arXiv subjects

Kai Liao

Publications and source records attributed to Kai Liao.

At least 55 records · Page 3Linked to original sources

arXiv2022

Constraints on compact dark matter from lensing of gravitational waves for the third-generation gravitational wave detector

Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of dark matter at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We firstly consider two channels of formation of BBH that contribute to low and high redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with $1000$ detected GW events of BBH, we find that the abundance of compact DM could be constrained to $\lesssim0.1\%$ in the mass range $\geq500~M_{\odot}$ at $68\%$ confidence level. In addition, if a GW event lensed by a compact DM object with $M_{\rm l}\in[100~M_{\odot},300~M_{\odot}]$ is detected in $100$ detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from $2.3\%$ to $25.2\%$ in this mass range with the Bayesian analysis.

astro-ph.CO↗

arXiv2022

Strongly Lensed Transient Sources: A Review

The past decades have witnessed a lot of progress in gravitational lensing with two main targets: stars and galaxies (with active galactic nuclei). The success is partially attributed to the continuous luminescence of these sources making the detection and monitoring relatively easy. With the running of ongoing and upcoming large facilities/surveys in various electromagnetic and gravitational-wave bands, the era of time-domain surveys would guarantee constant detection of strongly lensed explosive transient events, for example, supernovae in all types, gamma ray bursts with afterglows in all bands, fast radio bursts and even gravitational waves. Lensed transients have many advantages over the traditional targets in studying the Universe and magnification effect helps to understand the transients themselves at high redshifts. In this review article, basing on the recent achievements in the literature, we summarize the methods of searching for different kinds of lensed transient signals, the latest results on detection and their applications in fundamental physics, astrophysics and cosmology. At the same time, we give supplementary comments as well as prospects of this emerging research direction that may help readers who are interested in entering this field.

astro-ph.HE↗

arXiv2022

Impact of gravitational lensing on black hole mass function inference with third-generation gravitational wave detectors

The recent rapid growth of the black hole (BH) catalog from gravitational waves (GWs), has allowed us to study the substructure of black hole mass function (BHMF) beyond the simplest Power-Law distribution. However, the BH masses inferred from binary BH merger events, may be systematically 'brightened' or 'dimmed' by the gravitational lensing effect. In this work, we investigate the impact of gravitational lensing on the BHMF inference considering the detection of the third-generation GW detector -- the Einstein Telescope (ET). We focus on high redshift, $z=10$, in order to obtain the upper limits of this effect. We use Monte Carlo (MC) method to simulate the data adopting 3 original BHMFs under Un-Lensed and Lensed scenarios, then recover the parameters of BHMFs from the mock data, and compare the difference of results, respectively. We found that all the parameters are well recovered within one standard deviation(std., 1$σ$), and all 3 BHMF models are reconstructed within 68\% credible interval, suggesting that lensing would not change the main structure drastically, even at very high redshifts and with high precision of ET. And the modest influence beyond $50M_{\odot}$, depends on the modeling of the high mass tail or substructure of BHMF. We conclude that the impact of lensing on BHMF inference with ET can be safely ignored in the foreseeable future. Careful handling of lensing effects is required only when focusing on an accurate estimation of the high mass end of BHMF at high redshifts.

astro-ph.CO↗

arXiv2022

Identifying lensed quasars and measuring their time-delays from unresolved light curves

Identifying multiply imaged quasars is challenging due to their low density in the sky and the limited angular resolution of wide field surveys. We show that multiply imaged quasars can be identified using unresolved light curves, without assuming a light curve template or any prior information. After describing our method, we show using simulations that it can attain high precision and recall when we consider high-quality data with negligible noise well below the variability of the light curves. As the noise level increases to that of the Zwicky Transient Facility (ZTF) telescope, we find that precision can remain close to $100\%$ while recall drops to $\sim 60\%$. We also consider some examples from the Time Delay Challenge 1 (TDC1) and demonstrate that the time delays can be accurately recovered from the joint light curve data in realistic observational scenarios. We further demonstrate our method by applying it to publicly available COSMOGRAIL data of the observed lensed quasar SDSS J1226-0006. We identify the system as a lensed quasar based on the unresolved light curve and estimate a time delay in good agreement with the one measured by COSMOGRAIL using the individual image light curves. The technique shows great potential to identify lensed quasars in wide field imaging surveys, especially the soon to be commissioned Vera Rubin Observatory.

astro-ph.CO↗

arXiv2022

Forecast of observing time delay of the strongly lensed quasars with Muztagh-Ata 1.93m telescope

As a completely independent method, the measurement of time delay of strongly lensed quasars (TDSL) are crucial to resolve the Hubble tension. Extensive monitoring is required but so far limited to a small sample of strongly lensed quasars. Together with several partner institutes, Beijing Normal University is constructing a 1.93m reflector telescope at the Muztagh-Ata site in west China, which has the world class observing conditions. The telescope will be equipped with both a three-channel imager/photometer which covers $3500-11000$ Angstrom wavelength band, and a low-medium resolution ($λ/δλ=500/2000/7500$) spectrograph. In this paper, we investigate the capability of Muztagh-Ata 1.93m telescope in measuring time delays of strongly lensed quasars. We generate mock strongly lensed quasar systems and light curves with microlensing effects based on five known strongly lensed quasars, i.e., RX J1131-1231, HE 0435-1223, PG 1115+080, WFI 2033-4723 and SDSS 1206+4332. In particular, RX J1131-1231 is generated with lens modeling in this work. Due to lack of enough information, we simulate the other 4 systems with the public data without lens modeling. According to simulations, for RX J1131-like systems (wide variation in time delay between images) the TDSL measurement can be achieved with the precision about $Δt=0.5$ day with 4 seasons campaign length and 1 day cadence. This accuracy is comparable to the up-coming TDCOSMO project. And it would be better when the campaign length keeps longer and with high cadence. As a result, the capability of Muztagh-Ata 1.93m telescope allows it to join the network of TDSL observatories. It will enrich the database for strongly lensed quasar observations and make more precise measurements of time delays, especially considering the unique coordinate of the site.

astro-ph.CO↗

arXiv2022

Search for lensing signatures from the latest fast radio burst observations and constraints on the abundance of primordial black holes

The possibility that primordial black holes (PBHs) form a part of dark matter has been considered for a long time but poorly constrained over a wide mass range. Fast radio bursts (FRBs) are bright radio transients with millisecond duration. Lensing effect of them has been proposed as one of the cleanest probes for constraining the presence of PBHs in the stellar mass window. In this paper, we first apply the normalised cross-correlation algorithm to search and identify candidates of lensed FRBs in the latest public FRB observations, i.e. $593$ FRBs which mainly consist of the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, and then derive constraints on the abundance of PBHs from the null search result of lensing signature. For a monochromatic mass distribution, the fraction of dark matter made up of PBHs could be constrained to $\leq87\%$ for $\geq500~M_{\odot}$ at 95\% confidence level by assuming flux ratio thresholds dependent signal-to-noise ratio for each FRB and that apparently one-off events are intrinsic single bursts. This result would be improved by a three times factor when a conventional constant flux ratio threshold is considered. Moreover, we derive constraints on PBHs with a log-normal mass function naturally predicted by some popular inflation models and often investigated with gravitational wave detections. We find that, in this mass distribution scenario, the constraint from currently public FRB observations is relatively weaker than the one from gravitational wave detections. It is foreseen that upcoming complementary multi-messenger observations will yield considerable constraints on the possibilities of PBHs in this intriguing mass window.

astro-ph.CO↗

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

Searching for gravitationally lensed gamma-ray bursts with their afterglows

Gamma-ray bursts (GRBs) at high redshifts are expected to be gravitationally lensed by objects of different mass scales. Besides a single recent claim, no lensed GRB has been detected so far by using the gamma-ray data only. In this paper, we suggest that the multi-band afterglow data might be an efficient way to search for lensed GRB events. Using the standard afterglow model we calculate the characteristics of the lensed afterglow lightcurves under the assumption of two popular analytic lens models: point mass and Singular Isothermal Sphere (SIS) model. In particular, when different lensed images cannot be resolved, their signals would be superimposed together with a given time delay. In this case, the X-ray afterglows are likely to contain several X-ray flares of similar width in linear scale and similar spectrum, and the optical afterglow lightcurve will show rebrightening signatures. Since the lightcurves from the image arriving later would be compressed and deformed in the logarithmic time scale, the larger time delay (i.e. the larger mass of the lens), the easier is to identify the lensing effect. We analyzed the archival data of optical afterglows and found one potential candidate of the lensed GRB (130831A) with time delay $\sim$500 s, however, observations of this event in gamma-ray and X-ray band seem not to support the lensing hypothesis. In the future, with the cooperation of the all-sky monitoring gamma-ray detectors and multi-band sky survey projects, our method proposed in this paper would be more efficient in searching for strongly lensed GRBs.

astro-ph.HE↗

arXiv2021

Improved time-delay lens modelling and $H_0$ inference with transient sources

Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant ($H_0$) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: the lensed host galaxy can be observed before or after the transient's appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock datasets of 48 quasar lensing systems (i.e., adding AGN in the galaxy center) and 48 galaxy-galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and $H_0$. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of $H_0$ precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which in turn plays a key role in breaking the mass-sheet degeneracy and constraining $H_0$.

astro-ph.CO↗

arXiv2020

Impact of Microlensing on Observational Strategies for Gravitational Time Delay Measurements

Microlensing not only brings extra magnification lightcurves on top of the intrinsic ones but also shifts them in time domain, making the actual time-delays between images of strongly lensed active galactic nucleus change on the $\sim$ day(s) light-crossing time scale of the emission region. The microlensing-induced time-delays would bias strong lens time-delay cosmography if uncounted. However, due to the uncertainties of the disk size and the disk model, the impact is hard to accurately estimate. In this work, we study how to reduce the bias with designed observation strategy based on a standard disk model. We find long time monitoring of the images could alleviate the impact since it averages the microlensing time-lag maps due to the peculia motion of the source relative to the lens galaxy. In addition, images in bluer bands correspond to smaller disk sizes and therefore benefit time-delay measurements as well. We conduct a simulation based on a PG 1115+080-like lensed quasar. The results show the time-delay dispersions caused by microlensing can be reduced by $\sim40\%$ with 20-year lightcurves while u band relative to r band reduces $\sim75\%$ of the dispersions. Nevertheless, such an effect can not be totally eliminated in any cases. Further studies are still needed to appropriately incorporate it in inferring an accurate Hubble constant.

astro-ph.CO↗

arXiv2020

Chromatic Microlensing Time Delays

Due to the finite size of the disk and the temperature fluctuations producing the variability, microlensing changes the actual time delays between images of strongly lensed AGN on the $\sim$day(s) light-crossing time scale of the emission region. This microlensing-induced time delay depends on the disk model, primarily the disk size $R_\mathrm{disk}$ which has been found to be larger than predicted by the thin-disk model. In this work, we propose that light curves measured in different bands will give different time delays since $R_\mathrm{disk}$ is a function of wavelength, and by measuring the time delay differences between bands, one can 1) directly verify such an new effect; 2) test the thin-disk model of quasars. For the second goal, our method can avoid the potential inconsistency between multi-band light curves that may bias the results by continuum reverberation mapping. We conduct a simulation based on a PG 1115+080-like lensed quasar, calculating the theoretical distributions of time delay differences between two bands: u and i centered around 354nm and 780nm, under and beyond the thin-disk model, respectively. Assuming the disk size is twice larger than the standard one, we find that with a precision of 2 days in the time delay difference measurements, the microlensing time delay effect can be verified with $\sim4$ measurements while with $\sim35$ measurements the standard model can be excluded. This approach could be realized in the ongoing and upcoming multi-band wide-field surveys with follow-up observations.

astro-ph.GA↗

arXiv2020

Determining Model-independent $H_0$ and Consistency Tests

We determine the Hubble constant $H_0$ precisely ($2.3\%$ uncertainty) in a manner independent of cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable source can provide a time-delay distance $D_{Δt}$ and angular diameter distance to the lens $D_{\rm{d}}$. These absolute distances can anchor Type Ia supernovae, which give an excellent constraint on the shape of the distance-redshift relation. Updating our previous results to use the H0LiCOW program's milestone dataset consisting of six lenses, four of which have both $D_{Δt}$ and $D_{\rm{d}}$ measurements, we obtain $H_0=72.8_{-1.7}^{+1.6}\rm{\ km/s/Mpc}$ for a flat universe and $H_0=77.3_{-3.0}^{+2.2}\rm{\ km/s/Mpc}$ for a non-flat universe. We carry out several consistency checks on the data and find no statistically significant tensions, though a noticeable redshift dependence persists in a particular systematic manner that we investigate. Speculating on the possibility that this trend of derived Hubble constant with lens distance is physical, we show how this can arise through modified gravity light propagation, which would also impact the weak lensing $σ_8$ tension.

astro-ph.CO↗

arXiv2020

Constraints on compact dark matter with fast radio burst observations

Fast Radio Bursts (FRBs) are bright radio transients with millisecond duration at cosmological distances. Since compact dark matter/objects (COs) could act as lenses and cause split of this kind of very short duration signals, Mu$\rm{\tilde{n}}$oz et al. (2016) has proposed a novel method to probe COs with lensing of FRBs. In this Letter, we for the first time apply this method to real data and give constraints of the nature of COs with currently available FRB observations. We emphasize the information from dynamic spectra of FRBs is quite necessary for identifying any lensed signals and find no echoes in the existing data. The null search gives a constraint comparable to that from galactic wide binaries, though the methods of redshift inference from dispersion measure would impact a little. Furthermore, we make an improved forecast basing on the distributions of real data for the ongoing and upcoming telescopes. Finally, we discuss the situation where one or more lensed signals will be detected. In such a case, the parameter space of COs can be pinned down very well since the lens mass can be directly determined through the observed flux ratio and time delay between split images.

astro-ph.CO↗

arXiv2020

Probing compact dark matter with gravitational wave fringes detected by the Einstein Telescope

Unlike the electromagnetic radiation from astrophysical objects, gravitational waves (GWs) from binary star mergers have much longer wavelengths and are coherent. For ground-based GW detectors, when the lens object between the source and the earth has mass $\sim 1-10^5M_\odot$, the diffraction effect should be considered since the chirping wavelengths are comparable to the scale of the barrier (its Schwarzschild radius). The waveform will thus be distorted as the fringes. In this work, we show that signals from the third-generation GW detectors like the Einstein Telescope (ET) would be a smoking gun for probing the nature of compact dark matter (CDM) or primordial black holes. Detection of the lensing effects becomes harder when the lens mass is smaller. ET is more sensitive than LIGO, the constraint is available for CDM mass $>5M_\odot$ while LIGO can only detect the mass $>100M_\odot$. For a null search of the fringes, one-year observation of ET can constrain the CDM density fraction to $\sim10^{-2}-10^{-5}$ in the mass range $M_{\rm{CDM}}=10M_\odot-100M_\odot$.

astro-ph.CO↗

arXiv2020

Gravitational Wave Interference via Gravitational Lensing: Measurements of Luminosity Distance, Lens Mass, and Cosmological Parameters

The gravitational lensing of gravitational waves might cause beat patterns detectable by interferometers. The feature of this kind of signal is the existence of the beat pattern in the early inspiral phase, followed by a seemingly randomly changing profile. After the strain peaks for the first time, the signal takes the usual waveform and the strain peaks for the second time. Once this signal is detected, the actual magnification factors can be obtained, so the true luminosity distance of the binary system is known. If the lens can be described by a point mass or a singular isothermal sphere, the functional forms of the time delay and the magnification factors are simple enough, so we can infer the mass of the lens or the cosmological parameters.

gr-qc↗

arXiv2020

Multiple measurements of quasars acing as standard probes: exploring the cosmic distance duality relation at higher redshift

General relativity reproduces main current cosmological observations, assuming the validity of cosmic distance duality relation (CDDR) at all scales and epochs. However, CDDR is poorly tested in the redshift interval between the farthest observed Type Ia supernovae (SN Ia) and that of the Cosmic Microwave background (CMB). We present a new idea of testing the validity of CDDR, through the multiple measurements of high-redshift quasars. Luminosity distances are derived from the relation between the UV and X-ray luminosities of quasars, while angular diameter distances are obtained from the compact structure in radio quasars. This will create a valuable opportunity where two different cosmological distances from the same kind of objects at high redshifts are compared. Our constraints are more stringent than other currently available results based on different observational data and show no evidence for the deviation from CDDR at $z\sim 3$. Such accurate model-independent test of fundamental cosmological principles can become a milestone in precision cosmology.

astro-ph.CO↗

arXiv2020

Black hole mass function and its evolution -- the first prediction for the Einstein Telescope

The knowledge about the black hole mass function (BHMF) and its evolution would help to understand the origin of the BHs and how BH binaries formed at different stages of the history of the Universe. We demonstrate the ability of future third generation gravitational wave (GW) detector -- the Einstein Telescope (ET) to infer the slope of the BHMF and its evolution with redshift. We perform the Monte Carlo simulation of the measurements of chirp signals from binary BH systems (BBH) that could be detected by ET, including the BH masses and their luminosity distances ($d_L$). We use the mass of a primary black hole in each binary system to infer the BHMF as a power-law function with slope parameter as $α$. Taking into account the bias that could be introduced by the uncertainty of measurements and by the selection effect, we carried out the numerical tests and find that only one thousand of GW events registered by ET ($\sim1\%$ amount of its yearly detection rate) could accurately infer the $α$ with a precision of $α\sim0.1$. Furthermore, we investigate the validity of our method to recover a scenario where $α$ evolves with redshift as $α(z) = α_0 + α_1\frac{z}{1+z}$. Taking a thousand of GW events and using $d_L$ as the redshift estimator, our tests show that one could infer the value of evolving parameter $α_1$ accurately with the uncertainty level of $\sim0.5$. Our numerical tests verify the reliability of our method. The uncertainty levels of the inferred parameters can be trusted directly for the several sets of the parameter we assumed, yet shouldn't be treated as a universal level for the general case.

astro-ph.GA↗

arXiv2020

Calibrating the standard candles with strong lensing

We propose a new model-independent strategy to calibrate the distance relation in Type Ia supernova (SN) observations and to probe the intrinsic properties of SNe Ia, especially the absolute magnitude $M_B$, basing on strong lensing observations in the upcoming Large Synoptic Survey Telescope (LSST) era. The strongly lensed quasars can provide the Time Delay Distances (TDD) and the Angular Diameter Distances (ADD) to the lens galaxies. These absolute distance measurements can model-independently anchor the SNe Ia at cosmological distances. We simulated 55 high-quality lensing systems with $5\%$ uncertainties for both TDD and ADD measurements basing on future observation conditions. For the time delay distances and the angular diameter distances as the calibration standards, the calibrated $1σ$ uncertainties of $M_{B}$ are approximately 0.24 mag and 0.03 mag, respectively. Besides, we also consider an evolving distance relation, for example, caused by the cosmic opacity. In this case, the $1σ$ uncertainties of $M_B$ calibrated with TDD and ADD are approximately 0.31 mag and 0.06 mag, respectively. The results show that the ADD method will be a promising tool for calibrating supernovae.

astro-ph.CO↗