Extreme Magnification Research Articles

Statistics of magnification for extremely lensed high redshift stars

Microlensing of stars in strongly lensed galaxies can lead to temporary extreme magnification factors (μ> 1000), enabling their detection at high redshifts. Following the discovery of Icarus, several stars at cosmological distances (z > 1) have been observed using the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). This emerging field of gravitational lensing holds promise to study individual high redshift stars. It also offers the opportunity to study the substructure in the lens plane with implications for dark matter models, as more lensed stars are detected and analysed statistically. Due to the computational demands of simulating microlensing at large magnification factors, it is important to develop fast and accurate analytical approximations for the probability of magnification in such extreme scenarios. In this study, we consider different macro-model magnification and microlensing surface mass density scenarios and study how the probability of extreme magnification factors depends on these factors. To achieve this, we created state-of-the-art large simulations of the microlensing effect in these scenarios. Through the analysis of these simulations, we derived analytical scaling relationships that can bypass the need for expensive numerical simulations. Our results are useful to interpret current observations of stars at cosmic distances which are extremely magnified and under the influence of microlenses.

Plasma lensing interpretation of FRB 20201124A bursts at the end of September 2021

ABSTRACT When radio photons propagate through a non-uniform electron density volume, the plasma lensing effect can induce an extreme magnification to the observed flux at certain frequencies. Because the plasma lens acts as a diverging lens, it can extremely suppress the observed flux when aligned with the source. These two properties can theoretically cause a highly magnified fast radio burst (FRB) to become faint or even disappear for a period of time. In this paper, we interpret that the significant increase in burst counts followed by a sudden quenching in FRB 20201124A in September 2021 can be attributed to plasma lensing. Based on the one-dimensional Gaussian lens model, we search for double main-peak structures in the spectra just before its extinction on 2021 September 29. After the de-dispersion and de-scintillation procedures, we find eight bursts with double main-peaks at stable positions. There are three parameters in our modelling, the height N0, width a of the lens and its distance DLS to the source. We reformulate them as a combined parameter ${P}_0 \propto \left(\frac{a}{\mathrm{au}}\right)\sqrt{\frac{\mathrm{kpc}}{D_{\mathrm{LS}}} \frac{\mathrm{pc}\mathrm{cm}^{-3}}{N_0} }$. The frequency spectra can give an accurate estimation of P0 corresponding to $\left(\frac{a}{\mathrm{au}}\right)\sqrt{\frac{\mathrm{kpc}}{D_{\mathrm{LS}}} \frac{\mathrm{pc}\mathrm{cm}^{-3}}{N_0} } \approx 28.118$, while the time of arrival only give a relatively loose constraint on a2/DLS. Comparing with the observation dynamic spectra, we suggest that for a plasma lens in host galaxy, e.g. DLS ≈ 1 kpc, the width of lens can not be larger than 40 au. At last, we estimate the relative transverse motion velocity between the lens and source, $v\approx 98\left(\frac{a}{\mathrm{au}}\right)\mathrm{km\,s^{-1}}$.

#6669 ANALYSIS OF KIDNEY BIOPSIES AND URINE SEDIMENT USING SCANNING ELECTRON MICROSCOPY (SEM) AND ATOMIC FORCE MICROSCOPY (AFM)

Abstract Background and Aims The classification of renal diseases is dependent on the evaluation of kidney biopsies using light microscopy techniques. Ultrastructural details (e.g. podocyte foot processes, amyloid fibrils, Fabri's intracellular inclusions) need transmission electron microscopy (TEM) which has high costs, requires specialized personnel and is time consuming. Therefore, alternative techniques are highly desirable. Here we report our experience with scanning electron microscopy (SEM) and atomic force microscopy (AFM). Method Paraffin-embedded kidney sections (3μm thick) were examined after dewaxing and Jones-methenamine methane staining for type IV collagen fibers. Dried urine sediments were prepared using standard methods for urine cytological analysis. Analysis was then performed using atomic force microscopy (nGauge system) on dried specimens and with Scanning Electron Microscopy (Zeiss) after gold-spattering of the surface. Reference images were obtained by standard microscopy. Results The combination of SEM and thin paraffin sections allows the observation of ultrastructural details in kidney biopsies with a very simple and fast preparation. AFM is even faster than SEM, as it does not require any preparation of the surface of the sample. An important advantage of SEM is the possibility to view the sample at low magnification, which makes it easier to identify the location of the glomeruli. It is thus possible to switch from small magnifications (100x) to very extreme magnifications (10000x). Notably, the interpretation of the images requires knowledge of the artifacts induced by paraffin inclusion. Specifically, structures and cells containing lipids (for example foamy cells) appear empty. Chromatin is also condensed in the nuclei around the periphery of the nucleus and in spike structures whit large empty areas. The recognition of nuclei in SEM and AFM is important for the subsequent interpretation of the images. Podocyte pedicles fusion can be identified relatively easily in SEM and in AFM. Both techniques add relevant ultrastructural details of urine sediment cells, from epithelial cells to isolated tubular cells. Also, casts show many ultrastructural features which are not evident in classical optical microscopy. It is also possible to measure the thickness of the basement membrane with great precision both in SEM and with AFM. The major limitation of this approach is the limited experience of pathologists with these methods and the absence of an atlas of normal and pathological kidney. Conclusion Considering the affordable costs of SEM and AFM instruments and the simple preparation of samples for their analysis, these should be considered a valid alternative to TEM. SEM and AFM are alternative methods, simple and relatively cheap and very fast to obtain ultrastructural details of renal biopsies. We thank ANED and AST for the great support given to research.

RXJ0437+00: constraining dark matter with exotic gravitational lenses

ABSTRACT We present the first strong-gravitational-lensing analysis of the galaxy cluster RX J0437.1+0043 (RXJ0437; z = 0.285). Newly obtained, deep MUSE observations, Keck/MOSFIRE near-infrared spectroscopy, and Hubble Space Telescope SNAPshot imaging reveal 13 multiply imaged background galaxies, three of them (at z = 1.98, 2.97, and 6.02, respectively) in hyperbolic umbilic (H–U) lensing configurations. The H–U images are located only 20–50 kpc from the cluster centre, i.e. at distances well inside the Einstein radius where images from other lens configurations are demagnified and often unobservable. Extremely rare (only one H–U lens was known previously) these systems are able to constrain the inner slope of the mass distribution – and unlike radial arcs, the presence of H–U configurations is not biased towards shallow cores. The galaxies lensed by RXJ0437 are magnified by factors ranging from 30 to 300 and (in the case of H–U systems) stretched nearly isotropically. Taking advantage of this extreme magnification, we demonstrate how the source galaxies in H–U systems can be used to probe for small-scale (∼109 M⊙) substructures, providing additional insight into the nature of dark matter.

The Light of Earendel – The Most Distant Star Yet Observed

The gravity of massive objects can magnify background objects, making them appear larger and brighter. Precise alignment between a background star and a foreground lens leads to extreme magnifications, allowing individual stars to be detected at great distances. This technique has recently revealed the most distant star yet observed, which existed when the universe was only 900 million years old.

Godzilla, a monster lurks in the Sunburst galaxy

We model the strong lensing effect in the galaxy cluster PSZ1 G311.65-18.48 (z = 0.443) with an improved version of the hybrid method WSLAP+. We extend the number of constraints by including the position of critical points, which are combined with the classic positional constraints of the lensed galaxies. We pay special attention to a transient candidate source (Tr) previously discovered in the giant Sunburst arc (z = 2.37). Our lens model predicts Tr to be within a fraction of an arcsecond from the critical curve, which has a larger magnification factor than previously found, but still not large enough to explain the observed flux and lack of counterimages. Possible candidate counterimages are discussed that would lower the magnification required to explain Tr, but extreme magnification factors (μ > 600) are still required, even in that case. The presence of a small mass perturber with a mass comparable to a dwarf galaxy (M ∼ 108 M⊙) near the position of Tr is needed in order to explain the required magnification and morphology of the lensed galaxy. We discuss how the existence of this perturber could potentially be used to constrain models of dark matter. The large apparent brightness and unresolved nature of the magnified object implies a combination of extreme magnification and a very luminous and compact source (r < 0.4 pc). Possible candidates are discussed, including an hyperluminous star, a small group of stars, or an accretion disk around a relatively small supermassive black hole (SMBH). Based on spectral information and flux requirements, we argue that a luminous blue variable (LBV) star caught during an outburst is the most likely candidate. Owing to the extreme magnification and luminosity of this source, we dub it Godzilla.

Fast algorithm for simulating light curves of stars at extreme magnification affected by microlensing

We present a fast algorithm aimed at reproducing the light curves of distant stars undergoing microlensing near critical curves. The need for these type of algorithms has been motivated by recent observations of microlensing events of distant stars at high redshift and involving extreme magnification factors. The algorithm relies on a low-resolution computation of the deflection field due to an ensemble of microlenses near critical curves and takes advantage of the gradually varying nature of the deflection field to infer the magnification of the unresolved images. The algorithm is capable of resolving microlenses at cosmological distances with planet-sized masses, as well as typical background luminous stars of a few solar radii. Using this algorithm, light curves covering decades of relative motion between the source and the web of microcaustics, at nanoarcsec resolution, can be reproduced within a matter of minutes on a basic laptop. Classic inverse ray tracing simulations at the same resolution would take days or weeks to produce, consuming massive computational resources.

An Earth-mass planet in a time of COVID-19: KMT-2020-BLG-0414Lb

We report the discovery of KMT-2020-BLG-0414Lb, with a planet-to-host mass ratio q 2 = 0.9–1.2 × 10−5 = 3–4 ⊕ at 1σ, which is the lowest mass-ratio microlensing planet to date. Together with two other recent discoveries (4 ≲ q/q ⊕ ≲ 6), it fills out the previous empty sector at the bottom of the triangular (log s, log q) diagram, where s is the planet-host separation in units of the angular Einstein radius θE. Hence, these discoveries call into question the existence, or at least the strength, of the break in the mass-ratio function that was previously suggested to account for the paucity of very low-q planets. Due to the extreme magnification of the event, A max ∼ 1450 for the underlying single-lens event, its light curve revealed a second companion with q 3 ∼ 0.05 and |log s 3| ∼ 1, i.e., a factor ∼ 10 closer to or farther from the host in projection. The measurements of the microlens parallax π E and the angular Einstein radius θE allow estimates of the host, planet and second companion masses, (M 1, M 2, M 3) ∼ (0.3 M ⊙, 1.0 M ⊕, 17 MJ ), the planet and second companion projected separations, (a ⊥,2, a ⊥,3) ∼ (1.5, 0.15 or 15) au, and system distance D L ∼ 1 kpc. The lens could account for most or all of the blended light (I ∼ 19.3) and so can be studied immediately with high-resolution photometric and spectroscopic observations that can further clarify the nature of the system. The planet was found as part of a new program of high-cadence follow-up observations of high-magnification events. The detection of this planet, despite the considerable difficulties imposed by COVID-19 (two KMT sites and OGLE were shut down), illustrates the potential utility of this program.

Apparent radio transients mapping the near-Earth plasma environment

ABSTRACT We report the discovery of bright, fast, radio flashes lasting tens of seconds with the AARTFAAC high-cadence all-sky survey at 60 MHz. The vast majority of these coincide with known, bright radio sources that brighten by factors of up to 100 during such an event. We attribute them to magnification events induced by plasma near the Earth, most likely in the densest parts of the ionosphere. They can occur both in relative isolation, during otherwise quiescent ionospheric conditions, and in large clusters during more turbulent ionospheric conditions. Using a toy model, we show that the likely origin of the more extreme (up to a factor of 100 or so) magnification events likely originate in the region of peak electron density in the ionosphere, at an altitude of 300–400 km. Distinguishing these events from genuine astrophysical transients is imperative for future surveys searching for low frequency radio transient at time-scales below a minute.

Gravitational Lensing Signatures of Axion Dark Matter Minihalos in Highly Magnified Stars

Abstract Axions are a viable candidate for cold dark matter, which should generically form minihalos of subplanetary masses from white-noise isocurvature density fluctuations if the Peccei–Quinn phase transition occurs after inflation. Despite being denser than the larger halos formed out of adiabatic fluctuations from inflation, axion minihalos have surface densities much smaller than the critical value required for gravitational lensing to produce multiple images or high magnification, and hence are practically undetectable as lenses in isolation. However, their lensing effect can be enhanced when superposed near critical curves of other lenses. We propose a method to detect them through photometric monitoring of recently discovered caustic transiting stars behind cluster lenses, under extreme magnification factors μ ≳ 103–104 as the lensed stars cross microlensing caustics induced by intracluster stars. For masses of the first gravitationally collapsed minihalos in the range ∼10−15–10−8 h −1 M ⊙, we show that axion minihalos in galaxy clusters should collectively produce subtle surface density fluctuations of amplitude ∼10−4–10−3 on projected length scales of ∼10–104 au, which imprint irregularities on the microlensing lightcurves of caustic transiting stars. We estimate that, inside a cluster halo and over the age of the universe, most of these minihalos are likely to avoid dynamic disruption by encounters with stars or other minihalos.

The Universe at extreme magnification

Extreme magnifications of distant objects by factors of several thousand have recently become a reality. Small, very luminous compact objects, such as supernovae (SNe), giant stars at z = 1 − 2, Pop III stars at z > 7, and even gravitational waves (GWs) from merging binary black holes near caustics of gravitational lenses can be magnified many thousands or even tens of thousands of times thanks to their small size. We explore the probability of such extreme magnifications in a cosmological context and include the effect of microlenses near critical curves. We show how the presence of microlenses near the critical curve sets a limit on the maximum magnification. We use a combination of state of the art halo mass functions, high-resolution analytical models for the density profiles, and inverse ray tracing to estimate the probability of magnification near caustics. We estimate the rate of highly magnified events in the case of SNe, GWs, and very luminous stars including Pop III stars. Our findings reveal that future observations will increase the number of events at extreme magnifications, and will open the door not only to studying individual sources at cosmic distances, but also to constraining compact dark matter candidates.

Probing Dark Matter Subhalos in Galaxy Clusters Using Highly Magnified Stars

Abstract Luminous stars in background galaxies straddling the lensing caustic of a foreground galaxy cluster can be individually detected due to extreme magnification factors of ∼102–103, as recently observed in deep HST images. We propose a direct method to probe the presence of dark matter subhalos in galaxy clusters by measuring the astrometric perturbation they induce on the image positions of magnified stars or bright clumps: lensing by subhalos breaks the symmetry of a smooth critical curve, traced by the midpoints of close image pairs. For the giant arc at z = 0.725 behind the lensing cluster Abell 370 at z = 0.375, a promising target for detecting image pairs of stars, we find that subhalos of masses in the range of 106–108 M ⊙ with the abundance predicted in the cold dark matter theory should typically imprint astrometric distortions at the level of 20–80 mas. We estimate that ∼10 hr integrations with JWST at ∼1–3 μm may uncover several magnified stars whose image doublets will reveal the subhalo-induced structures of the critical curve. This method can probe a dynamic range in the subhalo-to-cluster halo mass ratio of m/M ∼ 10−7–10−9, thereby placing new constraints on the nature of dark matter.

Cosmic flashing lights

Gravitational lensing is becoming increasingly important to the study of distant galaxies and dark matter. Two groups have recently detected transient events emanating from far-away lensed galaxies, apparently due to extreme magnification of individual stars.

Extreme magnification of an individual star at redshift 1.5 by a galaxy-cluster lens

Galaxy-cluster gravitational lenses can magnify background galaxies by a total factor of up to ~50. Here we report an image of an individual star at redshift z = 1.49 (dubbed MACS J1149 Lensed Star 1) magnified by more than ×2,000. A separate image, detected briefly 0.26″ from Lensed Star 1, is probably a counterimage of the first star demagnified for multiple years by an object of ≳3 solar masses in the cluster. For reasonable assumptions about the lensing system, microlensing fluctuations in the stars’ light curves can yield evidence about the mass function of intracluster stars and compact objects, including binary fractions and specific stellar evolution and supernova models. Dark-matter subhaloes or massive compact objects may help to account for the two images’ long-term brightness ratio.

Compound lensing: Einstein zig-zags and high-multiplicity lensed images

Compound strong gravitational lensing is a rare phenomenon, but a handful of such lensed systems are likely to be discovered in forthcoming surveys. In this work, we use a double SIS lens model to analytically understand how the properties of the system impact image multiplicity for the final source. We find that up to six images of a background source can form, but only if the second lens is multiply imaged by the first and the Einstein radius of the second lens is comparable to, but does not exceed that of the first. We then build a model of compound lensing masses in the Universe, using SIE lenses, and assess how the optical depth for multiple imaging by a galaxy-galaxy compound lens varies with source redshift. For a source redshift of 4, we find optical depths of $6 \times 10^{-6}$ for multiple imaging and $5 \times 10^{-8}$ for multiplicity of 6 or greater. We find that extreme magnifications are possible, with magnifications of 100 or more for $6 \times 10^{-9}$ of $z=10$ sources with 0.1 kpc radii. We show some of the image configurations that can be generated by compound lenses, and demonstrate that they are qualitatively different to those generated by single-plane lenses; dedicated compound lens finders will be necessary if these systems are to be discovered in forthcoming surveys.

Primordial star clusters at extreme magnification

Gravitationally lensed galaxies with magnification ~10-100 are routinely detected at high redshifts, but magnifications significantly higher than this are hampered by a combination of low probability and large source sizes. Magnifications of ~1000 may nonetheless be relevant in the case of intrinsically small, high-redshift objects with very high number densities. Here, we explore the prospects of detecting compact (< 10 pc), high-redshift (z > 7) Population III star clusters at such extreme magnifications in large-area surveys with planned telescopes like Euclid, WFIRST and WISH. We find that the planned WISH 100 sq. deg ultradeep survey may be able to detect a small number of such objects, provided that the total stellar mass of these star clusters is > 10000 solar masses. If candidates for such lensed Population III star clusters are found, follow-up spectroscopy of the surrounding nebula with the James Webb Space Telescope or groundbased Extremely Large Telescopes should be able to confirm the Population III nature of these objects. Multiband photometry of these objects with the James Webb Space Telescope also has the potential to confirm that the stellar initial mass function in these Population III star clusters is top-heavy, as supported by current simulations.

Nano-Pattern Recognition and Correlation Technique for Sub-Nanometer In-Plane Displacement Measurement

An experimental technique to measure sub-nanometer scale in-plane deformations on a micron scale region of interest is proposed. The proposed Nano-Pattern Recognition and Correlation Technique (N-PRCT) utilizes regularly oriented patterns. Displacements are obtained by tracking the movement of each pattern on the images before and after loading through pattern recognition and correlation. The regularity offers a special benefit, relative to the random markings used in the existing techniques, which makes the proposed technique less sensitive to the random noise inherent in digital images at extreme magnifications (a region of interest less than 10 µm). The method is implemented to document thermally-induced deformations of a microelectronics circuit. E-beam lithography is implemented using a standard SEM to fabricate regularly oriented patterns required for N-PRCT. The patterns are produced on a polished cross-section of a flip-chip package, and the package is subsequently subjected to a temperature excursion inside the SEM chamber. Thermal deformations are obtained in a region of interest of approximately 7 × 6 µm.

Calculation of complex singular solutions to the 3D incompressible Euler equations

This paper presents numerical computations of complex singular solutions to the 3D incompressible Euler equations. The Euler solutions found here consist of a complex valued velocity field u + that contains all positive wavenumbers; u + satisfies the usual Euler equations but with complex initial data. The real valued velocity u = u + + u − (where u − = u ¯ + ) is an approximate singular solution to the Euler equations under Moore’s approximation. The method for computing singular solutions is an extension of that in Caflisch (1993) [25] for axisymmetric flow with swirl, but with several improvements that prevent the extreme magnification of round-off error which affected previous computations. This enables the first clean analysis of the singular surface in three-dimensional complex space. We find singularities in the velocity field of the form u + ∼ ξ α − 1 for α near 3/2 and u + ∼ log ξ , where ξ = 0 denotes the singularity surface. The logarithmic singular surface is related to the double exponential growth of vorticity observed in recent numerical simulations.

Microlensing of close binary stars

The gravity due to a multiple-mass system has a remarkable gravitational effect: the extreme magnification of background light sources along extended so-called caustic lines. This property has been the channel for some remarkable astrophysical discoveries over the past decade, including the detection and characterization of extrasolar planets, the routine analysis of limb darkening, and, in one case, limits set on the apparent shape of a star several kiloparsec distant. In this paper, we investigate the properties of the microlensing of close binary star systems. We show that in some cases it is possible to detect flux from the Roche lobes of close binary stars. Such observations could constrain models of close binary stellar systems.

Counting contacts between neurons in 3D in confocal laser scanning images

Study of neuronal networks requires an inventory of the neurons, knowledge of fiber in- and output, and qualitative and quantitative data on the intrinsic connectivity. For this purpose we combined in rat hippocampus fluorescence neuroanatomical tracing and intracellular fluorochrome injection of neurons. Multichannel confocal laser scanning microscopy was followed by computer assisted 3D object- and contact recognition. We describe the factors involved in scanning (‘from biological object to voxel’) and we compare operator-mediated manual recognition of small 3D objects and contacts with ‘objective’ processing through software. As in all digital object recognition, thresholding is pivotal. We obtained reproducible, ‘objective’ thresholds via 3D object-threshold analysis with ImageJ. Objective thresholds were subsequently used in SCIL_Image scripts to identify 3D objects, and to identify and count contacts between labeled fibers and intracellularly injected target neurons. At the extreme magnification necessary to distinguish contacts, Abbe diffraction causes voxels that belong to the pre-contact structure to overlap voxels belonging to the post-contact structure. We call this overlap the ‘footprint’ and we introduce such footprints and their size as criteria to recognize contacts. Automated contact recognition, applying footprints of 100 voxels (involved structures imaged in their specific channel) gave the highest correlation with findings using the manual approach. We conclude that computer identification and counting of contacts is the method of choice, since it combines reduced human bias with good reproducibility of results and saving of time. Of major importance is that threshold selection is not dependent on the human computer operator.