arXiv subjects

Liliya L. R. Williams

Publications and source records attributed to Liliya L. R. Williams.

At least 37 records · Page 2Linked to original sources

arXiv2024

Dark Matter distinguished by skewed microlensing in the "Dragon Arc"

Microlensed stars recently discovered by JWST & HST follow closely the winding critical curve of A370 along all sections of the ``Dragon Arc" traversed by the critical curve. These transients are fainter than $m_{AB}>26.5$, corresponding to the Asymptotic Giant Branch (AGB) and microlensed by diffuse cluster stars observed with $\simeq 18M_\odot/pc^2$, or about $\simeq 1$\% of the projected dark matter density. Most microlensed stars appear along the inner edge of the critical curve, following an asymmetric band of width $\simeq 4$kpc that is skewed by $-0.7\pm0.2$kpc. Some skewness is expected as the most magnified images should form along the inner edge of the critical curve with negative parity, but the predicted shift is small $\simeq -0.04$kpc and the band of predicted detections is narrow, $\simeq 1.4$kpc. Adding CDM-like dark halos of $10^{6-8}M_\odot$ broadens the band as desired but favours detections along the outer edge of the critical curve, in the wrong direction, where sub-halos generate local Einstein rings. Instead, the interference inherent to ``Wave Dark Matter" as a Bose-Einstein condensate ($ψ$DM) forms a symmetric band of critical curves that favours negative parity detections. A de Broglie wavelength of $\simeq 10$pc matches well the observed $4$kpc band of microlenses and predicts negative skewness $\simeq -0.6$kpc, similar to the data. The implied corresponding boson mass is $\simeq 10^{-22}$eV, in good agreement with estimates from dwarf galaxy cores when scaled by momentum. Further JWST imaging may reveal the pattern of critical curves by simply ``joining the dots" between microlensed stars, allowing wave corrugations of $ψ$DM to be distinguished from CDM sub-halos

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arXiv2024

Imaging dark matter at the smallest scales with $z\approx1$ lensed stars

Observations of caustic-crossing galaxies at redshift $0.7 2$ and the number density of events is greater around substructureand the number density of events is greater around substructures, and (ii) negative imaging regime where $β<2$. We study the particular case of seven microlensing events found by HST in the Dragon arc (at z=0.725). We find that a population of supergiant stars with a steep LF with $β=2.55$ fits the distribution of these events. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of $\sim 1.3 \times 10^8\,\Msun$ (within its Einstein radius).

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arXiv2024

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

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 discretised 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 generalised 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.

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arXiv2024

Essentials of strong gravitational lensing

Of order one in 10^3 quasars and high-redshift galaxies appears in the sky as multiple images as a result of gravitational lensing by unrelated galaxies and clusters that happen to be in the foreground. While the basic phenomenon is a straightforward consequence of general relativity, there are many non-obvious consequences that make multiple-image lensing systems (aka strong gravitational lenses) remarkable astrophysical probes in several different ways. This article is an introduction to the essential concepts and terminology in this area, emphasizing physical insight. The key construct is the Fermat potential or arrival-time surface: from it the standard lens equation, and the notions of image parities, magnification, critical curves, caustics, and degeneracies all follow. The advantages and limitations of the usual simplifying assumptions (geometrical optics, small angles, weak fields, thin lenses) are noted, and to the extent possible briefly, it is explained how to go beyond these. Some less well-known ideas are discussed at length: arguments using wavefronts show that much of the theory carries over unchanged to the regime of strong gravitational fields; saddle-point contours explain how even the most complicated image configurations are made up of just two ingredients. Orders of magnitude, and the question of why strong lensing is most common for objects at cosmological distance, are also discussed. The challenges of lens modeling, and diverse strategies developed to overcome them, are discussed in general terms, without many technical details.

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arXiv2023

Flashlights: Properties of Highly Magnified Images Near Cluster Critical Curves in the Presence of Dark Matter Subhalos

Dark matter subhalos with extended profiles and density cores, and globular stars clusters of mass $10^6-10^8 M_\odot$, that live near the critical curves in galaxy cluster lenses can potentially be detected through their lensing magnification of stars in background galaxies. In this work we study the effect such subhalos have on lensed images, and compare to the case of more well studied microlensing by stars and black holes near critical curves. We find that the cluster density gradient and the extended mass distribution of subhalos are important in determining image properties. Both lead to an asymmetry between the image properties on the positive and negative parity sides of the cluster that is more pronounced than in the case of microlensing. For example, on the negative parity side, subhalos with cores larger than about $50\,$pc do not generate any images with magnification above $\sim 100$ outside of the immediate vicinity of the cluster critical curve. We discuss these factors using analytical and numerical analysis, and exploit them to identify observable signatures of subhalos: subhalos create pixel-to-pixel flux variations of $\gtrsim 0.1$ magnitudes, on the positive parity side of clusters. These pixels tend to cluster around (otherwise invisible) subhalos. Unlike in the case of microlensing, signatures of subhalo lensing can be found up to $1''$ away from the critical curves of massive clusters.

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arXiv2023

Free-Form and Hybrid Lens Models for SDSS J1004+4112: Substructure and Central Image Time Delay Constraints

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 {\tt 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 (BCG) 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 MCMC routine, performed on completed {\tt 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 center. Similarly, all the mass distributions are fit by the Navarro-Frenk-White (NFW) profile, finding results consistent with previous parametric reconstructions and those derived from Chandra X-ray observations. We identify a $\sim 5 \times 10^{11} M_{\odot}$ 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 $\sim 2980 \pm 270$ and $\sim 3280 \pm 215$ days, respectively. A potential future measurement of this time delay will, while being an observational challenge, further constrain the steepness of the central density profile.

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arXiv2023

What Multiple Images Say About the Large-Scale Mass Maps of Galaxy Clusters

All lens modeling methods, simply-parametrized, hybrid, and free-form, use assumptions to reconstruct galaxy clusters with multiply imaged sources, though the nature of these assumptions (priors) can differ considerably between methods. This raises an important question in strong lens modeling: how much information about the mass model comes from the lensed images themselves, and how much is a consequence of model priors. One way to assess the relative contributions of the lensing data vs. model priors is to estimate global lens properties through images alone, without any prior assumptions about the mass distribution. This is our approach. We use 200 mock cluster lenses, half of which have substructures which vary from clumpy and compact to smooth and extended; a simulated cluster Ares; and real clusters Abell 1689 and RXJ1347.5-1145 to show that the center, ellipticity, and position angle can be estimated quite well, and nearly perfectly for weakly substructured clusters, implying that the recovery of these properties is largely driven by the images, not priors. However, the correlation between the true and image-estimated amount of substructure has a lot of scatter, suggesting that multiple images do not uniquely constrain substructure. Therefore in general, lens model priors have a stronger effect on smaller scales. Our analysis partly explains why reconstructions using different methodologies can produce qualitatively different mass maps on substructure scales. Our analysis is not meant to aide or replace lens inversion methods, but only to investigate what cluster properties are constrained with multiple images.

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arXiv2023

An excursion into the core of the cluster lens Abell 1689

Abell 1689 is a well studied cluster of galaxies and one of the largest gravitational lens systems ever observed. We have obtained a reconstruction of the cluster Abell 1689 using Grale, a free-form lens inversion method that relies exclusively on the multiple image data. Non-inclusion of any data related to cluster member galaxies ensures an unbiased measure of the mass distribution, which is the most notable feature of free-form methods like Grale. We used two different sets of multiple image systems from the available strong lensing data - one containing only the secure systems (107 images), and the other containing all available systems, only excluding some very non-secure systems (151 images). For the very well-constrained central $\sim$100 kpc region of the cluster we made detailed comparison of the Grale reconstructed lensing mass and stellar mass retrieved by the Spectral Energy Distribution (SED) fitting software FAST++. We found a light-unaccompanied mass peak in this region, whose existence, while tentative, is favored by the distribution of nearby images that are local maxima in the Fermat potential. However, further tests, using different methodologies are needed to confirm the reality of this feature. If it shown to be real, this light-unaccompanied mass peak is consistent with dark matter self-interaction cross-section $σ\lesssim 1$cm$^2$/g, while being in tension with larger cross-sections.

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arXiv2023

Constraints on the Inner Regions of Lensing Galaxies from Central Images using a Recent AGN Offset Distribution

In gravitational lensing, central images in quads can serve as a powerful probe of the inner regions of lens galaxies. The presence of an offset central supermassive black hole (SMBH) has the potential to distort the time-delay surface in a way such that 3 central images form: a strongly de-magnified image near the SMBH, and two less de-magnified (and potentially observable) images at a central maximum and saddle point. Using a quad lens macro model, we simulate the constraints that could be placed on various lens galaxy parameters based on their central images probability of detection or non-detection. Informed by a recent low-redshift distribution of off-nucleus AGN, we utilize Bayesian inference to constrain the mean SMBH off-nucleus distance and galactic core radius for a sample of 6 quads. In general, we find that a detection of the central image in any quad would favor larger SMBH off-nucleus distances and galaxy core sizes. Assuming a linear relationship between core radii and velocity dispersion $r_c = bσ$, these results similarly imply strong constraints on $b$, where the likely case of a central image non-detection in each quad constraining $b$ to $3.11^{+2.72}_{-2.26} \times 10^{-4}$ kpc km$^{-1}$ s. Our results show that tight constraints on lens galaxy parameters can be made regardless of a detection or non-detection of a central image. Therefore, we recommend observational searches for the central image, possibly using our suggested novel detection technique in UV filters, to formalize stronger constraints on lens galaxy parameters.

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arXiv2023

Flashlights: An Off-Caustic Lensed Star at Redshift $z$ = 1.26 in Abell 370

We report the discovery of a transient seen in a strongly lensed arc at redshift $z_{\rm s}=1.2567$ in \emph{Hubble Space Telescope} imaging of the Abell 370 galaxy cluster. The transient is detected at $29.51\pm0.14$ AB mag in a WFC3/UVIS F200LP difference image made using observations from two different epochs, obtained in the framework of the \emph{Flashlights} program, and is also visible in the F350LP band ($m_{\rm F350LP} \approx 30.53\pm0.76$ AB mag). The transient is observed on the negative-parity side of the critical curve at a distance of $\sim 0.6"$ from it, greater than previous examples of lensed stars. The large distance from the critical curve yields a significantly smaller macromagnification, but our simulations show that bright, O/B-type supergiants can reach sufficiently high magnifications to be seen at the observed position and magnitude. In addition, the observed transient image is a trailing image with an observer-frame time delay of $\sim+0.8$ days from its expected counterpart, so that any transient lasting for longer than that should have also been seen on the minima side and is thus excluded. This, together with the blue colour we measure for the transient ($m_{\rm F200LP} - m_{\rm F350LP} \approx [-0.3,-1.6]$ AB), rules out most other transient candidates such as (kilo)novae, for example, and makes a lensed star the prime candidate. Assuming the transient is indeed a lensed star as suggested, many more such events should be detected in the near future in cluster surveys with the \emph{Hubble Space Telescope} and \emph{James Webb Space Telescope}.

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arXiv2022

Flashlights: More than A Dozen High-Significance Microlensing Events of Extremely Magnified Stars in Galaxies at Redshifts z=0.7-1.5

Once only accessible in nearby galaxies, we can now study individual stars across much of the observable universe aided by galaxy-cluster gravitational lenses. When a star, compact object, or multiple such objects in the foreground galaxy-cluster lens become aligned, they can magnify a background individual star, and the timescale of a magnification peak can limit its size to tens of AU. The number and frequency of microlensing events therefore opens a window into the population of stars and compact objects, as well as high-redshift stars. To assemble the first statistical sample of stars in order to constrain the initial mass function (IMF) of massive stars at redshift z=0.7-1.5, the abundance of primordial black holes in galaxy-cluster dark matter, and the IMF of the stars making up the intracluster light, we are carrying out a 192-orbit program with the Hubble Space Telescope called "Flashlights," which is now two-thirds complete owing to scheduling challenges. We use the ultrawide F200LP and F350LP long-pass WFC3 UVIS filters and conduct two 16-orbit visits separated by one year. Having an identical roll angle during both visits, while difficult to schedule, yields extremely clean subtraction. Here we report the discovery of more than a dozen bright microlensing events, including multiple examples in the famous "Dragon Arc" discovered in the 1980s, as well as the "Spocks" and "Warhol" arcs that have hosted already known supergiants. The ultradeep observer-frame ultraviolet-through-optical imaging is sensitive to hot stars, which will complement deep James Webb Space Telescope infrared imaging. We are also acquiring Large Binocular Telescope LUCI and Keck-I MOSFIRE near-infrared spectra of the highly magnified arcs to constrain their recent star-formation histories.

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arXiv2022

Statistical Mechanics of Collisionless Orbits. V. The approach to equilibrium for idealized self-gravitating systems

Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exist. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, $n(E) \propto \exp (-β(E-Φ_0))-1$, known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark-matter halos with central cusps, $ρ\sim r^{-1}$, and outer parts, $ρ\sim r^{-4}$. Here we define a non-equilibrium functional, $S_D$, which is maximized for DARKexp and increases monotonically during the evolution towards equilibrium of idealized collisionless systems of the Extended Spherical Infall Model. Systems that undergo more mixing more closely approach DARKexp.

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arXiv2021

Bridging the Gap Between Simply Parametrized and Free-Form Pixelated Models of Galaxy Lenses: The Case of WFI 2033-4723 Quad

We study the radial and azimuthal mass distribution of the lensing galaxy in WFI2033-4723. Mindful of the fact that modeling results depend on modeling assumptions, we examine two very different recent models: simply parametrized (SP) models from the H0LiCOW collaboration, and pixelated free-form (FF) GLASS models. In addition, we fit our own models which are a compromise between the astrophysical grounding of SP, and the flexibility of FF approaches. Our models consist of two offset parametric mass components, and generate many solutions, all fitting the quasar point image data. Among other results, we show that to reproduce point image properties the lensing mass must be lopsided, but the origin of this asymmetry can reside in the main lens plane or along the line of sight. We also show that there is a degeneracy between the slope of the density profile and the magnitude of external shear, and that the models from various modeling approaches are connected not by the mass sheet degeneracy, but by a more generalized transformation. Finally, we discuss interpretation degeneracy which afflicts all mass modeling: inability to correctly assign mass to the main lensing galaxy vs. nearby galaxies or line of sight structures. While this may not be a problem for the determination of $H_0$, interpretation degeneracy may become a major issue for the detailed study of galaxy structure.

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arXiv2021

Further support for a trio of mass-to-light deviations in Abell 370: free-form Grale lens inversion using BUFFALO strong lensing data

We use the Beyond Ultra-deep Frontier Fields and Legacy Observations (BUFFALO) strong lensing image catalog of the merging galaxy cluster Abell 370 to obtain a mass model using the free-form lens inversion algorithm GRALE. The improvement of the strong lensing data quality results in a lens plane rms of only 0.45 arcsec, about a factor of two lower than that of our existing HFF v4 reconstruction. We attribute the improvement to spectroscopic data and use of the full reprocessed HST mosaics. In our reconstructed mass model, we found indications of three distinct mass features in Abell 370: (i) a $\sim 35$ kpc offset between the northern BCG and the nearest mass peak, (ii) a $\sim 100$ kpc mass concentration of roughly critical density $\sim 250$ kpc east of the main cluster, and (iii) a probable filament-like structure passing N-S through the cluster. While (i) is present in some form in most publicly available reconstructions spanning the range of modeling techniques: parametric, hybrid, and free-form, (ii) and (iii) are recovered by only about half of the reconstructions. We tested our hypothesis on the presence of the filament-like structure by creating a synthetic cluster - Irtysh IIIc - mocking the situation of a cluster with external mass. We also computed the source plane magnification distributions. Using them we estimated the probabilities of magnifications in the source plane, and scrutinized their redshift dependence. Finally, we explored the lensing effects of Abell 370 on the luminosity functions of sources at $z_s=9.0$, finding it consistent with published results.

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arXiv2021

Galaxy-lens determination of $H_0$: the effect of the ellipse+shear modeling assumption

Galaxy lenses are frequently modeled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are inconsistent with these assumptions, and require a dipole-like contribution to the mass with respect to the light. Simplifying assumptions about the shape of mass distributions can lead to the incorrect recovery of parameters such as $H_0$. We create several tests of synthetic quad populations with different deviations from an elliptical shape, then fit them with an ellipse+shear model, and measure the recovered values of $H_0$. Kinematic constraints are not included. We perform two types of fittings -- one with a single point source and one with an array of sources emulating an extended source. We carry out two model-free comparisons between our mock quads and the observed population. One result of these comparisons is a statistical inconsistency not yet mentioned in the literature: the image distance ratios with respect to the lens center of observed quads appear to span a much wider range than those of synthetic or simulated quads. Bearing this discrepancy in mind, our mock populations can result in biases on $H_0$ $\sim10\%$.

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arXiv2021

The Hubble constant from eight time-delay galaxy lenses

We present a determination of the Hubble constant from the joint, free-form analysis of 8 strongly, quadruply lensing systems. In the concordance cosmology, we find $H_0 = 71.8^{+3.9}_{-3.3}\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ with a precision of $4.97\%$. This is in agreement with the latest measurements from Supernovae Type Ia and Planck observations of the cosmic microwave background. Our precision is lower compared to these and other recent time-delay cosmography determinations, because our modelling strategies reflect the systematic uncertainties of lensing degeneracies. We furthermore are able to find reasonable lensed image reconstructions by constraining to either value of $H_0$ from local and early Universe measurements. This leads us to conclude that current lensing constraints on $H_0$ are not strong enough to break the "Hubble tension" problem of cosmology.

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arXiv2020

Galaxy-lens determination of $H_0$: constraining density slope in the context of the mass sheet degeneracy

Gravitational lensing offers a competitive method to measure $H_0$ with the goal of 1% precision. A major obstacle comes in the form of lensing degeneracies, such as the mass sheet degeneracy (MSD), which make it possible for a family of density profiles to reproduce the same lensing observables but return different values of $H_0$. The modeling process artificially selects one choice from this family, potentially biasing $H_0$. The effect is more pronounced when the profile of a given lens is not perfectly described by the lens model, which will always be the case to some extent. To explore this, we quantify the bias and spread in $H_0$ by creating quads from two-component mass models and fitting them with a power-law ellipse+shear model. We find that the bias does not correspond to the estimate one would calculate by transforming the profile into a power law near the image radius. We also emulate the effect of including stellar kinematics by performing fits where the slope is constrained to the true value. Informing the fit using the true value near the image radius can introduce substantial bias (0-23% depending on the model). We confirm using Jeans arguments that kinematic constraints can result in a biased value of $H_0$, though the degree of bias depends on the region kinematic modeling probes in specific lenses. We conclude that lensing degeneracies manifest through commonplace modeling approaches in a more complicated way than is assumed in the literature. If stellar kinematics incorrectly break the MSD, their inclusion may introduce more bias than their omission.

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arXiv2020

Two-component mass models of the lensing galaxy in the quadruply imaged supernova iPTF16geu

The first resolved, multiply imaged supernova Type Ia, iPTF16geu, was observed 4 years ago, five decades after such systems were first envisioned. Because of the unique properties of the source, these systems hold a lot of promise for the study of galaxy structure and cosmological parameters. However, this very first example presented modelers with a few puzzles. It was expected that to explain image fluxes a contribution from microlensing by stars would be required, but to accommodate the magnitude of microlensing, the density slope of the elliptical power law lens model had to be quite shallow, $ρ_{2D} \propto r^{-0.7}$. Furthermore, the center of mass had to be displaced from that of observed light by ~0.1 kpc, and the position angle of light distribution was misaligned with that of mass by ~40 degrees. In this paper we present mass models that resolve the first two problems, and suggest a resolution of the third. Motivated by observations of local ellipticals, and some recent analysis of galaxy-scale lenses, our mass models consist of two offset (baryonic) mass components. The resulting mass distributions have a single centroid, but are lopsided, and have isodensity contours that are not purely elliptical and not self-similar with radius. For many of our models the microlensing requirements are modest, and the ring formed by the extended supernova host galaxy resembles the observed one.

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