Lensing Probability Research Articles

Foreground biases in strong gravitational lensing

Strong gravitational lensing is a competitive tool to probe the dark matter and energy content of the Universe. However, significant uncertainties can arise from the choice of lens model, and in particular the parameterisation of the line of sight. In this work, we consider the consequences of ignoring the contribution of foreground perturbers in lens modelling. We derive the explicit form of the degeneracy between the foreground shear and the ellipticity of a power law lens, which renders the former quantity effectively unmeasurable from strong lensing observables, and biases measurements of the latter by a few percent. Nonetheless, we demonstrate that this degeneracy does not affect measurements of the Einstein radius. Foreground tidal effects are also not expected to bias the slope of the potential, and any biases in this slope should not affect the recovery of the Hubble constant. The foreground convergence term adds an additional uncertainty to the measurement of H 0, and we show that this uncertainty will be on the order of 1% for lensing systems located along random lines of sight. There is evidence to indicate that the probability of strong lensing is higher towards overdense lines of sight, and this could result in a small systematic bias towards overestimations of H 0.

A persistent excess of galaxy-galaxy strong lensing observed in galaxy clusters

Context. Previous studies have revealed that the estimated probability of galaxy-galaxy strong lensing in observed galaxy clusters exceeds the expectations from the Λ cold dark matter cosmological model by one order of magnitude. Aims. We aim to understand the origin of this excess by analyzing a larger set of simulated galaxy clusters, and investigating how the theoretical expectations vary under different adopted prescriptions and numerical implementations of star formation and feedback in simulations. Methods. We performed a ray-tracing analysis of 324 galaxy clusters from the THREE HUNDRED project, comparing the GADGET-X and GIZMO-SIMBA runs. These simulations, which start from the same initial conditions, were performed with different implementations of hydrodynamics and galaxy formation models tailored to match different observational properties of the intracluster medium and cluster galaxies. Results. We find that galaxies in the GIZMO-SIMBA simulations develop denser stellar cores than their GADGET-X counterparts. Consequently, their probability for galaxy-galaxy strong lensing is higher by a factor of ∼3. This increment is still insufficient to fill the gap with observations as a discrepancy by a factor ∼4 still persists. In addition, we find that several simulated galaxies have Einstein radii that are too large compared to observations. Conclusions. We conclude that a persistent excess of galaxy-galaxy strong lensing exists in observed galaxy clusters. The origin of this discrepancy with theoretical predictions is still unexplained in the framework of the cosmological hydrodynamical simulations. This might signal a hitherto unknown issue with either the simulation methods or our assumptions regarding the standard cosmological model.

Future Constraints on Dark Matter with Gravitationally Lensed Fast Radio Bursts Detected by BURSTT

Understanding dark matter is one of the most urgent questions in modern physics. A very interesting candidate is primordial black holes (PBHs). For the mass ranges <10−16 M ⊙ and >100 M ⊙, PBHs have been ruled out. However, they are still poorly constrained in the mass range 10−16–100 M ⊙. Fast radio bursts (FRBs) are millisecond flashes of radio light of unknown origin, mostly from outside the Milky Way. Due to their short timescales, gravitationally lensed FRBs, which are yet to be detected, have been proposed as a useful probe for constraining the presence of PBHs in the mass window of <100 M ⊙. Up to now, the most successful project in finding FRBs has been CHIME. Due to its large field of view, CHIME has detected at least 600 FRBs since 2018. However, none of them is confirmed to be gravitationally lensed. Taiwan plans to build a new telescope, the Bustling Universe Radio Survey Telescope in Taiwan (BURSTT), dedicated to detecting FRBs. Its survey area will be 25 times greater than CHIME. BURSTT can localize all of these FRBs through very long baseline interferometry. We estimate the probability to find gravitationally lensed FRBs, based on the scaled redshift distribution from the latest CHIME catalog and the lensing probability function from Munõz et al. BURSTT-2048 can detect ∼24 lensed FRBs out of ∼1700 FRBs per annum. With BURSTT’s ability to detect nanosecond FRBs, we can constrain PBHs to form a part of dark matter down to 10−4 M ⊙.

Astrometric microlensing of primordial black holes with Gaia

The Gaia space telescope allows for unprecedented accuracy for astrometric measurements of stars in the Galaxy. In this work, we explore the sensitivity of Gaia to detect primordial black hole (PBH) dark matter through the distortions that PBHs would create in the apparent trajectories of background stars, an effect known as astrometric microlensing (AML). We present a novel calculation of the lensing probability, and we combine this with the existing publicly released Gaia eDR3 stellar catalog to predict the expected rate of AML events that Gaia will see. We also compute the expected distribution of a few event observables, which will be useful for reducing backgrounds.Assuming that the astrophysical background rate of AML like events due to other sources is negligible, we then compute the potential exclusion that could be set on the parameter space of PBHs with a monochromatic mass function. We find that Gaia is sensitive to PBHs in the range of 0.4 M ⊙–5 × 107 M ⊙, and has peak sensitivity to PBHs of ∼ 10 M ⊙ for which it can rule out as little as a fraction 3 × 10-4 of dark matter composed of PBHs. With this exquisite sensitivity, Gaia has the potential to rule out a PBH origin for the gravitational wave signals seen at LIGO/Virgo. Our novel calculation of the lensing probability includes for the first time, the effect of intermediate duration lensing events, where the lensing event lasts for a few years, but for a period which is still shorter than the Gaia mission lifetime. The lower end of our predicted mass exclusion is especially sensitive to this class of lensing events. As and when time-series data for Gaia is released, and once we have a better understanding of the astrophysical background rate to AML signals, our prediction of the lensing rate and event observable distributions will be useful to estimate the true exclusion/discovery of the PBH parameter space utilizing this data.

Enhancing cosmic shear with the multiscale lensing probability density function

ABSTRACT We quantify the cosmological constraining power of the ‘lensing probability density function (PDF)’ – the one-point probability density of weak lensing convergence maps – by modelling this statistic numerically with an emulator trained on w cold dark matter cosmic shear simulations. After validating our methods on Gaussian and lognormal fields, we show that ‘multiscale’ PDFs – measured from maps with multiple levels of smoothing – offer considerable gains over two-point statistics, owing to their ability to extract non-Gaussian information: For a mock Stage-III survey, lensing PDFs yield 33 per cent tighter constraints on the clustering parameter $S_8=\sigma _8\sqrt{\Omega _{\rm m}/0.3}$ than the two-point shear correlation functions. For Stage-IV surveys, we achieve &amp;gt;90 per cent tighter constraints on S8, but also on the Hubble and dark energy equation-of-state parameters. Interestingly, we find improvements when combining these two probes only in our Stage-III set-up; in the Stage-IV scenario the lensing PDFs contain all information from the standard two-point statistics and more. This suggests that while these two probes are currently complementary, the lower noise levels of upcoming surveys will unleash the constraining power of the PDF.

A machine learning based approach to gravitational lens identification with the International LOFAR Telescope

ABSTRACT We present a novel machine learning based approach for detecting galaxy-scale gravitational lenses from interferometric data, specifically those taken with the International LOFAR Telescope (ILT), which is observing the northern radio sky at a frequency of 150 MHz, an angular resolution of 350 mas and a sensitivity of 90 μJy beam−1 (1σ). We develop and test several Convolutional Neural Networks to determine the probability and uncertainty of a given sample being classified as a lensed or non-lensed event. By training and testing on a simulated interferometric imaging data set that includes realistic lensed and non-lensed radio sources, we find that it is possible to recover 95.3 per cent of the lensed samples (true positive rate), with a contamination of just 0.008 per cent from non-lensed samples (false positive rate). Taking the expected lensing probability into account results in a predicted sample purity for lensed events of 92.2 per cent. We find that the network structure is most robust when the maximum image separation between the lensed images is ≥3 times the synthesized beam size, and the lensed images have a total flux density that is equivalent to at least a 20σ (point-source) detection. For the ILT, this corresponds to a lens sample with Einstein radii ≥0.5 arcsec and a radio source population with 150 MHz flux densities ≥2 mJy. By applying these criteria and our lens detection algorithm we expect to discover the vast majority of galaxy-scale gravitational lens systems contained within the LOFAR Two Metre Sky Survey.

Evidence for lensing of gravitational waves from LIGO-Virgo data

Recently, the LIGO-Virgo Collaboration (LVC) concluded that there is no evidence for lensed gravitational waves (GW) in the first half of the O3 run, claiming "We find the observation of lensed events to be unlikely, with the fractional rate at $\mu>2$ being $3.3\times 10^{-4}$". While we agree that the chance of an individual GW event being lensed at $\mu>2$ is smaller than $10^{-3}$, the number of observed events depends on the product of this small probability times the rate of mergers at high redshift. Observational constraints from the stochastic GW background indicate that the rate of conventional mass BBH mergers (8 < M (M$_{\odot}$) < 15) in the redshift range 1<z< 2 could be as high as O($10^7$) events per year, more than sufficient to compensate for the intrinsically low probability of lensing. To reach the LVC trigger threshold these events require high magnification, but would still produce up to 10 to 30 LVC observable events per year. Thus, all the LVC observed ordinary stellar mass BBH mergers from this epoch must be strongly lensed. By adopting low-rates at high redshift, LVC assumes that lensed events can not be taking place, thus incorrectly assigning them a closer distance and higher masses by a factor of a few (typically 2 to 5). The LVC adopted priors on time delay are in tension with the distribution of observed time delays in lensed quasars. Pairs of events like GW190421-GW190910 and GW190424-GW190910, which are directly assigned a probability of zero by LVC, should be instead considered as prime candidates to be strongly lensed GW pairs, since their separation in time is consistent with observations of time delays in lensed quasars. Correcting for the LVC wrong Bayesian priors, maximum merger rate of conventional mass BBH in 1<z<2, and gravitational lensing time-delay model, reverses the LVC conclusions and supports the strong gravitational lensing hypothesis.

Gravitational lensing probability for the Konus-Wind gamma-ray bursts detected in the triggered mode

Although half a century has passed since the discovery of Gamma-ray bursts (GRBs), there is no evidence for any strongly lensed event. Using GRB luminosity function and GRB formation rate estimates for the Konus-Wind burst sample with known redshifts, and a Singular Isothermal Sphere as a gravitational lens model, we predict the detection rate of both GRB images being ≈ 0.02–0.05 events per year. The result is consistent with the non-detection of lensed bursts in the KW triggered GRB sample.

Quasi-stellar objects acting as potential strong gravitational lenses in the SDSS-III BOSS survey

We present a sample of 12 quasi-stellar objects (QSOs) that potentially act as strong gravitational lenses on background emission line galaxies (ELG) or Lyman-α emitters (LAEs) selected through a systematic search of the 297 301 QSOs in the Sloan Digital Sky Survey (SDSS)-III Data Release 12. Candidates were identified by looking for compound spectra, where emission lines at a redshift larger than that of the quasar can be identified in the residuals after a QSO spectral template is subtracted from the observed spectra. The narrow diameter of BOSS fibers (2″) then ensures that the object responsible for the additional emission lines must lie close to the line of sight of the QSO and hence provides a high probability of lensing. Among the 12 candidates identified, nine have definite evidence for the presence of a background ELG identified by at least four higher-redshift nebular emission lines. The remaining three probable candidates present a strong asymmetrical emission line attributed to a background Lyman-α emitter (LAE). The QSO-ELG (QSO-LAE) lens candidates have QSO lens redshifts in the range 0.24 ≲ zQSO ≲ 0.66 (0.75 ≲ zQSO ≲ 1.23 ) and background galaxy redshifts in the range 0.48 ≲ zS, ELG ≲ 0.94 (2.17 ≲ zS, LAE ≲ 4.48). We show that the algorithmic search is complete at &gt; 90% for QSO-ELG systems, whereas it falls at 40−60% for QSO-LAE, depending on the redshift of the source. Upon confirmation of the lensing nature of the systems, this sample may quadruple the number of known QSOs acting as strong lenses. We have determined the completeness of our search, which allows future studies to compute lensing probabilities of galaxies by QSOs and differentiate between different QSO models. Future imaging of the full sample and lens modelling offers a unique approach to study and constrain key properties of QSOs.

Periodic self-lensing from accreting massive black hole binaries

Nearly 150 massive black hole binary (MBHB) candidates at sub-pc orbital separations have been reported in recent literature. Nevertheless, the definitive detection of even a single such object remains elusive. If at least one of the black holes is accreting, the light emitted from its accretion disc will be lensed by the other black hole for binary orbital inclinations near to the line of sight. This binary self-lensing could provide a unique signature of compact MBHB systems. We show that, for MBHBs with masses in the range 10^6 - 10^10 solar masses and with orbital periods less than ~10 yr, strong lensing events should occur in one to 10s of percent of MBHB systems that are monitored for an entire orbit. Lensing events will last from days for the less massive, shorter period MBHBs up to a year for the most massive ~10 year orbital period MBHBs. At small inclinations of the binary orbit to the line of sight, lensing must occur and will be accompanied by periodicity due to the relativistic Doppler boost. Flares at the same phase as the otherwise average flux of the Doppler modulation would be a smoking gun signature of self-lensing and can be used to constrain binary parameters. For MBHBs with separation >100 Schwarzschild radii, we show that finite-sized source effects could serve as a probe of MBH accretion disc structure. Finally, we stress that our lensing probability estimate implies that ~10 of the known MBHB candidates identified through quasar periodicity should exhibit strong lensing flares.

Baryon effects on the dark matter haloes constrained from strong gravitational lensing

Simulations are expected to be the powerful tool to investigate the baryon effects on dark matter (DM) halos. Recent high resolution, cosmological hydrodynamic simulations (\citealt{Cintio14}, DC14) predict that the inner density profiles of DM halos depend systematically on the ratio of stellar to DM mass ($M_{\ast}/M_{\rm halo}$) which is thought to be able to provide good fits to the observed rotation curves of galaxies. The DC14 profile is fitted from the simulations which are confined to $M_{\rm halo}\le 10^{12}M_{\sun}$, in order to investigate the physical processes that may affect all halos, we extrapolate it to much larger halo mass, including that of galaxy clusters. The inner slope of DC14 profile is flat for low halo mass, it approaches 1 when the halo mass increases towards $10^{12}M_{\sun}$ and decreases rapidly after that mass. We use DC14 profile for lenses and find that it predicts too few lenses compared with the most recent strong lensing observations SQLS (\citealt{Inada12}). We also calculate the strong lensing probabilities for a simulated density profile which continues the halo mass from the mass end of DC14 ($\sim 10^{12}M_{\sun}$) to the mass that covers the galaxy clusters (\citealt{Schaller15}, Schaller15), and find that this Schaller15 model predict too many lenses compared with other models and SQLS observations. Interestingly, Schaller15 profile has no core, however, like DC14, the rotation curves of the simulated halos are in excellent agreement with observational data. Furthermore, we show that the standard two-population model SIS+NFW cannot match the most recent SQLS observations for large image separations.

Testing Models of Quasar Hosts With Strong Gravitational Lensing by Quasar Hosts

Abstract We perform a statistical analysis of strong gravitational lensing by quasar hosts of background galaxies, in the two competing models of dark matter halos of quasars, HOD and CS models. Utilizing the BolshoiP Simulation we demonstrate that strong gravitational lensing provides a potentially very powerful test of models of quasar hosting halos. For quasars at z = 0.5, the lensing probability by quasars of background galaxies in the HOD model is higher than that of the CS model by two orders of magnitude or more for lensing image separations in the range of θ ∼ 1.2 − 12 arcsec. To observationally test this, we show that, as an example, at the depth of the CANDELS wide field survey and with a quasar sample of 1000 at z = 0.5, the two models can be differentiated at 3 − 4σ confidence level. This observational capability is within the reach of HSC and WFIRST Survey.

A NEW NONPLANETARY INTERPRETATION OF THE MICROLENSING EVENT OGLE-2013-BLG-0723

ABSTRACT Recently, the discovery of a Venus-mass planet orbiting a brown-dwarf host in a binary system was reported from the analysis of the microlensing event OGLE-2013-BLG-0723. We reanalyze the event considering the possibility of other interpretations. From this, we find a new solution where the lens is composed of two bodies, in contrast to the three-body solution of the previous analysis. The new solution better explains the observed light curve than the previous solution with Δχ 2 ∼ 202, suggesting that the new solution is a correct model for the event. From the estimation of the physical parameters based on the new interpretation, we find that the lens system is composed of two low-mass stars with ∼0.2 M ⊙ and ∼0.1 M ⊙ and located at a distance of ∼3 kpc. The fact that the physical parameters correspond to those of the most common lens population located at a distance with a large lensing probability further supports the likelihood of the new interpretation. Considering that two dramatically different solutions can approximately explain the observed light curve, the event suggests the need for carefully testing all possible lens-system geometries.

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts (GRBs) trace the high-z Universe, there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe. Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies. Assuming that all halos have the singular isothermal sphere (SIS) mass profile in the mass range $10^{10} h^{-1} M_\odot < M < 2\times 10^{13} h^{-1}M_\odot $ and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample, we calculated the gravitational lensing probability in BATSE, Swift/BAT and Fermi/GBM GRBs, respectively. With an derived probability result in BATSE GRBs, we searched for lensed GRB pairs in the BATSE 5B GRB Spectral catalog. The search did not find any convincing gravitationally lensed events. We discuss our result and future observations for GRB lensing observation.

Gravitational lensing effects on submillimetre galaxy counts

We study the effects on the number counts of submillimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross-section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalization σ8). We show that the ellipticity does not strongly affect the magnification cross-section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two-halo-population model is explored where galaxies are modelled as a singular isothermal sphere profile and clusters as a Navarro, Frenk and White profile. We find that the transition mass between the two has modest effects on the lensing probability. The cosmological parameter σ8 alters the abundance of haloes and therefore affects our results. Compared with other methods, our model is simpler and more realistic. The conclusions of previous works confirm that gravitational lensing is a natural explanation for the number count excess at the bright end.

Accurate modeling of weak lensing with the stochastic gravitational lensing method

We revise and extend the stochastic approach to cumulative weak lensing (hereafter the sGL method) first introduced in Ref. [1]. Here we include a realistic halo mass function and density profiles to model the distribution of mass between and within galaxies, galaxy groups and galaxy clusters. We also introduce a modeling of the filamentary large-scale structures and a method to embed halos into these structures. We show that the sGL method naturally reproduces the weak lensing results for the Millennium Simulation. The strength of the sGL method is that a numerical code based on it can compute the lensing probability distribution function for a given inhomogeneous model universe in a few seconds. This makes it a useful tool to study how lensing depends on cosmological parameters and its impact on observations. The method can also be used to simulate the effect of a wide array of systematic biases on the observable PDF. As an example we show how simple selection effects may reduce the variance of observed PDF, which could possibly mask opposite effects from very large scale structures. We also show how a JDEM-like survey could constrain the lensing PDF relative to a given cosmological model. The updated turboGL code is available at turboGL.org.

Contradiction between strong lensing statistics and a feedback solution to the cusp/core problem

Standard cosmology has many successes on large scales, but faces some fundamental difficulties on small, galactic scales. One such difficulty is the cusp/core problem. High resolution observations of the rotation curves for dark matter dominated low surface brightness (LSB) galaxies imply that galactic dark matter halos have a density profile with a flat central core, whereas N-body structure formation simulations predict a divergent (cuspy) density profile at the center. It has been proposed that this problem can be resolved by stellar feedback driving turbulent gas motion that erases the initial cusp. However, strong gravitational lensing prefers a cuspy density profile for galactic halos. In this paper, we use the most recent high resolution observations of the rotation curves of LSB galaxies to fit the core size as a function of halo mass, and compare the resultant lensing probability to the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). The lensing probabilities based on such density profiles are too low to match the observed lensing in CLASS/JVAS. High baryon densities in the galaxies that dominate the lensing statistics can reconcile this discrepancy, but only if they steepen the mass profile rather than making it more shallow. This places contradictory demands upon the effects of baryons on the central mass profiles of galaxies.

Large-Scale Inhomogeneities May Improve the Cosmic Concordance of Supernovae

We reanalyze the supernova data from the Union Compilation including the weak-lensing effects caused by inhomogeneities. We compute the lensing probability distribution function for each background solution described by the parameters Ω(M), Ω(Λ), and w in the presence of inhomogeneities, approximately modeled with a single-mass population of halos. We then perform a likelihood analysis in the parameter space of Friedmann-Lemaître-Robertson-Walker models and compare our results with the standard approach. We find that the inclusion of lensing can move the best-fit model significantly towards the cosmic concordance of the flat Lambda-Cold Dark Matter model, improving the agreement with the constraints coming from the cosmic microwave background and baryon acoustic oscillations.

SOFT X-RAY EXCESS OF CLUSTERS: A THERMAL FILAMENT MODEL AND THE STRONG LENSING OF BACKGROUND GALAXY GROUPS

The observational and theoretical status of the search for missing cosmological baryons is summarized, with a discussion of some indirect methods of detection. The thermal interpretation of the cluster soft X-ray and EUV excess phenomenon is examined in the context of emission filaments, which are the higher density part of the warm hot intergalactic medium (WHIM) residing at the outskirt of clusters. We derived an analytic radial profile of the soft excess surface brightness using a simple filament model, which provided us a means of observationally constraining the WHIM parameters, especially the total mass budget of warm gas associated with a cluster. We then pointed out a new scenario for soft excess emission, viz. a cluster that can strongly lens the soft X-rays from background WHIM knots. If, as seems quite likely, the missing baryons are mostly in the WHIM halos of galaxy groups, the lensing probability will be quite high ($\sim$ 10 %). This way of accounting for at least part of a cluster's soft excess may also explain the absence of O VII absorption at the redshift of the cluster.

The Impact of Baryonic Cooling on Giant Arc Abundances

Using ray tracing for simple analytic profiles, we demonstrate that the lensing cross section for producing giant arcs has distinct contributions due to arcs formed through image distortion only, and arcs form from the merging of two or three images. We investigate the dependence of each of these contributions on halo ellipticity and on the slope of the density profile, and demonstrate that at fixed Einstein radius, the lensing cross section increases as the halo profile becomes steeper. We then compare simulations with and without baryonic cooling of the same cluster for a sample of six clusters, and demonstrate that cooling can increase the overall abundance of giant arcs by factors of a few. The net boost to the lensing probability for individual clusters is mass dependent, and can lower the effective low-mass limit of lensing clusters. This last effect can potentially increase the number of lensing clusters by an extra 50%. While the magnitude of these effects may be overestimated due to the well-known overcooling problem in simulations, it is evident that baryonic cooling has a nonnegligible impact on the expected abundance of giant arcs, and hence cosmological constraints from giant arc abundances may be subject to large systematic errors.