The cosmic distance scale is built on multiple different techniques for estimating distances in space that are often connected and dependent on multiple measurements and assumptions. Double white dwarf binaries (DWDs) are common objects and are expected to produce gravitational wave (GW) signals that can be observed with space-based detectors such as LISA. By analyzing these signals we should be able to estimate the distance and sky location of the source. Previous studies have done this for circular binaries which, while they are abundant, have, in general, weaker signals than eccentric binaries and it is not possible to differentiate whether a circular binary is in the field or in a dense environment such as a globular cluster (GC). In this paper we used eccentric binaries from MOCCA GC simulations, simulated the GW signal from each binary at locations related to GCs in the Milky Way and estimated the precision on the distance and the sky location of the source. We find that distances can be estimated with higher precision than current day methods even with low eccentricity binaries and higher eccentricity further increases this precision. Although the probability of finding a tight and eccentric DWD is far lower than a circular one, we can expect to find at least a few in the dense environments of the Milky Way, such as GCs. These estimations would be independent measurements with high precision to objects inside dense environments, such as GCs inside the Milky Way and the Magellanic Clouds.

The density profiles of Dark matter (DM) halos carry imprints of the DM nature and may be constrained through the lensing effects on gravitational waves (GWs) arising from the halo gravitational potential. In this paper, we investigate GW lensing by two representative types of halo density profiles, i.e., the generalized Navarro-Frenk-White (gNFW) density profile and the Einasto density profile. Using the gravitational lensing equation, we first examine the parameter-space distribution and the imaging characteristics of both profiles under strong lensing, partitioning the parameter space into distinct regions according to the Morse index. We then conduct a detailed analysis of the modulus |F| and phase Arg(F) of the amplification factor F(w,y) at low frequency regime. Our results show that, for a fixed lens mass , increasing the gNFW slope γ leads to a larger amplitude, more rapid oscillation, and more distinct wave-packet morphology in the multiple-image regime. Compared with the gNFW case, the Einasto case (with α=0.16, y<0.6, and the same M_200) produces a stronger lensing effect. Notably, the evolution of F(w,y) with frequency for the Einasto profile differs from that of the gNFW case, making its behavior particularly distinctive.

The discovery of the gravitational-wave event GW170817 from a binary neutron star merger, together with its multi-wavelength electromagnetic counterparts, marks the beginning of the era of multi-messenger gravitational wave astronomy. Observations of gravitational-wave signals from compact binary mergers enable an independent measurement of the luminosity distance to the source. This implies that gravitational-wave sources can serve as standard sirens to probe the expansion history of the Universe, providing a new approach to constrain cosmological parameters. In this paper, we review the basic principles of using gravitational-wave standard sirens to constrain cosmology. We discuss various methods for determining the source distance and redshift, as well as the capabilities of second and third generation ground-based detectors and space-based detectors in constraining cosmological parameters, especially the Hubble constant and dark energy parameters. By examining two types of standard sirens, binary neutron star mergers with electromagnetic counterparts as bright sirens and stellar-mass binary black hole mergers as dark sirens, we illustrate the methodology, challenges, and future prospects of the standard siren approach.

The gravitational lensing of multi-messenger signals from binary neutron star mergers (BNSs), including gravitational waves (GWs), short Gamma-Ray bursts (sGRBs), kilonovae, and afterglows, can serve as a unique probe to constrain the mass of the graviton and cosmological parameters. In this paper, we estimate the detection rates of lensed electromagnetic counterparts associated with lensed BNS GW events detected by Cosmic Explorer and Einstein Telescope. For kilonovae and afterglows, we further consider a complementary pointed follow-up strategy targeting pre-identified galaxy-scale lens candidates within the GW localization region. By utilizing both numerical and observational constraints on BNS mergers, we find that: (1) Future γ-ray telescopes, even with a sensitivity more than ten times better than that of Fermi-GBM, may only detect lensed sGRB prompt emission at a rate ∼ 0.1 yr^-1, corresponding to ∼ 2× 10^-3 of detectable lensed BNS GW events. (2) For the known-lens pointed strategy, the identifiable lensed-host fraction is approximately 0.15-0.30 for the fiducial deep lens-catalog case considered, suggesting a possible gain in per-lens sensitivity for faint kilonovae and afterglows. (3) An RST-like near-infrared facility could detect lensed kilonovae at rates of approximately ∼ 0.45^+0.81_-0.34, 0.55^+0.98_-0.41, and 0.078^+0.139_-0.059 yr^-1 in the F106, F158, and F213 bands, respectively. (4) Lensed afterglows remain difficult to detect in the optical and radio bands, while ATHENA-like X-ray observations may detect 0.5-5 events over ten years.

Stellar-mass binary black holes (sBBHs) formed in globular clusters (GCs) are promising sources for multiband gravitational-wave (GW) observations, particularly with low- and middle-frequency detectors. These sBBHs can retain detectable eccentricities when they enter the sensitivity bands of low-frequency GW observatories. We study multiband GW observations of eccentric sBBHs that escape from GC models simulated with the MOCCA code, focusing on how low- and middle-frequency detectors can constrain their eccentricities and other parameters. Using Monte Carlo simulations, we generate 10 realizations of cosmic sBBHs by combining the MOCCA sample with a cosmological model for GC formation and evolution. We then assess their detectability and the precision of parameter estimation. Our results show that LISA, Taiji, the LISA-Taiji (LT) network, and AMIGO could detect 0.8 ± 0.7, 11.6 ± 2.0, 15.4 ± 2.7, and 7.9 ± 1.3 escaping sBBHs, respectively, over 4 yr, while LT-AMIGO could detect 20.6 ± 3.0 multiband sBBHs in the same period. LT and AMIGO can measure initial eccentricities with relative errors of approximately 10 ^−6 –2 × 10 ^−4 and 10 ^−3 –0.7, respectively. Joint LT-AMIGO observations have a similar ability to estimate eccentricities as LT alone.

This study aims to test whether a supermassive binary black hole (SMBBH) system with a triple-disc accretion structure can explain the observed similar to 173-d periodic microlensing variations and spectral energy distribution (SED) of the gravitationally lensed quasar Q J0158-4325. We construct a triple-disc model for the SMBBH system, incorporating realistic accretion disc structures, orbital motion, and microlensing effects. The model is used to simulate optical and X-ray microlensing light curves and SEDs, which are compared with long-term optical monitoring, X-ray observations, and ultraviolet (UV)-optical spectra from the Hubble Space Telescope and XSHOOTER. Bayesian analysis and Markov chain Monte Carlo fitting are applied to constrain model parameters. The model successfully reproduces the periodic microlensing variations. Combined light curve and SED fitting favour a high mass ratio ( q > 0 . 5 ) SMBBH system with total mass similar to 10 (9 . 5) M-circle dot, and nearly equal-mass binaries ( q similar to 1) provide the best agreement with both the optical/UV spectrum and the microlensing signal. This model predicts larger X-ray microlensing amplitudes than in the optical, but the available X-ray observations lack the precision needed to place strong constraints. We emphasize the need for future high-cadence monitoring to resolve remaining uncertainties. This study demonstrates the effectiveness of combining multiwavelength microlensing signatures with spectral modelling to provide robust constraints on SMBBH systems, with the developed framework applicable to other lensed quasars for identifying and characterizing candidate SMBBHs.

Gravitational Waves(GWs)emitted from distant astrophysical sources can be gravitationally lensed by objects or systems encountered along their propagation paths.Strong astrophysical GW sources include inspiralling and merging stellar-mass compact binaries(stellar-mass binary black holes and binary neutron stars),and intermediate-mass and supermassive-binary-black-holes.Lenses range from stars,primordial black holes,dark matter halos to galaxies and galaxy clusters.Depending on the ratio of the GW wavelength to the lensing scale,GW lensing can occur in two regimes:geometric-optics,which produces multiple images of a single lensed event with relative time delays and magnifications,and wave-optics,which produces frequency-dependent amplifications and phase shifts in the observed waveform.Lensed GW signals can be identified either by overlap of inferred parameters between event pairs followed by joint Bayesian model comparison or by characteristic frequency-dependent amplification and phase modulation in the waveform that distinguish them from unlensed signals.The detection rates for different classes of lensed GW events are set by the redshift distributions of source populations and of intervening lenses,together with the lenses'mass and spatial distributions,of which the predictions are quite promising for future detection.Once confirmed,lensed GW events will become powerful probes of astrophysical processes,fundamental physics,and cosmology:they can constrain the nature and abundance of dark matter(including compact-object candidates),the mass function and internal structure of lensing galaxies and(sub)halos,the Hubble constant,and other cosmological parameters.In this paper,we provide a concise overview of the gravitational lensing of GWs,covering the theoretical framework,predicted detection rates for lensed inspirals and mergers,search strategies for lensed GW events,and their astrophysical and cosmological applications.We conclude with prospects and future directions for observing and exploiting the lensing of astrophysical GW events.

Aims. The microlensing of lensed quasars presents a promising avenue for understanding the structure of accretion disks around supermassive binary black holes (SMBBHs). We investigated the microlensing signatures in multiband (optical, UV, and X-ray) light curves of active SMBBH systems, focusing on how these signatures depend on the mass ratio, separation, and accretion rate. Methods. We analyzed the periodic fluctuations in microlensing light curves induced by the orbital motion of SMBBHs. We examined the relation between the mass ratio and the period of variations in light curves across optical, UV, and X-ray bands. Results. We find that the periodic fluctuations in the light curves depend on the mass ratio of the black holes: for nearly equal masses, variations occur at half the orbital period, whereas for low mass ratios, the period corresponds to the orbital period influenced by the secondary mini-disk. Furthermore, all optical, UV, and X-ray light curves exhibit the same period and phase, but the amplitude of variation is greater in the UV and X-ray bands than in the optical bands. These light curves provide insights into the motion and radiation regions of the disks through wavelength-dependent periodic variations, although they yield limited constraints on the system’s black hole mass or Eddington ratio, which can instead be derived from the spectral energy distribution (SED). Integrating microlensing data with SED observations is crucial for accurately constraining the parameters of SMBBH systems.

Active sub-pc supermassive binary black holes (SMBBHs) are expected to exhibit various electromagnetic signatures due to unique dynamical and geometric structures of their accretion, but observational identification of them remains challenging. In this paper, we adopt semianalytic models to investigate both deficits in spectral-energy-distributions (SEDs) of these systems induced by gaps/holes in their accretion disks and periodic variations in their light curves induced by either orbital-modulated Doppler boosting or accretion rate variation of each SMBH component. We construct a population model to generate SMBBHs across cosmic time by considering their orbital evolution and associated accretion and radiation processes. By estimating the continuum emission from each mock system and its variation, we investigate the detection of SMBBHs via either SED-deficit signature or light curve periodicity under reasonably given criteria. We find that all-sky surveys with filters similar to those of the China Space Station Telescope or Rubin/LSST could identify up to approximately 3× 10^2 SMBBHs via SED-deficit features and/or 10^3 SMBBHs via periodicity (≲5 yr), although both selections may suffer from a high rate of false positives. A few to a dozen SED-deficit SMBBHs may be detected by future pulsar timing arrays with signal-to-noise ratio ≳3, enabling multi-messenger observations. Only ∼20%-53% of SED-deficit selected SMBBHs may also be detected via periodic variations, and ∼7%-9% of periodic variation selected SMBBHs may be detected via SED-deficit signatures. The false positives for those SMBBHs selected jointly by both methods are negligible, highlighting the importance of searching for active SMBBH systems using joint methods.

Individual supermassive binary black holes (SMBBHs) are anticipated to be detected by pulsar timing arrays (PTAs) in the nanohertz band. The gravitational waves (GWs) from some of those individual SMBBHs may be diffractionally lensed by intervening galaxies. If on circular orbits, however, it is difficult to identify these lensed SMBBHs only by their GW signals, as their monochromatic waveforms are different from the original unlensed ones only with a small amplitude amplification and phase shift, which can be fit by unlensed waveforms with larger chirp masses or smaller distances. In this paper, we investigate whether we can identify the lensed nanohertz GW signals from highly eccentric SMBBHs by exploiting the dependence of their amplification on the frequencies of different harmonics. We adopt the second postNewtonian GW waveform from eccentric SMBBHs and the singular isothermal sphere lens model to calculate the difference between the lensed waveforms and the matched filtering ones with unlensed GW templates for different lensed systems, and find the larger the eccentricity, the larger the difference. Assuming the square kilometer array-PTA configuration, we adopt the fitting factor to justify the distinguishability of lensed GW signals from unlensed ones and find that we may identify some of the lensed sources with higher eccentricities (greater than or similar to 0.6) via 30-yr observations. The identification of diffraction lensed SMBBHs may provide an important probe to the wave nature of GWs and its astrophysical applications.

Binary neutron stars (BNSs) are one of the most important gravitational wave (GW) sources, which provide key insights into the evolution of massive binary stars and nuclear physics. The Beyond Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin missions' proposed concepts for next-generation space-based GW observatories, including LISAmax, Folkner, and eASTROD, aim to explore the submillihertz (mHz) to microhertz frequency band. Because the proposed designs substantially suppress low-frequency noise, these detectors are expected to outperform LISA, Taiji, and Tianqin in detecting eccentric Galactic BNS systems. In this paper, we estimate the detectability of nearby inspiraling BNSs using future sub-mHz GW detectors. By utilizing compact binary population synthesis simulations to generate mock BNS samples and estimate their signal-to-noise ratios (SNRs) correspondingly for each GW detector over an observation period of five to ten years, we find that LISAmax may detect 520-900 Galactic BNSs, whereas Folkner and eASTROD may detect 780-1370 Galactic BNSs. Notably, LISAmax excels in detecting highly eccentric systems (e > 0.90) owing to its higher sensitivity at relatively higher sub-mHz frequencies. We further identify seven observed radio BNSs as viable candidates for validation, in particular, J0737-3039, which reaches an SNR of 100. The expected detection number of Large Magellanic Cloud inspiraling BNSs is 4-18 for these sub-mHz detectors over an observation period of five to ten years, while detecting inspiraling BNSs in the Small Magellanic Cloud is challenging. This study highlights the significant potential of future sub-mHz GW missions in unraveling BNS formation and evolution physics.

In sufficiently compact neutron star-white dwarf (NSWD) binary systems, orbital decay means the white dwarf eventually fills its shrinking Roche lobe, initiating a phase of mass transfer. The exchange of angular momentum - both internal and external - plays a critical role in determining the binary's evolutionary outcome. For neutron stars with relatively low magnetic fields and spin frequencies, whether the orbital separation continues to shrink depends on the interplay between gravitational wave (GW) radiation and mass transfer dynamics. We compute the orbital evolution of NSWD binaries across a broad parameter space, incorporating four key variables. Our results reveal distinct boundaries in the NSWD mass-mass diagram: binaries with white dwarf masses above these thresholds undergo rapid orbital decay and direct coalescence. The dependence of these boundaries on system parameters indicates that Roche-lobe-filling NSWD binaries can follow multiple evolutionary pathways - a phenomenon we refer to as branched or polymorphic evolution. NSWD binary systems emit strong and diverse GW signals, many of which would be detectable by space-based GW observatories. The morphology of the evolving GW waveform provides a direct diagnostic for the NSWD binary configuration, including any contribution from an accretion disc. Our models can provide critical waveform templates for identifying merging binary signals in real-time GW data.

We simulate the optical searching of gravitational-wave electromagnetic counterpart of the binary neutron star (BNS) merger event (i.e., a kilonova) using the ground based SiTian project prototype telescope with a 5-min limiting magnitude of 22.0, triggered by LIGO and Virgo gravitational wave detectors during the ongoing O4 run. Our simulations show that an average of 0.17-0.25 kilonova events can be observed over the entire O4 period of ∼ 2 years in the most optimistic case we set, while no kilonova can be detected in other cases. We note that it is beneficial for SiTian's kilonova searching by extending the exposure time to gain deeper limiting magnitude despite the rapid decline of kilonova luminosity.

With the rapid advancements in next-generation ground-based gravitational wave (GW) detectors, it is anticipated that 10(3)-10(5) binary neutron star (BNS) mergers per year will be detected, with a significant fraction accompanied by observable merger-nova signals through future sky surveys. Merger-novae are typically powered by the radioactive decay of heavy elements synthesized via the r-process. If the post-merger remnant is a long-lived rapid-rotating neutron star, the merger-nova can be significantly enhanced due to strong magnetized winds. In this paper, we generate mock BNS merger samples using binary population synthesis model and classify their post-merger remnants-black hole (BH) and magnetar, (i.e., long-lived supramassive NS and stable NS), based on results from numerical simulations. We then construct merger-nova radiation models to estimate their luminosity function. We find that the luminosity function may exhibit a distinctive triple-peak structure, with the relative positions and heights of these peaks depending on the equation of state (EOS) of the BNS. Furthermore, we estimate the average Target-of-Opportunity (ToO) detection efficiency < f(eff)> with the Chinese Space Station Telescope (CSST) and find that due to possible enhanced luminosity, the largest source redshift with < f(eff)> > 0.1 can be enlarged from z(s) similar to 0.5 to z(s) similar to 1 - 1.5. Besides, we also generate the detectable mass spectrum for merger-novae by < f(eff)>, which may provide insights to the ToO searching strategy.

Lensed gravitational-wave (GW) events are expected to be powerful new probes of cosmology, contingent on redshift measurement by electromagnetic observations. Host galaxy identification is thus crucial but challenging due to poor localization by GW signal alone. In this Letter, we show that the third-generation ground-based GW detectors will detect a population of lensed events with three or more detectable images (including the central one), each arriving at distinct times and Earth locations in space, forming an effective network that reduces the typical localization area to ∼0.01 deg ^2 . For at least 90% (or 50%) of these events, the localization improves by more than a factor of 10 (or 30) compared with unlensed cases. Such precise localization and multiple-image detections enable robust host-galaxy identification and, through lens modeling, further yield subarcsecond position. As dark lensed sirens, these events become powerful probes of cosmological parameters. Using simulated lensed compact-binary mergers, we show that 2 yr or longer observations with third-generation GW detectors can measure the Hubble constant to ≲1% precision via “dark lensed sirens” (even when relying solely on lensed stellar-mass binary black hole events) while simultaneously constraining other cosmological parameters. This approach will provide an independent, complementary avenue for measuring cosmological parameters.

Binary neutron stars (BNSs) are among the most interesting sources for multimessenger studies. A number of recently discovered BNSs in the Milky Way by radio telescopes have added new information to the parameter distribution of the Galactic BNSs. The scarcity of BNS mergers during the O4 run of the LIGO-Virgo-Kagra suggests a BNS local merger rate six times lower than the previous constraint obtained by O1-O3 runs. With these new multimessenger observations, in this letter, we adopt the compact binary population synthesis model and Bayesian analysis to constrain the formation and evolution of BNSs, especially the common envelope (CE) evolution. We find that the following are required: (1) a fraction (f(HG) similar to 0.8) but not all of the Hertzsprung gap donors merged with their companions in the CE stage, in order to simultaneously explain the low BNS merger rate density and the existence of the short-orbital-period (less than or similar to 1 d) Galactic BNSs, different from either all (f(HG) = 1) or none (f(HG) = 0) adopted in previous studies; (2) a large CE ejection efficiency alpha(similar to 5), in order to explain the existence of the long-orbital-period (greater than or similar to 10 d) Galactic BNSs.

Binary neutron stars (BNSs) detected in the Milky Way have total masses distributing narrowly around similar to 2.6-2.7M circle dot, while the BNS merger GW190425 detected via a gravitational wave has a significantly larger mass (similar to 3.4M circle dot). This difference is not well understood, yet. In this paper, we investigate the BNS spin evolution via an improved binary star evolution model and its effects on the BNS observability, with the implementation of various relevant astrophysical processes. We find that the first-born neutron star component in low-mass BNSs can be spun up to millisecond pulsars by the accretion of Roche-lobe overflow from its companion and its radio lifetime can be comparable to the Hubble time. However, most high-mass BNSs have substantially shorter radio lifetimes than low-mass BNSs, and thus a smaller probability of being detected via radio emission. Adopting the star formation and metal enrichment history of the Milky Way given by observations, we obtain the survived Galactic BNSs with pulsar components from our population synthesis model and find that their distributions on the diagrams of the spin period versus the spin period time derivative ( P-P ) and the orbital period versus the eccentricity (Porb-e) can well match those of the observed Galactic BNSs. The total mass distribution of the observed Galactic BNSs can also be matched by the model. A significant fraction (similar to 19%-22%) of merging BNSs at redshift z similar to 0 have masses greater than or similar to 3M circle dot, which seems compatible with the GW observations. Future radio observations may detect many more Galactic BNSs, which will put strong constraints on the spin evolution of BNSs during their formation processes.

The gravitational wave (GW) signals from a large number of double white dwarfs (DWDs) in the Galaxy are expected to be detected by space GW detectors, e.g., the Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin in the millihertz band. In this paper, we present an alternative method by directly using the time-domain GW signal detected by space GW detectors to constrain the anisotropic structure of the Galaxy. The information of anisotropic distribution of DWDs is naturally encoded in the time-domain GW signal because of the variation of the detectors' directions and consequently the pattern functions due to their annual motion around the Sun. The direct use of the time-domain GW signal enables simple calculations, such as utilizing an analytical method to assess the noise arising from the superposition of random phases of DWDs and using appropriate weights to improve the constraints. We investigate the possible constraints on the scale of the Galactic thin disk and bulge that may be obtained from LISA and Taiji by using this method with mock signals obtained from population synthesis models. We further show the different constraining capabilities of the low-frequency signal (foreground) and the high-frequency signal (resolvable sources) via the Markov Chain Monte Carlo method, and find that the scale height and length of the Galactic thin disk and the scale radius of the bulge can be constrained to a fractional accuracy of similar to 30%, 30%, 40% (or 20%, 10%, 40%) by using the low-frequency (or high-frequency) signal detected by LISA or Taiji.

In this letter, we present a systematic search for the electromagnetic counterparts of binary neutron star (BNS) merger candidate GW231109_235456 by examining all transients reported within the 90

Massive black holes (MBHs) exist in the Galactic center (GC) and other nearby galactic nuclei. As a natural outcome of galaxy mergers, some MBHs may have a black hole (BH) companion. In this paper, assuming that the MBHs in the GC and some nearby galaxies are in binaries with orbital periods ranging from months to years (gravitational-wave frequency similar to 1-100 nHz), we investigate the detectability of gravitational waves from these binary MBHs (BBHs) and constraints on the parameter space for the existence of BBHs in the GC, Large Magellanic Cloud (LMC), M31, M32, and M87 that may be obtained by current/future pulsar timing array (PTA) observations. We find that a BBH in the GC, if any, can be revealed by the Square Kilometre Array PTA (SKA-PTA) if it has mass ratio q greater than or similar to 10-4-10-3 and semimajor axis a similar to 20-103 au. The existence of a BH companion of the MBH can be revealed by SKA-PTA with similar to 20 yr observations in M31 if q greater than or similar to 10-4 and a similar to 102-104 au or in M87 if q greater than or similar to 10-5 and a similar to 103-2 x 104 au, but not in the LMC and M32 if q << 1. If a number of millisecond stable pulsars with distances less than or similar to 0.1-1 pc away from the central MBH in the GC, the LMC, M32, or M31 can be detected in future and applied to PTAs, a BH companion with mass even down to similar to 100 M circle dot, close to stellar masses, can be revealed by such PTAs. Future PTAs are expected to provide an independent way to reveal BBHs and low-mass MBH companions in the GC and nearby galaxies, improving our understandings of the formation and evolution of MBHs and galaxies.