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 Chapter, 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 $\sim$ 10\% of the dark matter may be in the form of compact objects with mass above $\sim 10^{-6}\, M_{\odot}$.
We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parameterisation proposed and detailed in Cassan (2008). As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain-Monte Carlo algorithm. We find a number of low-chi2 regions in the p…
It is shown that the linear approximation of the central caustic for the planetary ($q\ll1$) microlensing is valid if $|1-s|\gg q^{1/3}$ (where $q$ is the mass ratio and $s$ is the projected separation in the unit of the Einstein ring radius of the primary). The condition is also consistent with the requirement that the binary separation is far from those in the resonant binary regime resulting in a single six-cusp caustic. Given that the linear approximation of the caustic is invariant under $s\leftrightarrow s^{-1}$, the close/wide binary degeneracy observed under the same condition may be u…
Quasar microlensing offers a unique opportunity to resolve tiny sources in distant active galactic nuclei and study compact object populations in lensing galaxies. We therefore searched for microlensing-induced variability of the gravitationally lensed quasar QSO 2237+0305 (Einstein Cross) using 4374 optical frames taken with the 2.0 m Liverpool Telescope and the 1.5 m Maidanak Telescope. These $gVrRI$ frames over the 2006$-$2019 period were homogeneously processed to generate accurate long-term multi-band light curves of the four quasar images A-D. Through difference light curves, we found st…
Recent observations of lensed galaxies at cosmological distances have detected individual stars that are extremely magnified when crossing the caustics of lensing clusters. In idealized cluster lenses with smooth mass distributions, two images of a star of radius $R$ approaching a caustic brighten as $t^{-1/2}$ and reach a peak magnification $\sim 10^{6}\, (10\, R_{\odot}/R)^{1/2}$ before merging on the critical curve. We show that a mass fraction ($κ_\star \gtrsim \, 10^{-4.5}$) in microlenses inevitably disrupts the smooth caustic into a network of corrugated microcaustics, and produces ligh…
Observations of several gravitationally microlensed quasars in X-rays revealed variations in the profile of the iron K$α$ line in the course of microlensing events. We explore the effect by simulating a microlensing caustic crossing a spatially resolved model of emission from a thin accretion disk around a Kerr black hole. We demonstrate the sequence of spectral changes during the event, in particular the appearance of additional peaks and edges in the line profile due to microlensing. We trace the origin of these features to points on the disk, at which the total energy shift ($g$-factor) con…
Gravitational microlensing is a powerful method for detecting and characterizing free-floating planetary-mass objects (FFPs). FFPs could have exomoons rotating them. In this work, we study the probability of realizing these systems (i.e., free-floating moon-planet ones) through microlensing observations. These systems make mostly close caustic configurations with a considerable finite-source effect. We investigate finite-source microlensing light curves owing to free-floating moon-planet systems. We conclude that crossing planetary caustics causes an extensive extra peak at light curves' wing …
Galactic microlensing has been widely used to study the star and planet. The stellar wind plays an important role in the formation, environment and habitability of the planet. In this work we study a binary microlensing system including the stellar wind, i.e. a star with plasma environment plus a planet. Plasma surrounding the main lens causes chromatic deflection of the light rays, in addition to the gravitational one. As a result, such a lensing system can generate complicated caustics which depends on the different lensing parameters. In this work we study the magnification curves for diffe…
We present the analyses of two microlensing events, OGLE-2018-BLG-0567 and OGLE-2018-BLG-0962. In both events, the short-lasting anomalies were densely and continuously covered by two high-cadence surveys. The light-curve modeling indicates that the anomalies are generated by source crossings over the planetary caustics induced by planetary companions to the hosts. The estimated planet/host separation (scaled to the angular Einstein radius $θ_{\rm E}$) and mass ratio are $(s, q) = (1.81, 1.24\times10^{-3})$ and $(s, q) = (1.25, 2.38\times10^{-3})$, respectively. From Bayesian analyses, we esti…
To a first approximation, the microlensing phenomenon is achromatic, and great advancement has been achieved in the interpretation of the achromatic signals, which among other achievements has led to the discovery and characterization of well above $100$ new exoplanets. At higher order accuracy in the observations, microlensing has a chromatic component (a color term) which has so far been much less explored. Here, we analyze the chromatic microlensing effect of $4$ different physical phenomena, which have the potential to add important new knowledge about the stellar properties not easily rea…
We present a tool to generate mock quasar microlensing light curves and sample them according to any observing strategy. An updated treatment of the fixed and random velocity components of observer, lens, and source is used, together with a proper alignment with the external shear defining the magnification map caustic orientation. Our tool produces quantitative results on high magnification events and caustic crossings, which we use to study three lensed quasars known to display microlensing, viz. RX J1131-1231, HE 0230-2130, and Q 2237+0305, as they would be monitored by The Rubin Observator…
Recent studies have shown that line profile distortions are commonly observed in gravitationally lensed quasar spectra. We investigate the effect of gravitational microlensing on quasar broad emission line profiles and their underlying continuum, combining the emission from simple representative BLR models with generic microlensing magnification maps. Specifically, we considered Keplerian disk, polar, and equatorial wind BLR models of various sizes. The effect of microlensing has been quantified with four observables: $μ^{BLR}$, the total magnification of the broad emission line; $μ^{cont}$, t…
We conducted a project of reinvestigating the 2017--2019 microlensing data collected by the high-cadence surveys with the aim of finding planets that were missed due to the deviations of planetary signals from the typical form of short-term anomalies. The project led us to find three planets including KMT-2017-BLG-2509Lb, OGLE-2017-BLG-1099Lb, and OGLE-2019-BLG-0299Lb. The lensing light curves of the events have a common characteristic that the planetary signals were produced by the crossings of faint source stars over the resonant caustics formed by giant planets located near the Einstein rin…
We study three-dimensional microlensing where two lenses are located at different distances along the line of sight. We formulate the lens equation in complex notations and recover several previous results. There are in total either 4 or 6 images, with an equal number of images with positive and negative parities. We find that the sum of signed magnifications for six image configurations is unity. Furthermore, we show that the light curves can be qualitatively different from those for binary lensing in a single plane. In particular, the magnifications between a `U'-shaped caustic crossing can …
The offset microlensing degeneracy, recently proposed by Zhang et al. (2022), has been shown to generalize the close-wide and inner-outer caustic degeneracies into a unified regime of magnification degeneracy in the interpretation of 2-body planetary microlensing observations. While the inner-outer degeneracy expects the source trajectory to pass equidistant to the planetary caustics of the degenerate lens configurations, the offset degeneracy states that the same mathematical expression applies to any combination of the close, wide, and resonant caustic topologies, where the projected star-pl…
Recent near-IR power-spectra and panchromatic Extragalactic Background Light measurements provide upper limits on the near-IR surface brightness (SB>31 mag/arcsec^2) that may come from Pop III stars and accretion disks around resulting stellar-mass black holes (BHs) in the epoch of First Light (z=7-17). Physical parameters for zero metallicity Pop III stars at z>7 can be estimated from MESA stellar evolution models through helium-depletion, and for BH accretion disks from quasar microlensing results and multicolor accretion models. Second-generation stars can form at higher multiplicity, so th…
Three Saturn-mass Microlensing Planets Identified through Signals from Peripheral-caustic Perturbations
Chungbuk National University（忠北国立大学）；Korea Astronomy and Space Science Institute（韩国天文学与空间科学研究所）；Astronomical Observatory, University of Warsaw（华沙大学天文台）；Massey University（梅西大学）；University of Canterbury（坎特伯雷大学）；Ohio State University（俄亥俄州立大学）；University of Science and Technology（科学技术大学）
We report new results for the gravitational microlensing target OGLE-2011-BLG-0950 from adaptive optics (AO) images using the Keck observatory. The original analysis by Choi et al. 2012 reports degenerate solutions between planetary and stellar binary lens systems. This is due to a degeneracy in high magnification events where the shape of the light curve peak can be explained by a source approach to two different cusp geometries with different source radius crossing times. This particular case is the most important type of degeneracy for exoplanet demographics, because the distinction between…
We search for microlensing planets with signals exhibiting no caustic-crossing features, considering the possibility that such signals may be missed due to their weak and featureless nature. For this purpose, we reexamine the lensing events found by the KMTNet survey before the 2019 season. From this investigation, we find two new planetary lensing events, KMT-2018-BLG-1976 and KMT-2018-BLG-1996. We also present the analysis of the planetary event OGLE-2019-BLG-0954, for which the planetary signal was known, but no detailed analysis has been presented before. We identify the genuineness of the…
University of California, Berkeley（加州大学伯克利分校）；The Ohio State University（俄亥俄州立大学）
While gravitational microlensing by planetary systems provides unique vistas on the properties of exoplanets, observations of a given 2-body microlensing event can often be interpreted with multiple distinct physical configurations. Such ambiguities are typically attributed to the close-wide and inner-outer types of degeneracies that arise from transformation invariances and symmetries of microlensing caustics. However, there remain unexplained inconsistencies between aforementioned theories and observations. Here, leveraging a fast machine learning inference framework, we present the discover…
Gravitationally lensed extragalactic sources are often subject to statistical microlensing by stars in the galaxy or cluster lens. Accurate models of the flux statistics are required for inferring source and lens properties from flux observations. We derive an accurate semi-analytic approximation for calculating the mean and variance of the magnification factor, which are applicable to Gaussian source profiles and arbitrary non-uniform macro lens models, and hence can save the need to perform expensive numerical simulations. The results are given as single and double lens-plane integrals with …
The inner region of circumstellar discs makes an extra near-infrared emission (NIR bump). Detecting and studying these NIR bumps from nearby stars have been done mostly through infrared interferometry. In this work, we study the feasibility of detecting NIR bumps for Galactic bulge stars through microlensing from observations by The Nancy Grace Roman Space Telescope (RST) survey. We first simulate microlensing light curves from source stars with discs in near-infrared. Four main conclusions can be extracted from the simulations. (i) If the lens is crossing the disc inner radius, two extra and …
We study the highly magnified arc SGAS J122651.3+215220 caused by a star-forming galaxy at $z_s=2.93$ crossing the lensing caustic cast by the galaxy cluster SDSS J1226+2152 ($z_l=0.43$), using Hubble Space Telescope observations. We report in the arc several asymmetric surface brightness features whose angular separations are a fraction of an arcsecond from the lensing critical curve and appear to be highly but unequally magnified image pairs of underlying compact sources, with one brightest pair having clear asymmetry consistently across four filters. One explanation of unequal magnification…
Gravitational microlensing of planetary-mass objects (or "nanolensing", as it has been termed) can be used to probe the distribution of mass in a galaxy that is acting as a gravitational lens. Microlensing and nanolensing light curve fluctuations are indicative of the mass of the compact objects within the lens, but the size of the source is important, as large sources will smooth out a light curve. Numerical studies have been made in the past that investigate a range of sources sizes and masses in the lens. We extend that work in two ways - by generating high quality maps with over a billion …
Microlensing of multiply imaged quasars is a unique probe of quasar structure, down to the size of the accretion disc and the central black hole. Flux ratios between close pairs of images of lensed quasars can be used to constrain the accretion disc size and temperature profile. The starting point of any microlensing model is the macromodel of the lens, which provides the convergence and shear values at the location of the multiple images. Here I present a new approach of microlensing modelling independently of the macromodel of the lens. The technique is applied to the close pair of images A1…
Predictions of the Nancy Grace Roman Space Telescope Galactic Exoplanet Survey. V. Detection Rates of Multiplanetary Systems in High Magnification Microlensing Events
