing changes the phase of a gravitational-wave signal as well as its amplitude and arrival time. We study whether this phase information can distinguish between three dark-matter structures in the lens: a Navarro--Frenk--White halo (NFW), a self-interacting dark matter (SIDM) halo, and a fuzzy-dark-matter field (FDM). We generate waveforms for the detectable lensed massive-black-hole-binary population of a four-year LISA mission and fit every signal with the same smooth singular-isothermal-ellipsoid lens with external shear. In 132 lens systems, 311 images are resolved as separate signals in time. NFW and SIDM produce real waveform changes, but their slowly varying part is largely degenerate with the constant, gradient, and Hessian of the smooth Fermat potential at the image. The coherent density fluctuations of FDM leave a larger frequency-dependent residual after this fit. The NFW--FDM and SIDM--FDM populations become distinguishable with about 60 and 110 resolved image waveforms, respectively. These results show that repeated lensed LISA signals can probe the spatial form of dark matter in lens galaxies, rather than only the total lensing mass.

astro-ph.CO↗

arXiv2026

Finite-Core Signatures in LISA-Band Wave-Optics Lensing by Low-Mass Dark Matter Halos

LISA-band gravitational waves from massive binary black holes can be diffractively lensed by low-mass dark matter halos and subhalos, so their frequency-dependent amplification can probe the inner density profile. We isolate the generic finite-core part of this signal by comparing fixed-mass Navarro-Frenk-White (NFW) and cored-NFW lenses and propagating both profiles to the complex wave-optics amplification factor. A finite core smooths the time-delay response and reshapes the diffraction peak; an NFW template with a lower concentration can mimic part of the effect, but structured complex residuals remain after time and phase alignment. The residual peaks for intermediate cores, $r_c/r_s\simeq0.25$--$0.3$. An SIDM-inspired isothermal-core profile gives the same qualitative response, showing that the signal is not an artifact of one cored parameterization. For a fiducial LISA source, an appreciable mismatch requires favorable near alignment and $M_{\rm vir}\gtrsim 10^7M_\odot$. The result is a finite-core baseline for isolated line-of-sight halos and for subhalos perturbing strongly lensed macro-images.

astro-ph.CO↗

arXiv2026

Identification of Lensed Gravitational-Wave Beat Patterns by LISA

Strong lensing of massive black hole binaries can produce multiple gravitational-wave images with different magnifications and arrival times. LISA signals remain in band for months to years, allowing multiple lensed images to overlap during the inspiral stage and generate beat patterns. A singular isothermal sphere lens model is adopted to describe the lensing configuration, and two-image beat waveforms are constructed from massive black hole binary signals. To isolate the beat pattern itself, waveform mismatch is evaluated only during the overlapping inspiral stage before the coalescence of the first image, excluding contributions from the delayed merger peak of the second image. Using the HS-nod-SN (B+20) strong-lensing population, the occurrence rate of identifiable beat events is estimated, and Bayesian parameter estimation is performed with a beat template. Beat patterns are most readily identified when the lensing time delay is short and the delayed image has a relatively large magnification. Among 196 detectable two-image lensed events, 92 satisfy the temporal-overlap condition and 14 satisfy the beat-identification criterion, corresponding to an identifiable beat fraction of about 7\%. Posterior inference shows that the beat template can recover the lensing time delay and magnification parameters for a representative beat event. These results indicate that lensed beat patterns constitute a distinguishable subset of strongly lensed LISA events and provide a unique observational signature of strong lensing in the LISA band.

astro-ph.CO↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Space-borne Detectors

Future space-borne gravitational-wave (GW) detectors, such as LISA and DECIGO, are expected to detect a large number of GW events, a fraction of which may be strongly lensed by intervening galaxies or galaxy clusters. In this work, we develop a comprehensive framework to simulate strongly lensed GWs in the context of space-borne detectors. Based on realistic astrophysical models for both the source population and the lens distribution, we construct mock catalogs of lensed GW events, referred to as \textbf{GW-LMC-Space}. Our results show that, for a four-year LISA observation, the expected number of lensed events ranges from $0$ to $131$, depending on the adopted formation model of massive black hole binaries (MBHBs). The corresponding lensing probability for MBHBs can reach up to $\sim 0.3\%$. For DECIGO, we find that the number of lensed events in a one-year observation is expected to lie in the range of $0$--$44$, with a lensing probability of $\sim 0.15\%$ for stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star--black hole binaries (NSBHs). We further show that the overlap of lensed signals is a common feature in space-borne detectors, which can significantly affect both the signal-to-noise ratio (SNR) estimation and event identification. These results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations.

astro-ph.CO↗

arXiv2026

QPEs from Warped Disk Collisions with EMRIs: Brightness-Recurrence Diagram and Gravitational-Wave Follow-up

Quasi-Periodic Eruptions (QPEs) display correlated long/short and strong/weak patterns that remain unexplained by existing flat-disk collision models. We propose that these features arise from an extreme-mass-ratio inspiral (EMRI) colliding with a warped accretion disk, likely formed after a tidal disruption event. The warp modulates both recurrence time and burst energy, encoding the disk geometry -- and thus the spin of the central supermassive black hole (SMBH) -- into the X-ray light curve. We introduce the Brightness-Recurrence Diagram (BRD) to visualize this correlation, where QPE bursts trace an elliptical trajectory driven by the EMRI's apsidal precession; the tilt of this ellipse encodes whether the EMRI is prograde or retrograde relative to the SMBH spin. Applying this model to the prototypical QPE source GSN 069 successfully reproduces the observed patterns. The data are consistent with either a prograde stellar secondary or a retrograde stellar-mass black hole. In the stellar-mass black hole scenario, ongoing orbital decay could render the EMRI detectable by LISA within a few decades, facilitating gravitational-wave follow-up and independent multimessenger constraints on the system.

astro-ph.HE↗

arXiv2026

Evidence for Intermediate-Mass Black Holes From Microlensing Signatures in CHIME/FRB catalog 2

Intermediate-mass black holes (IMBHs) are the missing link in the cosmic hierarchy of black holes, bridging the gap between stellar-mass black holes and supermassive ones. They also serve as unique laboratories for testing strong-field gravity and are prime targets for future multi-messenger observations. However, IMBHs are a population that has remained notoriously difficult to detect. The microlensing effect of fast radio bursts (FRBs) can serve as a clean and powerful method to probe IMBHs. In this work, we develop a pipeline to search for microlensed FRBs based on their dynamic spectra and apply it to the CHIME/FRB Catalog 2. Two microlensing signatures have been identified in two separate sources, i.e. FRB~20190131D and FRB~20211115A. The inferred lens masses for these two signatures are $\sim[280-467]~M_{\odot}$ and $\sim[539-609]~M_{\odot}$, respectively. Here we interpret them as evidence for IMBHs. If there are no intervening structures-such as galaxies or clusters-along the line of sights for these two sources, the two identified IMBHs might be isolated and of primordial origins. In that case, we obtain primordial black holes (PBHs) within these two mass ranges would constitute $\sim4\%$ of dark matter. Moreover, if these two candidates are not genuine lensing signatures, the abundance of intermediate-mass PBHs with masses $>300,M_{\odot}$ is constrained to be $\sim13\%$ at $95\%$ confidence level. Therefore, more comprehensive observational information for FRBs, together with a deeper understanding of whether the intrinsic emission mechanisms of FRBs can produce lensing-like signals, will be crucial for establishing this effect as a powerful tool for probing (primordial) IMBHs.

astro-ph.HE↗

arXiv2026

Polarization Birefringence and Waveform Systematics in GW231123

GW231123 is a short, massive binary-black-hole event whose source properties show strong waveform dependence. We use this event to test gravitational-wave polarization birefringence, modeled as a frequency-dependent rotation of the tensor-polarization basis. Instead of sampling a distance-normalized coefficient directly, we sample the band-differential rotation $\delta_{\rm br}=\Delta(448\,\mathrm{Hz})-\Delta(20\,\mathrm{Hz})$ with prior $[-\pi,\pi]$, and report the derived coefficient $\beta_{\rm br}^{\rm derived}$ for comparison with standard propagation parametrizations. We analyze three waveform families: IMRPhenomXPHM (XPHM), IMRPhenomXO4a (XO4a), and NRSur7dq4. The derived posteriors are consistent with the general relativity value, giving $90\%$ upper limits $|\beta_{\rm br}^{\rm derived}|_{90}=0.378,\,0.097,\,0.273$ for XPHM, XO4a, and NRSur7dq4, respectively. The directly sampled $\delta_{\rm br}$ posterior remains broad, with $|\delta_{\rm br}|_{90}\simeq2.8\,\mathrm{rad}$, so the accumulated rotation across the analysis band is weakly constrained. The Bayes factors are waveform dependent: $\ln\mathcal{B}_{\rm br/GR}=-1.26\pm0.30$, $+3.64\pm0.28$, and $-0.86\pm0.29$, respectively. We therefore find no waveform-robust evidence for parity-violating propagation. The positive XO4a result is better interpreted as a waveform-dependent birefringence-like response associated with the mass-ratio--distance--spin degeneracy of this short high-mass event.

astro-ph.HE↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors

As plans for the construction of third-generation gravitational wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalog derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering the earth rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three or five image systems with a detectable central image, a feature distinct from optical lensing. For the joint ET+CE network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ($\mu > 3$), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

astro-ph.CO↗

arXiv2026

Parameter estimation of eccentric massive black hole binaries with LISA and its cosmological implications

Future space-based gravitational wave (GW) observatories such as LISA will detect massive black hole binaries (MBHBs), which are expected to be accompanied by electromagnetic counterparts, thereby providing bright standard sirens for cosmology. The orbital eccentricity of MBHBs can significantly improve the parameter estimation of GWs because the multiple harmonics induced by eccentricity provide additional information and help break down the degeneracies among waveform parameters. In this paper, we use the EccentricFD waveform and construct 5-year GW event catalogs for LISA under three population models (popIII, Q3d and Q3nod). For the three models, we find that an initial eccentricity of $e_0=0.4$ at $10^{-4}$ Hz yields improvements in sky localization and distance inference by a factor of $\mathcal{O}(10)$ in the best cases. As a consequence, the average number of bright sirens increases substantially: from 8 to 11 (PopIII), 6 to 12 (Q3d) and 13 to 24 (Q3nod). This increase in event number, together with enhanced localization and distance inference, leads to tighter cosmological constraints. In the $\Lambda$CDM model, for instance, the relative uncertainty on $H_0$ is reduced from $8.17\%$ to $4.35\%$ for the Q3d model, corresponding to an improvement of approximately $47\%$. We also investigate the improvement in constraints on the dark energy equation of state and modified GW propagation when combining bright sirens with the latest cosmic microwave background data. These results demonstrate that eccentricity is a remarkably significant feature in GW detection and parameter estimation, enabling more accurate measurements of the Universe with future space-based observatories.

astro-ph.IM↗

arXiv2026

Testing supermassive primordial black holes with lensing signals of binary black hole merges

Next-generation ground-based gravitational wave (GW) detectors are expected to observe millions of binary black hole mergers, a fraction of which will be strongly lensed by intervening galaxies or clusters, producing multiple images with characteristic distribution of time delay. Importantly, the predicted rate and properties of such events are sensitive to the abundance and distribution of strong lensing objects which directly depends on cosmological models. One such scenario posits the existence of supermassive primordial black holes (SMPBHs) in the early universe, which would enhance the formation of dark matter halos. This mechanism has been proposed to explain the abundance of high-redshift galaxies observed by James Webb Space Telescope. Crucially, the same cosmological model with SMPBHs would also leave a distinct imprint on the population of strongly lensed GWs. It predicts both an increased event rate and a modified distribution of time delays between the multiple images. Therefore, we propose statistical measurements of the rate and time delay distribution of strong lensing GW events as a powerful probe to directly constrain the abundance of SMPBHs. Considering $\Lambda$CDM cosmology with (non-)clustered SMPBHs, we find that the abundance of SMPBHs $f_{\rm PBH}$ with masses above $10^8~M_{\odot}$ is constrained to be $\sim10^{-4}$ at $95\%$ confidence level. It will be comparable and complementary to the currently available constraint from large scale structure observations.

astro-ph.CO↗

arXiv2025

Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations

We present a Bayesian framework that enhances the identification of strongly lensed gravitational waves (GWs) by incorporating informative positional priors from the Euclid galaxy lens catalog. The core of our method introduces a two-step reweighting scheme: first, gravitational wave parameter estimation is performed under a uniform sky prior; the resulting posterior is then used to reweight galaxy positions within the Euclid catalog, constructing an astrophysically informed positional prior. Comparing this Euclid-informed prior against a uniform prior within our framework reveals distinct behaviors. While the posterior estimates of the intrinsic waveform parameters show little sensitivity to the prior change, the Bayes factor for lensing identification exhibits significant prior dependence. Crucially, for truly lensed event pairs, the Bayes factor systematically increases, whereas for unlensed pairs it decreases. This dual effect is vital for robust discrimination. Our analysis demonstrates that this multi-messenger approach significantly improves the confidence of lensing searches. For lensed pairs, the method boosts the Bayes factor by an average factor of $\sim 10$, while effectively suppressing false positives for unlensed coincidences. This underscores the critical importance of prior specification and showcases the substantial gains achievable by synergizing gravitational-wave data with electromagnetic survey information.

astro-ph.CO↗

arXiv2025

Joint Constraints on Fuzzy and Warm Dark Matter from Satellite Populations of the Milky Way and Andromeda

We perform a joint analysis of the Milky Way (MW) and Andromeda (M31) satellite populations to constrain the properties of fuzzy dark matter (FDM) and thermal-relic warm dark matter (WDM). We combine MW satellite observations from the Dark Energy Survey (DES) and Pan-STARRS1 (PS1) with M31 satellite data from the Pan-Andromeda Archaeological Survey (PAndAS), and model the corresponding observable satellite populations using the empirical galaxy--halo connection model described in Nadler et al. (2020) together with the appropriate selection functions. Uncertainties in the virial masses of the MW and M31 are incorporated through host-mass priors that linearly scale the relevant model parameters, allowing us to infer the full posterior distributions of all parameters. For the FDM case, we obtain $m_{\mathrm{FDM}} > 1.74 \times 10^{-20}~\mathrm{eV}$ (95\% CL) and $m_{\mathrm{FDM}} > 1.42 \times 10^{-20}~\mathrm{eV}$ (20:1 posterior ratio). For thermal-relic WDM, we find $m_{\mathrm{WDM}} > 6.20~\mathrm{keV}$ (95\% CL) and $m_{\mathrm{WDM}} > 5.75~\mathrm{keV}$ (20:1 posterior ratio). These results represent a moderate improvement over MW-only constraints, and provide the strongest constraints to date on the FDM and WDM derived from satellite galaxy populations in the Local Group.

astro-ph.CO↗

arXiv2025

Probing Dark Matter Substructure with Image Number Anomaly in Strong Lensing Systems

Gravitational lensing observables, including anomalies in image positions, flux ratios, and time delays, serve as usual probes of dark matter (DM) substructure. When dark matter substructure possesses sufficient perturbations, it may lead to the formation of extra images in otherwise canonical doubly or quadruply imaged systems. With the advent of increasingly precise observational instruments, previously undetectable images may become measurable and image number anomalies therefore could be an increasingly viable method. In this paper, we utilize the gravitational lensing phenomenon of image number anomaly to derive constraints on dark matter substructure. We present the extra images induced by distinct forms of DM substructure, specifically primordial black holes (PBHs) and fuzzy dark matter (FDM) and show that higher angular resolution observations increase the probability of detecting additional lensed images. Based on a null detection of image number anomalies in a sample of 3500 lens systems generated from the \textit{Strong Lensing Halo model-based mock catalogs} (SL-Hammocks), we derive upper limits on the abundance of PBHs. At the 95\% confidence level, the PBH abundance is constrained to $\lesssim 0.125\%$, $0.08\%$, and $0.04\%$ for PBH masses in the range $\sim 10^{7}$--$10^{9}~M_{\odot}$, corresponding to angular resolutions of $0.1''$, $0.05''$, and $0.01''$, respectively. Similarly, we exclude particle masses below $0.4$, $0.6$, and $3.5 \times 10^{-22} \ \mathrm{eV}$ for FDM at the same confidence level for the respective resolutions. Furthermore, the abundance of PBHs $\lesssim 0.9\%$ could be constrained at an angular resolution of $0.5''$ for the Legacy Survey of Space and Time (LSST) Observations. Finally, we discuss methodologies for identifying image number anomalies in special cases and demonstrate feasibility using a fitting procedure.

astro-ph.CO↗

arXiv2025

Extended Components of Little Red Dots in the Rest-Frame Optical

Recent JWST observations have revealed a population of red, compact, high-redshift objects called Little Red Dots (LRDs), whose host components have remained largely unconstrained, possibly due to their extreme compactness. Current morphological studies suggest the presence of extended emission in LRDs at rest-frame ultraviolet wavelengths. However, in the rest-frame optical regime, investigations have been limited by small sample sizes and insufficient imaging depth, hindering reliable separation between point-like and potential extended components. Here we perform the image stacking analysis of 217 LRDs in four NIRCam bands, a large and homogeneous sample observed with the COSMOS-Web survey. Our results reveal the detection of faint extended emission in the F444W band, with a typical size of ~200 parsecs and magnitude of ~27.7 AB at z~6.5. We perform four-band photometric spectral energy distribution fitting based on galaxy templates and derive an average stellar mass of log(M*/M_sun) = 9.02 +0.20/-0.18. Given this stellar mass, the host galaxy is compact, that is, ~2.5 times smaller than star-forming galaxies of similar mass at comparable redshifts. This work provides direct observational evidence for the existence of LRD host galaxies at rest-frame optical wavelengths and offers new insights into the stellar buildup of these systems within the first billion years after the Big Bang.

astro-ph.GA↗

arXiv2025

Probing Primordial black holes with the distortion of Stochastic Gravitational Wave Background

The stochastic gravitational-wave background (SGWB), arising from the incoherent superposition of numerous compact binary coalescences, serves as a powerful probe of both astrophysical populations and fundamental physics. In this work, we investigate the influence of gravitational lensing on the SGWB, focusing on primordial black holes (PBHs) as potential lenses. Assuming PBHs as dark matter candidates with a broad cosmic distribution, we show that their lensing optical depth can be significantly enhanced, producing pronounced effects with relative deviations at the 10^-1 level. By systematically varying the PBH mass (M_PBH) and abundance (f_PBH), we demonstrate that the mass predominantly determines the frequency-dependent diffraction features of the spectrum, while the abundance primarily amplifies the overall lensing-induced deviation. Although the SGWB from binary black holes has not yet been observed, our analytical results provide theoretical insight into the possible imprint of lensing on its spectrum and suggest that future detections could offer a novel avenue to constrain dark matter scenarios.

astro-ph.CO↗

arXiv2025

HST Confirms Sub-5 kpc Dual Quasar Pairs at Cosmic Noon

During cosmic noon ($z\sim1-3$), when both star formation and black hole growth peaked, galaxy mergers are predicted to trigger dual active galactic nuclei (AGN) that eventually coalesce as supermassive black hole (SMBH) binaries. However, observations of dual quasars with sub-5 kpc separations-the critical phase preceding final coalescence-have remained challenging due to angular resolution limitations. We present the discovery and confirmation of two sub-arcsecond dual quasars at $z>1$, selected from 59,025 SDSS quasars, which fall within the footprint of the Hyper Suprime-Cam Survey. Using high-resolution Hubble Space Telescope (HST) imaging and slitless spectroscopy, we confirmed SDSS J1625+4309 ($z=1.647$, separation 0.55"/4.7 kpc) and SDSS J0229$-$0514 ($z=3.174$, separation 0.42"/3.2 kpc), probing the sub-5 kpc separation regime. Through novel combination of WFC3/IR direct imaging (F140W) and grism spectroscopy (G141), we resolve both components morphologically and spectroscopically confirm their dual nature via detection of H$\beta$+[OIII] and MgII emission lines in each nucleus. Two-dimensional image decomposition reveals distinct host galaxy morphologies: J1625+4309 shows an extended, disturbed structure ($R_e$=4.7 kpc) indicative of an ongoing major merger, while J0229$-$0514 exhibits a compact host ($R_e$=1.4 kpc) suggesting an advanced coalescence stage. Black hole mass estimates based on virial relations yield M$_{\mathrm{BH}} \sim 10^{8.1}-10^{8.7} M_\odot$ with line-of-sight velocity offsets of $(0.7\pm0.1)\times10^{3}$ km s$^{-1}$ and $(1.0\pm0.2)\times10^{3}$ km s$^{-1}$, respectively. These confirmations directly constrain the frequency and properties of close dual quasars, opening new avenues for studying SMBH mergers at cosmic noon.

astro-ph.GA↗

arXiv2025

Detecting dark matter substructure with lensed quasars in optical bands

Flux ratios of multiple images in strong gravitational lensing systems provide a powerful probe of dark matter substructure. Optical flux ratios of lensed quasars are typically affected by stellar microlensing, and thus studies of dark matter substructure often rely on emission regions that are sufficiently extended to avoid microlensing effects. To expand the accessible wavelength range for studying dark matter substructure through flux ratios and to reduce reliance on specific instruments, we confront the challenges posed by microlensing and propose a method to detect dark matter substructure using optical flux ratios of lensed quasars. We select 100 strong lensing systems consisting of 90 doubles and 10 quads to represent the overall population and adopt the Kolmogorov--Smirnov (KS) test as our statistical method. By introducing different types of dark matter substructure into these strong lensing systems, we demonstrate that using quads alone provides the strongest constraints on dark matter and that several tens to a few hundred independent flux ratio measurements from quads can be used to study the properties of dark matter substructure and place constraints on dark matter parameters. Furthermore, we suggest that the use of multi-band flux ratios can substantially reduce the required number of quads. Such sample sizes will be readily available from ongoing and upcoming wide-field surveys.

astro-ph.CO↗

arXiv2025

Gravitational lensing of gravitational waves: universal characteristics of strongly lensed memory waveforms

In this work, the strong lensing effect of the memory signal was considered. In the geometric optics limit, the lensed memory signal becomes oscillatory, while the unlensed is basically monotonic. This is because only the high frequency Fourier modes contribute strongly to the lensed signal. Due to the step function like behavior of the unlensed memory waveform, the lensed waveform possesses characteristic morphology that is dependent on the type of the image, but independent of the lens model and the binary system. That is, for each type of the lensed image, the lensed memory waveform has an approximate reflection symmetry about a symmetrical axis in the time domain. More specifically, for the type I and type III images, the lensed memory signals are nearly odd under the reflection, while the type II signal is roughly even. In addition, at the symmetrical axis, the sign of the slope for type I image is different from that for the type III image. These universal characteristic features would help determine the type of the lensed image. This is particularly because the memory waveform can be well approximated by a suitable step function, which involves just two parameters, the overall amplitude and the time of arrival. It is fast and cheap to simulate this approximated waveform. Once the type of the lensed image is determined with the approximated memory waveform, one can use the appropriate waveform template for the oscillatory component of the gravitational wave to perform the parameter estimation.

gr-qc↗