Quasar Images Research Articles

The abundance of clustered primordial black holes from quasar microlensing

While elementary particles are the favored candidate for the elusive dark matter, primordial black holes (PBHs) have also been considered to fill that role. Gravitational microlensing is a very well-suited tool to detect and measure the abundance of compact objects in galaxies. Previous studies based on quasar microlensing exclude a significant presence of substellar to intermediate-mass black holes (BHs; $ 100M_ However, these studies were based on a spatially uniform distribution of BHs while, according to current theories of PBH formation, they are expected to appear in clusters. We study the impact of clustering in microlensing flux magnification, finding that at large scales clusters act like giant pseudo-particles, strongly affecting the emission coming from the broad-line region, which can no longer be used to define the zero microlensing baseline. As an alternative, we set this baseline from the intrinsic magnification ratios of quasar images predicted by macro lens models and compared them with the observed flux ratios in emission lines, infrared, and radio. The (magnitude) differences are the flux-ratio anomalies attributable to microlensing, which we estimate for 35 image pairs corresponding to 12 lens systems. A Bayesian analysis indicates that the observed anomalies are incompatible with the existence of a significant population of clustered PBHs. Furthermore, we find that more compact clusters exhibit a stronger microlensing impact. Consequently, we conclude that clustering makes the existence of a significant population of BHs in the substellar to intermediate mass range even more unlikely.

Single-epoch and Differential Astrometric Microlensing of Quasars

We propose and discuss a new experimental approach to measure the centroid shift induced by gravitational microlensing in the images of lensed quasars (astrometric microlensing). Our strategy is based on taking the photocenter of a region in the quasar large enough as to be insensitive to microlensing as reference to measure the centroid displacement of the continuum. In this way, single-epoch measurements of astrometric microlensing can be performed. Using numerical simulations, we show that, indeed, the centroid shift monotonically decreases as the size of the emitting region increases, and only for relatively large regions, like the broad line region (BLR), does the centroid shift become negligible. This opens interesting possibilities to study the stratification of the different emitters in the accretion disk and the BLR. We estimate the amplitude of the centroid shifts for 79 gravitationally lensed images and study more thoroughly the special cases Q2237+030 A, RXJ1131-1231 A, PG1115+080 A2, and SDSS J1004+4112 A. We propose to use spectro-astrometry to simultaneously obtain the photocenters of the continuum and of different emission line regions since, with the precision of forthcoming instruments, astrometric microlensing by ∼1 M ⊙ mass microlenses may be detected in many quasar lensed images. When we consider more massive micro/millilenses, M ≳ 10 M ⊙, often proposed as the constituents of dark matter, the BLR becomes sensitive to microlensing and can no longer be used as a positional reference to measure centroid shifts. Differential microlensing between the images of a lensed quasar along several epochs should be used instead.

Size and kinematics of the C IV broad emission line region from microlensing-induced line profile distortions in two gravitationally lensed quasars

Microlensing of the broad emission line region (BLR) in gravitationally lensed quasars produces line profile distortions that can be used to probe the BLR size, geometry, and kinematics. Based on single-epoch spectroscopic data, we analyzed the C IV line profile distortions due to microlensing in two quasars, SDSS J133907.13+131039.6 (J1339) and SDSS J113803.73+031457.7 (J1138), complementing previous studies of microlensing in the quasars Q2237+0305 and J1004+4112. J1339 shows a strong, asymmetric line profile deformation, while J1138 shows a more modest, symmetric deformation, confirming the rich diversity of microlensing-induced spectral line deformations. To probe the C IV BLR, we compared the observed line profile deformations to simulated ones. The simulations are based on three simple BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), of various sizes, inclinations, and emissivities. These models were convolved with microlensing magnification maps specific to the microlensed quasar images, which produced a large number of distorted line profiles. The models that best reproduce the observed line profile deformations were then identified using a Bayesian probabilistic approach. We find that the line profile deformations can be reproduced with the simple BLR models under consideration, with no need for more complex geometries or kinematics. The models with disk geometries (KD and EW) are preferred, while the PW model is definitely less likely. In J1339, the EW model is favored, while the KD model is preferred in Q2237+0305, suggesting that various kinematical models can dominate the C IV BLR. For J1339, we find the C IV BLR half-light radii to be r1/2 = 5.1−2.9+4.6 light-days and r1/2 = 6.7−3.8+6.0 light-days from spectra obtained in 2014 and 2017, respectively. They do agree within uncertainties. For J1138, the amplitude of microlensing is smaller and more dependent on the macro-magnification factor. From spectra obtained in 2005 (single epoch), we find r1/2 = 4.9−2.7+4.9 light-days and r1/2 = 12−8+13 light-days for two extreme values of the macro-magnification factor. Combining these new measurements with those previously obtained for the quasars Q2237+0305 and J1004+4112, we show that the BLR radii estimated from microlensing do follow the C IV radius–luminosity relation obtained from reverberation mapping, although the microlensing radii seem to be systematically smaller, which could indicate either a selection bias or a real offset.

EIGER. V. Characterizing the Host Galaxies of Luminous Quasars at z ≳ 6

Abstract We report JWST/NIRCam measurements of quasar host galaxy emissions and supermassive black hole (SMBH) masses for six quasars at 5.9 < z < 7.1 in the Emission-line galaxies and Intergalactic Gas in the Epoch of Reionization (EIGER) project. We obtain deep NIRCam imaging in the F115W, F200W, and F356W bands, as well as F356W grism spectroscopy of the quasars. We use bright unsaturated stars to construct models of the point-spread functions (PSFs) and estimate the errors of these PSFs. We then measure or constrain the fluxes and morphology of the quasar host galaxies by fitting the quasar images as a point source plus an exponential disk. We successfully detect the host galaxies of three quasars, which have host-to-quasar-flux ratios of ∼1%–5%. Spectral energy distribution fitting suggests that these quasar host galaxies have stellar masses of M * ≳ 1010 M ⊙. For quasars with host galaxy nondetections, we estimate the upper limits of their stellar masses. We use the grism spectra to measure the Hβ line profile and the continuum luminosity, then estimate the SMBH masses for the quasars. Our results indicate that the positive relation between SMBH masses and host galaxy stellar masses already exists at redshift z ≳ 6. The quasars in our sample show a high BH-to-stellar-mass ratio of M BH/M * ∼ 0.15, which is about ∼2 dex higher than local relations. We find that selection effects only contribute partially to the high M BH/M * ratios of high-redshift quasars. This result hints at a possible redshift evolution of the M BH–M * relation.

The missing quasar image in the gravitationally lensed quasar HE0230−2130: Implications for the cored lens mass distribution and dark satellites

Strongly lensed systems with peculiar configurations allow us to probe the local properties of the deflecting lens mass while simultaneously testing general profile assumptions. The quasar HE0230−2130 is lensed by two galaxies at similar redshifts (Δz ∼ 0.003) into four observed images. Using modeled quasar positions from fitting the brightness of the quasar images in ground-based imaging data from the Magellan telescope, we find that lens-mass models where each of these two galaxies is parametrized with a singular power-law (PL) profile predict five quasar images. One of the predicted images is unobserved despite it being distinctively offset from the lensing galaxies and likely bright enough to be observable. This missing image gives rise to new opportunities to study the mass distribution of these galaxies. To interpret the quad configuration of the system, we tested 12 different profile assumptions with the aim of obtaining lens-mass models that correctly predict only four observed images. We tested the effects of adopting: cored profiles for the lensing galaxies; external shear; and additional profiles to represent a dark matter clump. We find that half of our model classes can produce the correct image multiplicity. By comparing the Bayesian evidence of different model parametrizations, we favor two model classes: (i) one that incorporates two singular PL profiles for the lensing galaxies and a cored isothermal sphere in the region of the previously predicted fifth image (rNIS profile), and (ii) one with a bigger lensing galaxy parametrized by a singular PL profile and the smaller galaxy by a cored PL profile with external shear. We estimated the mass of the rNIS clump for each candidate model of our final Markov chain Monte Carlo sample, and find that only 2% are in the range of 106 M⊙ ≤ MrNIS ≤ 109 M⊙, which is the predicted mass range of dark matter subhalos in cold dark matter simulations, or the mass of dark-matter-dominated and low-surface-brightness galaxies. We therefore favor the models with a cored mass distribution for the lens galaxy close to the predicted fifth image. Our study further demonstrates that lensed quasar images are sensitive to the dark matter structure in the gravitational lens. We are able to describe this exotic lensing configuration with relatively simple models, which demonstrates the power of strong lensing for studying galaxies and lens substructure.

Apparent correlation between extrinsic and intrinsic flux variations in the first gravitationally lensed quasar

ABSTRACT To better understand which sources contribute to optical passband fluxes of Q0957+561, we present and analyse light curves of the doubly imaged gravitationally lensed quasar from its discovery to 2023. After an early microlensing event, the difference light curves (describing delay-corrected flux ratios between the two quasar images) only show prominent microlensing gradients over the last 17 yr. In addition to these long time-scale gradients in the gr bands, we detect short time-scale, extrinsically induced differential variations that are highly correlated with the short time-scale intrinsic variability of the quasar in those bands. Both the accretion disc and the broad emission-line region (BELR) contribute to optical passband fluxes, and we also show that realistic contributions of the BELR account for the observed correlations in the gr bands. We would like to highlight that the BELR sources of optical passband fluxes of Q0957+561 should be taken into account when measuring accretion-disc source sizes from microlensing simulations.

Quasar Microlensing Statistics and Flux-ratio Anomalies in Lens Models

Precise lens modeling is a critical step in time delay studies of multiply imaged quasars, which are key for measuring some important cosmological parameters (especially H 0). However, lens models (in particular those semi-automatically generated) often show discrepancies with the observed flux ratios between the different quasar images. These flux-ratio anomalies are usually explained through differential effects between images (mainly microlensing) that alter the intrinsic magnification ratios predicted by the models. To check this hypothesis, we collect direct measurements of microlensing to obtain the histogram of microlensing magnifications. We compare this histogram with recently published model flux-ratio anomalies and conclude that they cannot be statistically explained by microlensing. The average value of the model anomalies (0.74 mag) significantly exceeds the mean impact of microlensing (0.33 mag). Moreover, the histogram of model anomalies presents a significant tail with high anomalies (∣Δm∣ ≥ 0.7 mag), which is completely unexpected from the statistics of microlensing observations. Microlensing simulations neither predict the high mean nor the fat tail of the histogram of model anomalies. We perform several statistical tests which exclude that microlensing can explain the observed flux-ratio anomalies (although Kolmogorov–Smirnov, which is less sensitive to the tail of the distributions, is not always conclusive). Thus, microlensing cannot statistically explain the bulk of flux-ratio anomalies, and models may explore different alternatives to try to reduce them. In particular, we propose to complement photometric observations with accurate flux ratios of the broad emission lines obtained from integral field spectroscopy to check and, ideally, constrain lens models.

Extrapolating the projected potential of gravitational lens models: property-preserving degeneracies

ABSTRACT While gravitational lens inversion holds great promise to reveal the structure of the light-deflecting mass distribution, both light and dark, the existence of various kinds of degeneracies implies that care must be taken when interpreting the resulting lens models. This article illustrates how thinking in terms of the projected potential helps to gain insight into these matters. Additionally it is shown explicitly how, when starting from a discretized version of the projected potential of one particular lens model, the technique of quadratic programming can be used to create a multitude of equivalent lens models that preserve all or a subset of lens properties. This method is applied to a number of scenarios, showing the lack of grasp on the mass outside the strong lensing region, revisiting mass redistribution in between images, and applying this to a recent model of the SDSS J1004+4112 cluster, as well as illustrating the generalized mass sheet degeneracy and source-position transformation. In the case of J1004, we show that this mass redistribution did not succeed at completely eliminating a dark mass clump recovered by grale near one of the quasar images.

Improving the light curves of gravitationally lensed quasars with Gaia proper motion data

Aims. We show how to significantly improve difference image analysis (DIA) of gravitationally lensed quasars over long periods of time using Gαία proper motions. Methods. DIA requires the subtraction of a reference image from the individual images of a monitoring campaign, using stars in the field to align the images. Since the proper motion of the stars can be of the same order as the pixel size during a several-year campaign, we use Gaia DR3 proper motions to enable a correct image alignment. The proper motion corrected star positions can be aligned by the ISIS package. DIA is carried out using the HOTPAnTS package. We apply point spread function (PSF) photometry to obtain light curves and add a proper motion correction of the PSF star to GALFIT. Results. We apply our method to the light curves of the three gravitationally lensed quasars HE1104-1805, HE2149-2745 and Q2237+0305 in the R and V band, respectively, obtained using 1 m telescopes of the Las Cumbres Observatory from 2014 to 2022. We show that the image alignment and the determination of the lensed quasar positions is significantly improved by this method. The light curves of individual quasar images display intrinsic quasar variations and are affected by chromatic microlensing.

Probing coherence in metal absorption towards multiple images of strong gravitationally lensed quasars

ABSTRACT We present a tomographic analysis of metal absorption lines arising from the circumgalactic medium (CGM) of galaxies at z ≈ 0.5–2, using Multi Unit Spectroscopic Explorer (MUSE) observations of two background quasars at z ≈ 2.2 and 2.8, which are two of the few currently known quasars with multiple images due to strong gravitational lensing by galaxy clusters at z ≈ 0.6 and 0.5, respectively. The angular separations between different pairs of quasar multiple images enable us to probe the absorption over transverse physical separations of ≈0.4–150 kpc, which are based on strong lensing models exploiting MUSE observations. The fractional difference in rest-frame equivalent width (ΔWr) of Mg ii, Fe ii, and C iv absorption increases on average with physical separation, indicating that the metal-enriched gaseous structures become less coherent with distance, with a likely coherence length-scale of ≈10 kpc. However, ΔWr for all the ions vary considerably over ≈0.08–0.9, indicating a clumpy CGM over the full range of length-scales probed. At the same time, paired Mg ii absorption is detected across ≈100–150 kpc at similar line-of-sight velocities, which could be probing cool gas clouds within the same halo. No significant dependence of ΔWr is found on the equivalent width and redshift of the absorbing gas and on the galaxy environment associated with the absorption. The high-ionization gas phase traced by C iv shows a higher degree of coherence than the low-ionization gas phase traced by Mg ii, with ≈90 per cent of C iv systems exhibiting ΔWr ≤ 0.5 at separations ≤10 kpc compared to ≈50 per cent of Mg ii systems.

Free-form and hybrid lens models for SDSS J1004+4112: substructure and central image time delay constraints

ABSTRACT SDSS J1004+4112 is a well-studied gravitational lens with a recently measured time delay between its first and fourth arriving quasar images. Using this new constraint, we present updated free-form lens reconstructions using the lens inversion method grale, which only uses multiple image and time delay data as inputs. In addition, we obtain hybrid lens reconstructions by including a model of the brightest cluster galaxy as a Sersic lens. For both reconstructions, we use two sets of images as input: one with all identified images, and the other a revised set leaving out images that have been potentially misidentified. We also develop a source position optimization Markov chain Monte Carlo (MCMC) routine, performed on completed grale runs, that allows each model to better match observed image positions and time delays. All the reconstructions produce similar mass distributions, with the hybrid models finding a steeper profile in the centre. Similarly, all the mass distributions are fitted by the Navarro–Frenk–White profile, finding results consistent with previous parametric reconstructions and those derived from Chandra X-ray observations. We identify an ∼5 × 1011 M⊙ substructure apparently unaffiliated with any cluster member galaxy and present in all our models, and study its reality. Using our free-form and hybrid models, we predict a central quasar image time delay of ∼2980 ± 270 and ∼3280 ± 215 d, respectively. A potential future measurement of this time delay will, while being an observational challenge, further constrain the steepness of the central density profile.

Survey of gravitationally lensed objects in HSC imaging (SuGOHI) – IX. Discovery of strongly lensed quasar candidates

ABSTRACT We report the discovery of new lensed quasar candidates in the imaging data of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Data Release 4, covering $1\, 310\deg ^2$ of the sky with median seeing in the i band of ≈0.6 arcsec. In addition to two catalogues of Million Quasars Catalog v7.2 and AllWISE Catalog of Mid-Infra Red Active Galactic Nuclei, containing confirmed and candidate quasars, we preselect quasar sources using colour cuts from the HSC (grizy) and unWISE (W1 + W2) photometric data based on SDSS spectroscopic catalogues. We search for the presence of multiple point sources with similar colour through the convolution of the Laplacian of the preselected quasar image cutouts with the Laplacian of the point spread function, resulting in a reduction of lens candidates from 1 652 329 to 121 511 (7.4 per cent). After visual binary classification, we grade 6 199 (0.4 per cent) potential lenses on a scale of 0 to 3, with 3 indicating a lens and 0 indicating a non-lens. Finally we obtain 162 lens candidates with an average grade of ≥2, and among them, we successfully recover 18 known lenses. By fitting the light distribution and removing the known contaminants, we discover that 57 new systems contain at least two point sources and a galaxy in between, including 10 possible quadruply lensed quasars. This new sample exhibits a median separation of 1.26 arcsec and a magnitude limit of i ≈ 22. Spectroscopic or high-resolution imaging follow up on these newly discovered lensed quasar candidates will further allow their natures to be confirmed.

Andromeda’s Parachute: Time Delays and Hubble Constant

The gravitational lens system PS J0147+4630 (Andromeda’s Parachute) consists of four quasar images ABCD and a lensing galaxy. We obtained r-band light curves of ABCD in the 2017−2022 period from monitoring with two 2 m class telescopes. Applying state-of-the-art curve-shifting algorithms to these light curves led to measurements of time delays between images, and the three independent delays relative to image D are accurate enough to be used in cosmological studies (uncertainty of about 4%): Δt AD = −170.5 ± 7.0, Δt BD = −170.4 ± 6.0, and Δt CD = −177.0 ± 6.5 days, where image D is trailing all the other images. Our finely sampled light curves and some additional fluxes in the years 2010−2013 also demonstrated the presence of significant microlensing variations. From the measured delays relative to image D and typical values of the external convergence, recent lens mass models yielded a Hubble constant that is in clear disagreement with currently accepted values around 70 km s−1 Mpc−1. We discuss how to account for a standard value of the Hubble constant without invoking the presence of an extraordinary high external convergence.

DPQP: A Detection Pipeline for Quasar Pair Candidates Based on QSO Photometric Images and Spectra

Quasars have an important role in the studies of galaxy evolution and star formation. The rare close projection of two quasars in the sky allows us to study the environment and matter exchange around the foreground quasar (QSOfg) and the background quasar (QSObg). This paper proposes a pipeline DPQP for quasar pair (QP) candidates’ detection based on photometric images and the corresponding spectra. The pipeline consists of three main parts: a target source detector, a regressor, and a discriminator. In the first part, the target source detection network–YOLOv4 (TSD-YOLOv4) and the target source classification network (TSCNet) are used in sequence to detect quasars in SDSS photometric images. In the second part, a depth feature extraction network of quasar images (DE-QNet) is constructed to estimate the redshifts of quasars from photometric images. In the third part, a quasar pair score (Q-Score) metric is proposed based on the spectral analysis. The larger the Q-Score, the greater the possibility of two pairs being a quasar pair. The experimental results show that between redshift 1.0 and 4.0, the MAE of DE-QNet is 0.316, which is 16.1% lower than the existing method. Samples with |Δz| < 0.15 account for 77.1% of the test dataset. A new table with 1025 QP candidates is provided by traversing 50,000 SDSS photometric images.

COOL-LAMPS. Discovery of COOL J0335−1927, a Gravitationally Lensed Quasar at z = 3.27 with an Image Separation of 23.″3

We report the discovery of COOL J0335−1927, a quasar at z = 3.27 lensed into three images with a maximum separation of 23.″3 by a galaxy cluster at z = 0.4178. To date, this is the highest redshift wide-separation lensed quasar known. In addition, COOL J0335−1927 shows several strong intervening absorbers visible in the spectra of all three quasar images with varying equivalent widths. The quasar also shows mini-broad line absorption. We construct a parametric strong gravitational lens model using ground-based imaging, constrained by the redshift and positions of the quasar images as well as the positions of three other multiply imaged background galaxies. Using our best-fit lens model, we calculate the predicted time delays between the three quasar images to be Δt AB = (stat) and Δt AC = (stat) days. Folding in systematic uncertainties, the model-predicted time delays are within the ranges 240 < Δt AB < 700 and −300 < Δt AC < −30. We also present g-band photometry from archival Dark Energy Camera Legacy Survey and Pan-STARRS imaging, and new multi-epoch observations obtained between 2022 September 18 UT and 2023 February 22 UT, which demonstrate significant variability in the quasar and will eventually enable the measurement of the time delay between the three quasar images. The currently available light curves are consistent with the model-predicted time delays. This is the fifth paper from the COOL-LAMPS collaboration.

COOL–LAMPS. III. Discovery of a 25.″9 Separation Quasar Lensed by a Merging Galaxy Cluster* * This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile, and the 2.5 m Nordic Optical Telescope located at Rocque de los Muchachos Observatory, La Palma.

In the third paper from the COOL–LAMPS Collaboration, we report the discovery of COOL J0542-2125, a gravitationally lensed quasar at z = 1.84, observed as three images due to an intervening massive galaxy cluster at z = 0.61. The lensed quasar images were identified in a search for lens systems in recent public optical imaging data and have separations on the sky up to 25.″9, wider than any previously known lensed quasar. The galaxy cluster acting as a strong lens appears to be in the process of merging, with two subclusters separated by ∼1 Mpc in the plane of the sky, and their central galaxies showing a radial velocity difference of ∼1000 km s−1. Both cluster cores show strongly lensed images of an assortment of background sources, as does the region between them. A preliminary strong lens model implies masses of and for the east and west subclusters, respectively. This line of sight is also coincident with an ROSAT ALL-sky Survey source, centered between the two confirmed cluster halos reminiscent of other major cluster-scale mergers. Archival and new follow-up imaging show flux variability in the quasar images of up to 0.4 mag within ∼1 yr, and new multicolor imaging data reveal a 2σ detection of the underlying quasar host. A lens system with this configuration offers rare opportunities for a range of future studies of both the lensed quasar and its host and the foreground cluster merger causing the lensing.

Stellar mass fraction and quasar accretion disk size in SDSS J1004+4112 from photometric follow-up

AbstractThe gravitational lens SDSS J1004+4112 was the first discovered system where a background quasar is lensed by a galaxy cluster instead of a single galaxy. We use the 14.5-year r-band light curves together with the recently measured time delay of the fourth brightest quasar image (Munõz et al. (2022)) and the mass model from Forés-Toribio et al. (2022) to study the microlensing effect in this system. We constrain the quasar accretion disk size to light-days at 2407Å in the restframe which is compatible with most previous estimates. We also infer the fraction of mass in stars at the positions of the quasar images: $${\alpha _A} = 0.058_{ - 0.032}^{ + 0.024},{\alpha _B} = 0.048_{ - 0.014}^{ + 0.032},{\alpha _C} = 0.018_{ - 0.018}^{ + 0.015}$$ and $${\alpha _D} = 0.008_{ - 0.008}^{ + 0.033}$$ . The stellar fraction estimates are reasonable for intracluster medium although the stellar fractions at images A and B are slightly larger, suggesting the presence of a near undetected galaxy.

The Longest Delay: A 14.5 yr Campaign to Determine the Third Time Delay in the Lensing Cluster SDSS J1004+4112

We present new light curves for the four bright images of the five image cluster-lensed quasar gravitational lens system SDSS J1004+4112. The light curves span 14.5 yr and allow the measurement of the time delay between the trailing bright quasar image D and the leading image C. When we fit all four light curves simultaneously and combine the models using the Bayesian information criterion, we find a time delay of Δt DC = 2458.47 ± 1.02 days (6.73 yr), the longest ever measured for a gravitational lens. For the other two independent time delays we obtain Δt BC = 782.20 ± 0.43 days (2.14 yr) and Δt AC = 825.23 ± 0.46 days (2.26 yr), in agreement with previous results. The information criterion is needed to weight the results for light curve models with different polynomial orders for the intrinsic variability and the effects of differential microlensing. The results using the Akaike information criterion are slightly different, but, in practice, the absolute delay errors are all dominated by the ∼4% cosmic variance in the delays rather than the statistical or systematic measurement uncertainties. Despite the lens being a cluster, the quasar images show slow differential variability due to microlensing at the level of a few tenths of a magnitude.

A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints from the Third Time Delay

We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster (ρ ∝ r −α ) allowing us to determine at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy and the dark matter halo of kpc at 68% (95%) confidence which is compatible with other galaxy cluster measurements. As an observational challenge, the estimated time delay between the leading image C and the faint (I = 24.7) fifth image E is roughly 8 yr.

Probing Spacetime Foam with Extragalactic Sources of High-Energy Photons

Quantum fluctuations can endow spacetime with a foamy structure. In this review article, we discuss our various proposals to observationally constrain models of spacetime foam. One way is to examine if the light wave-front from a distant quasar or GRB can be noticeably distorted by spacetime-foam-induced phase incoherence. As the phase fluctuations are proportional to the distance to the source but inversely proportional to the wavelength, ultra-high energy photons (&gt;1 TeV) from distant sources are particularly useful. We elaborate on several proposals, including the possibility of detecting spacetime foam by observing “seeing disks” in the images of distant quasars and active galactic nuclei. We also discuss the appropriate distance measure for calculating the expected angular broadening. In addition, we discuss our more recent work in which we investigate whether wave-front distortions on small scales (due to spacetime foam) can cause distant objects become undetectable because the phase fluctuations have accumulated to the point at which image formation is impossible. Another possibility that has recently become accessible is to use interferometers to observe cosmologically distant sources, thereby giving a large baseline perpendicular to the local wave vector over which the wave front could become corrugated and thus distorted, reducing or eliminating its fringe visibility. We argue that all these methods ultimately depend on the availability of ways (if any) to carry out proper averaging of contributions from different light paths from the source to the telescope.