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We present a new approach for fast calculation of gravitational lensing properties, including the lens potential, deflection angles, convergence, and shear, of elliptical Navarro–Frenk–White (NFW) and Hernquist density profiles, by approximating them by superpositions of elliptical density profiles for which simple analytic expressions of gravitational lensing properties are available. This model achieves high fractional accuracy better than 10 −4 in the range of the radius normalized by the scale radius of 10 −4 –10 3 . These new approximations are ∼300 times faster in solving the lens equation for a point source compared with the traditional approach resorting to expensive numerical integrations, and are implemented in glafic software.

Strong gravitational lensing and microlensing of supernovae (SNe) are emerging as a new probe of cosmology and astrophysics in recent years. We provide an overview of this nascent research field, starting with a summary of the first discoveries of strongly lensed SNe. We describe the use of the time delays between multiple SN images as a way to measure cosmological distances and thus constrain cosmological parameters, particularly the Hubble constant, whose value is currently under heated debates. New methods for measuring the time delays in lensed SNe have been developed, and the sample of lensed SNe from the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to provide competitive cosmological constraints. Lensed SNe are also powerful astrophysical probes. We review the usage of lensed SNe to constrain SN progenitors, acquire high-z SN spectra through lensing magnifications, infer SN sizes via microlensing, and measure properties of dust in galaxies. The current challenge in the field is the rarity and difficulty in finding lensed SNe. We describe various methods and ongoing efforts to find these spectacular explosions, forecast the properties of the expected sample of lensed SNe from upcoming surveys particularly the LSST, and summarize the observational follow-up requirements to enable the various scientific studies. We anticipate the upcoming years to be exciting with a boom in lensed SN discoveries.

Galaxy clusters as gravitational lenses play a unique role in astrophysics and cosmology: they permit mapping the dark matter distribution on a range of scales; they reveal the properties of high and intermediate redshift background galaxies that would otherwise be unreachable with telescopes; they constrain the particle nature of dark matter and are a powerful probe of global cosmological parameters, like the Hubble constant. In this review we summarize the current status of cluster lensing observations and the insights they provide, and offer a glimpse into the capabilities that ongoing, and the upcoming next generation of telescopes and surveys will deliver. While many open questions remain, cluster lensing promises to remain at the forefront of discoveries in astrophysics and cosmology.

Strong gravitational lensing of quasars has the potential to unlock the poorly understood physics of these fascinating objects, as well as serve as a probe of the lensing mass distribution and of cosmological parameters. In particular, gravitational microlensing by compact bodies in the lensing galaxy can enable mapping of quasar structure to < 10 − 6 arcsec scales. Some of this potential has been realized over the past few decades, however the upcoming era of large sky surveys promises to bring this promise to full fruition. In this article, we review the theoretical framework of this field, describe the prominent current methods for parameter inference from quasar microlensing data across different observing modalities, and discuss the constraints so far derived on the geometry and physics of quasar inner structure. We also review the application of strong lensing and microlensing to constraining the granularity of the lens potential, i.e. the contribution of the baryonic and dark matter components, and the local mass distribution in the lens, i.e. the stellar mass function. Finally, we discuss the future of the field, including the new possibilities that will be opened by the next generation of large surveys and by new analysis methods now being developed.

Strong gravitational lensing at the galaxy scale is a valuable tool for various applications in astrophysics and cosmology. Some of the primary uses of galaxy-scale lensing are to study elliptical galaxies’ mass structure and evolution, constrain the stellar initial mass function, and measure cosmological parameters. Since the discovery of the first galaxy-scale lens in the 1980s, this field has made significant advancements in data quality and modeling techniques. In this review, we describe the most common methods for modeling lensing observables, especially imaging data, as they are the most accessible and informative source of lensing observables. We then summarize the primary findings from the literature on the astrophysical and cosmological applications of galaxy-scale lenses. We also discuss the current limitations of the data and methodologies and provide an outlook on the expected improvements in both areas in the near future.

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.

Weak gravitational lensing is a powerful tool for studying the growth of structure across cosmic time. The shear signal required for weak lensing analyses is very small, so any undesirable detector-level effects which distort astronomical images can significantly contaminate the inferred shear. The Nancy Grace Roman Space Telescope (Roman) will fly a focal plane with 18 Teledyne H4RG-10 near-infrared (IR) detector arrays; these have never before been used for weak lensing and they present different instrument calibration challenges relative to charge-coupled devices. A pair of previous investigations demonstrated that spatiotemporal correlations of flat field images can effectively separate the brighter-fatter effect (BFE) and interpixel capacitance (IPC). A third paper in the series introduced a Fourier-space treatment of these correlations which allowed the authors to expand to higher orders in BFE, IPC, and classical nonlinearity. This work expands the previous formalism to include quantum yield and charge diffusion. We test the updated formalism on simulations and show that we can recover input visible characterization values to within a few percent. We then apply the formalism to visible and IR flat field data from three Roman flight candidate detectors. We find that BFE is present in all detectors and that the magnitude of its central pixel value is comparable between visible data and IR data. We fit a 2D Gaussian model to the charge diffusion at 0.5 μ m wavelength, and find variances of C 11 = 0.1066 ± 0.0011 pix 2 in the horizontal direction, C 22 = 0.1136 ± 0.0012 pix 2 in the vertical direction, and a covariance of C 12 = 0.0001 ± 0.0007 pix 2 (stat) for SCA 20829. Last, we convert the asymmetry of the charge diffusion into an equivalent shear signal using the sensitivity coefficients for the Roman survey, and find a contamination of the shear correlation function to be ξ + ∼ 10 −6 for each detector. This exceeds Roman’s allotted error budget for the measurement by a factor of  ( 10 ) in power (amplitude squared) but can likely be mitigated through standard methods for fitting the point-spread function (PSF) since for weak lensing applications the charge diffusion can be treated as a contribution to the PSF. Further work considering the impact of charge diffusion and quantum yield on shear measurements will follow once all detectors covering the Roman focal plane are selected.

Microlensing near macro-caustics is a complex phenomenon in which swarms of micro-images produced by micro-caustics form on both sides of a macro-critical curve. Recent discoveries of highly magnified images of individual stars in massive galaxy cluster lenses, predicted to be formed by these micro-image swarms, have stimulated studies on this topic. In this article, we explore microlensing near macro-caustics using both simulations and analytic calculations. We show that the mean total magnification of the micro-image swarms follows that of an extended source in the absence of microlensing. Micro-caustics join into a connected network in a region around the macro-critical line of a width proportional to the surface density of microlenses; within this region, the increase of the mean magnification toward the macro-caustic is driven by the increase of the number of micro-images rather than individual magnifications of micro-images. The maximum achievable magnification in micro-caustic crossings decreases with the mass fraction in microlenses. We conclude with a review of applications of this microlensing phenomenon, including limits to the fraction of dark matter in compact objects, and searches of Population III stars and dark matter subhalos. We argue that the discovered highly magnified stars at cosmological distances already imply that less than ∼ 10% of the dark matter may be in the form of compact objects with mass above ∼ 10 − 6 M ⊙ .

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale, L*, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*, L*=5.716×1010 m, while for M87* black hole, L*=3.264×1013 m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of L* (or the Planck length, lPl). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for quantum black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of L* and M are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world.

Microlensing events observed from locations separated by ∼au have different peak times and peak magnifications due to microlensing parallax. K2 Campaign 9 (K2C9) was the first space-based microlensing parallax survey capable of measuring microlensing parallaxes of free-floating planet candidate microlensing events. Simultaneous to K2C9 observations we conducted the K2C9 Canada-France-Hawaii Telescope Multi-Color Microlensing Survey (K2C9-CFHT MCMS) in order to measure the colors of microlensing source stars to improve the accuracy of K2C9's parallax measurements. We describe the difference imaging photometry analysis of the K2C9-CFHT MCMS observations, and present the project's first data release. This includes instrumental difference flux light curves in up to three filters (g, r, and i) of 217 microlensing events identified by other microlensing surveys, reference image photometry of more than 30 million point sources calibrated to PanSTARRS data release 1 photometry with an absolute accuracy better than 0.02 mag . We derive accurate analytic transformations between the PanSTARRS bandpasses and the Kepler bandpass, as well as color-surface brightness relations in the PanSTARRS bandpasses. To demonstrate the use of our data set, we analyze ground-based and K2 data of a short timescale microlensing event, OGLE-2016-BLG-0795. We find the event has a timescale tE = 4.5 0.1 days and microlens parallax πE = 0.09 0.03 or 0.91 0.04, subject to the standard satellite parallax degeneracy. We argue that the smaller value of the parallax is more likely, which implies that the lens is likely a stellar-mass object in the Galactic bulge as opposed to a super-Jupiter mass object in the Galactic disk.