Caustic Crossings Research Articles

Revealing dark matter dress of primordial black holes by cosmological lensing

Stellar-mass primordial black holes (PBHs) from the early Universe can directly contribute to the gravitational wave (GW) events observed by LIGO, but can only comprise a subdominant component of the dark matter (DM). The primary DM constituent will generically form massive halos around seeding stellar-mass PBHs. We demonstrate that gravitational lensing of sources at cosmological (≳Gpc) distances can directly explore DM halo dresses engulfing PBHs, challenging for lensing of local sources in the vicinity of Milky Way. Strong lensing analysis of fast radio bursts detected by CHIME survey already starts to probe parameter space of dressed stellar-mass PBHs, and upcoming searches can efficiently explore dressed PBHs over ∼10−105M⊙ mass-range and provide a stringent test of the PBH scenario for the GW events. Our findings establish a general test for a broad class of DM models with stellar-mass PBHs, including those where QCD axions or WIMP-like particles comprise predominant DM. The results open a new route for exploring dressed PBHs with various types of lensing events at cosmological distances, such as supernovae and caustic crossings.

Systematic KMTNet Planetary Anomaly Search. VIII. Complete Sample of 2019 Subprime Field Planets

We complete the publication of all microlensing planets (and “possible planets”) identified by the uniform approach of the KMT AnomalyFinder system in the 21 KMT subprime fields during the 2019 observing season, namely, KMT-2019-BLG-0298, KMT-2019-BLG-1216, KMT-2019-BLG-2783, OGLE-2019-BLG-0249, and OGLE-2019-BLG-0679 (planets), as well as OGLE-2019-BLG-0344 and KMT-2019-BLG-0304 (possible planets). The five planets have mean log mass ratio measurements of (−2.6, −3.6, −2.5, −2.2, −2.3), median mass estimates of (1.81, 0.094, 1.16, 7.12, 3.34) M Jup, and median distance estimates of (6.7, 2.7, 5.9, 6.4, 5.6) kpc, respectively. The main scientific interest of these planets is that they complete the AnomalyFinder sample for 2019, which has a total of 25 planets that are likely to enter the statistical sample. We find statistical consistency with the previously published 33 planets from the 2018 AnomalyFinder analysis according to an ensemble of five tests. Of the 58 planets from 2018–2019, 23 were newly discovered by AnomalyFinder. Within statistical precision, half of the planets have caustic crossings, while half do not; an equal number of detected planets result from major- and minor-image light-curve perturbations; and an equal number come from KMT prime fields versus subprime fields.

Two Lensed Star Candidates at z ≃ 4.8 behind the Galaxy Cluster MACS J0647.7+7015

We report the discovery of two extremely magnified lensed star candidates behind the galaxy cluster MACS J0647.7+015 using recent multiband James Webb Space Telescope (JWST) NIRCam observations. The star candidates are seen in a previously known, z phot ≃ 4.8 dropout giant arc that straddles the critical curve. The candidates lie near the expected critical curve position, but lack clear counter-images on the other side of it, suggesting these are possibly stars undergoing caustic crossings. We present revised lensing models for the cluster, including multiply imaged galaxies newly identified in the JWST data, and use them to estimate background macro-magnifications of at least ≳90 and ≳50 at the positions of the two candidates, respectively. With these values, we expect effective, caustic-crossing magnifications of ∼[103–105] for the two star candidates. The spectral energy distributions of the two candidates match well the spectra of B-type stars with best-fit surface temperatures of ∼10,000 K, and ∼12,000 K, respectively, and we show that such stars with masses ≳20 M ⊙ and ≳50 M ⊙, respectively, can become sufficiently magnified to be observable. We briefly discuss other alternative explanations and conclude that these objects are likely lensed stars, but also acknowledge that the less-magnified candidate may alternatively reside in a star cluster. These star candidates constitute the second highest-redshift examples to date after Earendel at z phot ≃ 6.2, establishing further the potential of studying extremely magnified stars at high redshifts with JWST. Planned future observations, including with NIRSpec, will enable a more detailed view of these candidates in the near future.

Variation of the stellar color in high-magnification and caustic-crossing microlensing events

Context. To a first approximation, the microlensing phenomenon is achromatic and great advancements have been achieved with regard to the interpretation of the achromatic signals, leading to the discovery and characterization of well above 100 new exoplanets. At a higher order accuracy in the observations, microlensing has a chromatic component (a color term) that has thus far been explored to a much lesser extent. Aims. Here, we analyze the chromatic microlensing effect of four different physical phenomena, which have the potential to contribute key knowledge of the stellar properties that is not easily achievable with other methods of observation. Our simulation is limited to the case of main-sequence source stars. Methods. Microlensing is particularly sensitive to giant and sub-giant stars near the Galactic center. While this population can be studied in short snapshots by the largest telescopes in the world, a general monitoring and characterization of the population can be achieved by use of more accessible medium-sized telescopes with specialized equipment via dual-color monitoring from observatories at sites with excellent seeing. We limit the results of this study to what will be achievable from the Danish 1.54 m telescope at La Silla observatory based on the use of the existing dual-color lucky imaging camera. Such potential monitoring programs of the bulge population from medium-sized telescopes include the characterization of starspots, limb-darkening, the frequency of close-in giant planet companions, and gravity darkening for blended source stars. Results. We conclude our simulations with quantifying the likelihood of detecting these different phenomena per object where they are present to be ~60 and ~30% for the above-mentioned phenomena when monitored during both high-magnification and caustic crossings, respectively.

A quasar microlensing light-curve generator for LSST

ABSTRACT 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 Observatory Legacy Survey of Space and Time (LSST). We conclude that depending on the location on the sky, the lens and source redshift, and the caustic network density, the microlensing variability may deviate significantly than the expected ∼20-yr average time-scale (Mosquera & Kochanek 2011). We estimate that ∼300 high magnification events with Δmag>1 mag could potentially be observed by LSST each year. The duration of the majority of high magnification events is between 10 and 100 d, requiring a very high cadence to capture and resolve them. Uniform LSST observing strategies perform the best in recovering microlensing high magnification events. Our web tool can be extended to any instrument and observing strategy, and is freely available as a service at http://gerlumph.swin.edu.au/tools/lsst_generator/, along with all the related code.

Gravitational microlensing by dark matter in extended structures

Dark matter may be in the form of non-baryonic structures such as compact subhalos and boson stars. Structures weighing between asteroid and solar masses may be discovered via gravitational microlensing, an astronomical probe that has in the past helped constrain the population of primordial black holes and baryonic MACHOs. We investigate the non-trivial effect of the size of and density distribution within these structures on the microlensing signal, and constrain their populations using the EROS-2 and OGLE-IV surveys. Structures larger than a solar radius are generally constrained more weakly than point-like lenses, but stronger constraints may be obtained for structures with mass distributions that give rise to caustic crossings or produce larger magnifications.

KMT-2018-BLG-1990Lb: A Nearby Jovian Planet From A Low-cadence Microlensing Field

Abstract We report the discovery of KMT-2018-BLG-1990Lb, a Jovian planet orbiting a late M dwarf at a distance of , and projected at 2.6 ± 0.6 times the snow line distance, i.e., . This is the second Jovian planet discovered by the Korea Microlensing Telescope Network (KMTNet) in its low-cadence (0.4 hr−1) fields, demonstrating that this population can be probed based on relatively low-cadence survey-only microlensing data. However, while many Jovian-planet microlensing events will not have caustic crossings (e.g., the previous case, KMT-2016-BLG-1397) and some that do will be well characterized by low-cadence survey observations (e.g., the current case), in general higher-cadence follow-up observations of the caustic crossings are preferable. Such follow-up observations require microlensing alerts, which KMTNet now provides.

Polarization in caustic-crossing binary microlensing events

Here, we revisit the polarization signal in caustic-crossing binary microlensing and introduce the maps of the polarization signals of the source star as a function of its position projected on the lens plane. The behavior of these maps depends on the source size in comparison with the caustic. If the source size is so smaller than the caustic curve, the maximum polarization signal occurs while the source edge is crossing the nearest folds to the position of the primary. When the source size is larger than the caustic, the polarization signal maximizes over a circular ring around the primary whose radius normalized to the source radius is ~0.96. In cusp caustic crossings, the polarization curves have three peaks, the largest and widest one happens when the source edge is on the corner of the cusp and the source center is inside the caustic curve. When the source is entirely inside the caustic, the polarization signal significantly decreases. Despite the low magnification factor between two parts of planetary caustics, its polarization signal is considerable and can reach to 0.2\% for early-type stars. While crossing the connection line between different parts of caustic, the polarimetry curve have three close peaks that the middle one appears when the source center is upon the connection line.

Spitzer Microlensing Parallax for OGLE-2016-BLG-1067: A Sub-Jupiter Orbiting an M Dwarf in the Disk

Abstract We report the discovery of a sub-Jupiter-mass planet orbiting beyond the snow line of an M dwarf most likely in the Galactic disk as part of the joint Spitzer and ground-based monitoring of planetary microlensing anomalies toward the Galactic bulge. Most of the microlensing parameters are strongly constrained by the light-curve modeling, and in particular there is a Spitzer-based measurement of the microlens parallax, π E. However, there are no caustic crossings, so the angular Einstein radius has only an upper limit based on the light-curve modeling alone. Additionally, the analysis leads us to identify eight degenerate configurations: the fourfold microlensing parallax degeneracy being doubled by a degeneracy in the caustic structure present at the level of the ground-based solutions. To calculate the physical parameters, and at the same time to break the parallax degeneracy, we make use of a series of arguments: the χ 2 hierarchy, the Rich argument (stating that the small-parallax solution is more likely), and a prior Galactic model. The preferred configuration, favored by a likelihood ratio of at least 4000, is for a host at with mass , orbited by a Saturn-like planet with at projected separation , about 2.1 times beyond the system snow line. Therefore, it adds to the growing population of sub-Jupiter planets orbiting beyond the snow line of M dwarfs discovered by microlensing. Based on the rules of the real-time protocol for the selection of events to be followed up with Spitzer, this planet will not enter the sample for measuring the Galactic distribution of planets.

OGLE-2017-BLG-0039: Microlensing Event with Light from a Lens Identified from Mass Measurement

Abstract We present an analysis of the caustic-crossing binary microlensing event OGLE-2017-BLG-0039. Thanks to the very long duration of the event, with a time scale t E ∼ 130 days, the microlens parallax is measured precisely despite its low value of . Analysis of the well-resolved caustic crossings during the source star’s entrance and exit of the caustic yields an angular Einstein radius of mas. The measured and indicate that the lens is a binary composed of two stars with masses and ∼0.15 M ⊙, and is located at a distance of ∼6 kpc. From the color and brightness of the lens estimated from its determined mass and distance, it is expected that ∼2/3 of the I-band blended flux comes from the lens. Therefore, the event is a rare case of a bright lens event for which high-resolution follow-up observations can confirm its nature.

OGLE-2017-BLG-0329L: A Microlensing Binary Characterized with Dramatically Enhanced Precision Using Data from Space-based Observations

Abstract Mass measurements of gravitational microlenses require one to determine the microlens parallax π E, but precise π E measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which π E is measured with a dramatically improved precision using additional data from space-based Spitzer observations. We find that while the parallax model based on the ground-based data cannot be distinguished from a zero-π E model at the 2σ level, the addition of the Spitzer data enables us to identify two classes of solutions, each composed of a pair of solutions according to the well-known ecliptic degeneracy. It is found that the space-based data reduce the measurement uncertainties of the north and east components of the microlens-parallax vector by factors ∼18 and ∼4, respectively. With the measured microlens parallax combined with the angular Einstein radius measured from the resolved caustic crossings, we find that the lens is composed of a binary with component masses of either (M 1, M 2) ∼ (1.1, 0.8) M ⊙ or ∼(0.4, 0.3) M ⊙ according to the two solution classes. The first solution is significantly favored but the second cannot be securely ruled out based on the microlensing data alone. However, the degeneracy can be resolved from adaptive optics observations taken ∼10 years after the event.

OGLE-2014-BLG-0289: Precise Characterization of a Quintuple-peak Gravitational Microlensing Event

Abstract We present the analysis of the binary-microlensing event OGLE-2014-BLG-0289. The event light curve exhibits five very unusual peaks, four of which were produced by caustic crossings and the other by a cusp approach. It is found that the quintuple-peak features of the light curve provide tight constraints on the source trajectory, enabling us to precisely and accurately measure the microlensing parallax π E . Furthermore, the three resolved caustics allow us to measure the angular Einstein radius θ E . From the combination of π E and θ E , the physical lens parameters are uniquely determined. It is found that the lens is a binary composed of two M dwarfs with masses M 1 = 0.52 ± 0.04 M ⊙ and M 2 = 0.42 ± 0.03 M ⊙ separated in projection by a ⊥ = 6.4 ± 0.5 au . The lens is located in the disk with a distance of D L = 3.3 ± 0.3 kpc . The reason for the absence of a lensing signal in the Spitzer data is that the time of observation corresponds to the flat region of the light curve.

Understanding caustic crossings in giant arcs: Characteristic scales, event rates, and constraints on compact dark matter

The recent discovery of fast transient events near critical curves of massive galaxy clusters, which are interpreted as highly magnified individual stars in giant arcs due to caustic crossing, opens up the possibility of using such microlensing events to constrain a range of dark matter models such as primordial black holes and scalar field dark matter. Based on a simple analytic model, we study lensing properties of a point mass lens embedded in a high magnification region, and derive the dependence of the peak brightness, microlensing time scales, and event rates on the mass of the point mass lens as well as the radius of a source star that is magnified. We find that the lens mass and source radius of the first event MACS J1149 Lensed Star 1 (LS1) are constrained, with the lens mass range of $0.1~M_\odot \lesssim M \lesssim 4\times 10^3M_\odot$ and the source radius range of $40~R_\odot \lesssim R \lesssim 260~R_\odot$. In the most plausible case with $M\approx 0.3~M_\odot$ and $R\approx 180~R_\odot$, the source star should have been magnified by a factor of $\approx 4300$ at the peak. The derived lens properties are fully consistent with the interpretation that MACS J1149 LS1 is a microlensing event produced by a star that contributes to the intra-cluster light. We argue that compact dark matter models with high fractional mass densities for the mass range $10^{-5}M_\odot \lesssim M\lesssim 10^2M_\odot$ are inconsistent with the observation of MACS J1149 LS1 because such models predict too low magnifications. Our work demonstrates a potential use of caustic crossing events in giant arcs to constrain compact dark matter.

Measuring the Innermost Stable Circular Orbits of Supermassive Black Holes

Abstract We present a promising new technique, the g-distribution method, for measuring the inclination angle (i), the innermost stable circular orbit (ISCO), and the spin of a supermassive black hole. The g-distribution method uses measurements of the energy shifts in the relativistic iron line emitted by the accretion disk of a supermassive black hole due to microlensing by stars in a foreground galaxy relative to the g-distribution shifts predicted from microlensing caustic calculations. We apply the method to the gravitationally lensed quasars RX J1131–1231 (z s = 0.658, z l = 0.295), QJ 0158–4325 (z s = 1.294, z l = 0.317), and SDSS 1004+4112 (z s = 1.734, z l = 0.68). For RX J1131−1231, our initial results indicate that r ISCO ≲ 8.5 gravitational radii (r g) and i ≳ 55° (99% confidence level). We detect two shifted Fe lines in several observations, as predicted in our numerical simulations of caustic crossings. The current ΔE distribution of RX J1131–1231 is sparsely sampled, but further X-ray monitoring of RX J1131–1231 and other lensed quasars will provide improved constraints on the inclination angles, ISCO radii, and spins of the black holes of distant quasars.

OGLE-2015-BLG-0479LA,B: BINARY GRAVITATIONAL MICROLENS CHARACTERIZED BY SIMULTANEOUS GROUND-BASED AND SPACE-BASED OBSERVATIONS

We present a combined analysis of the observations of the gravitational microlensing event OGLE-2015-BLG-0479 taken both from the ground and by the {\it Spitzer Space Telescope}. The light curves seen from the ground and from space exhibit a time offset of $\sim 13$ days between the caustic spikes, indicating that the relative lens-source positions seen from the two places are displaced by parallax effects. From modeling the light curves, we measure the space-based microlens parallax. Combined with the angular Einstein radius measured by analyzing the caustic crossings, we determine the mass and distance of the lens. We find that the lens is a binary composed of two G-type stars with masses $\sim 1.0\ M_\odot$ and $\sim 0.9\ M_\odot$ located at a distance $\sim 3$ kpc. In addition, we are able to constrain the complete orbital parameters of the lens thanks to the precise measurement of the microlens parallax derived from the joint analysis. In contrast to the binary event OGLE-2014-BLG-1050, which was also observed by {\it Spitzer}, we find that the interpretation of OGLE-2015-BLG-0479 does not suffer from the degeneracy between $(\pm,\pm)$ and $(\pm,\mp)$ solutions, confirming that the four-fold parallax degeneracy in single-lens events collapses into the two-fold degeneracy for the general case of binary-lens events. The location of the blend in the color-magnitude diagram is consistent with the lens properties, suggesting that the blend is the lens itself. The blend is bright enough for spectroscopy and thus this possibility can be checked from future follow-up observations.

A SUPER-JUPITER MICROLENS PLANET CHARACTERIZED BY HIGH-CADENCE KMTNET MICROLENSING SURVEY OBSERVATIONS OF OGLE-2015-BLG-0954

We report the characterization of a massive (m p = 3:9±1:4M jup ) microlensing planet (OGLE-2015-BLG-0954Lb) orbiting an M dwarf host (M = 0:33 0:12M ⊙ ) at a distance toward the Galactic bulge of 0:6 +0.4 -0.2 kpc, which is extremely nearby by microlensing standards. The planet-host projected separation is a⊥~ 1.2AU. The characterization was made possible by the wide-feld (4 deg 2 ) high cadence(Ґ = 6 hr -1 ) monitoring of the Korea Microlensing Telescope Network (KMTNet), which had two of its three telescopes in commissioning operations at the time of the planetary anomaly. The source crossing time t * = 16 min is among the shortest ever published. The high-cadence, wide-eld observations that are the hallmark of KMTNet are the only way to routinely capture such short crossings. High-cadence resolution of short caustic crossings will preferentially lead to mass and distance measurements for the lens. This is because the short crossing time typically implies a nearby lens, which enables the measurement of additional effects (bright lens and/or microlens parallax). When combined with the measured crossing time, these eects can yield planet/host masses and distance.

Gravitational lensing size scales for quasars

AbstractWe review results from our monitoring observations of several lensed quasars performed in the optical, UV, and X‐ray bands. Modeling of the multi‐wavelength light curves provides constraints on the extent of the optical, UV, and X‐ray emission regions. One of the important results of our analysis is that the optical sizes as inferred from the microlensing analysis are significantly larger than those predicted by the theoretical‐thin‐disk estimate. In a few cases we also constrain the slope of the size‐wavelength relation. Our size constraints of the soft and hard X‐ray emission regions of quasars indicate that in some objects of our sample the hard X‐ray emission region is more compact than the soft and in others the soft emission region is smaller. This difference may be the result of the relative strengths of the disk‐reflected (harder and extended) versus corona‐direct (softer and compact) components in the quasars of our sample. Finally, we present the analysis of several strong microlensing events where we detect an evolution of the relativistic Fe line profile as the magnification caustic traverses the accretion disk. These caustic crossings are used to provide constraints on the innermost stable circular orbit (ISCO) radius and the accretion disk inclination angle of the black hole in quasar RX J1131–1231. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

RESOLVING THE INNERMOST REGION OF THE ACCRETION DISK OF THE LENSED QUASAR Q2237+0305 THROUGH GRAVITATIONAL MICROLENSING

We study three high magnification microlensing events, generally recognized as probable caustic crossings, in the optical light curves of the multiply imaged quasar Q 2237+0305. We model the light curve of each event as the convolution of a standard thin disk luminosity profile with a straight fold caustic. We also allow for a linear gradient that can account for an additional varying background effect of microlensing. This model not only matches noticeably well the global shape of each of the three independent microlensing events but also gives remarkably similar estimates for the disk size parameter. The measured average half-light radius, $R_{1/2}=(3.0\pm 1.5)\sqrt{M/0.3M\odot}$ light-days, agrees with previous estimates. In the three events, the core of the magnification profile exhibits "fine structure" related to the innermost region of the accretion disk (located at a radial distance of $2.7\pm 1.4$ Schwarzschild radii according to our measurement). Relativistic beaming at the internal rim of the accretion disk can explain the shape and size of the fine structure, although alternative explanations are also possible. This is the first direct measurement of the size of a structure, likely the innermost stable circular orbit, at $\sim 3$ Schwarzschild radii in a quasar accretion disk. The monitoring of thousands of lensed quasars with future telescopes will allow the study of the event horizon environment of black holes in hundreds of quasars in a wide range of redshifts $(0.5<z<5)$.

LENS MASSES AND DISTANCES FROM MICROLENS PARALLAX AND FLUX

I present a novel method for measuring lens masses for microlensing events. By combining a measured lens flux with the microlens parallax it is possible to derive the mass of the lens system without knowing the angular size of the Einstein ring, This enables mass and distance measurements for single, luminous lenses, as well as binary and planetary lenses without caustic crossings. I discuss applications of this method in the contexts of the Spitzer, Kepler, and WFIRST microlensing missions.

OGLE-2013-BLG-0578 L: A MICROLENSING BINARY COMPOSED OF A BROWN DWARF AND AN M DWARF

Determining physical parameters of binary microlenses is hampered by the lack of information about the angular Einstein radius due to the difficulty of resolving caustic crossings. In this paper, we present the analysis of the binary microlensing event OGLE-2013-BLG-0578, for which the caustic exit was precisely predicted in advance from real-time analysis, enabling to densely resolve the caustic crossing and to measure the Einstein radius. From the mass measurement of the lens system based on the Einstein radius combined with the additional information about the lens parallax, we identify that the lens is a binary that is composed of a late-type M-dwarf primary and a substellar brown-dwarf companion. The event demonstrates the capability of current real-time microlensing modeling and the usefulness of microlensing in detecting and characterizing faint or dark objects in the Galaxy.