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NASA NTRS1987

Gravitational microlensing and gamma-ray bursts

Models of gravitational microlensing at small and large optical depth are presented, with a special emphasis on the time delays between microimages. The time distribution of microimage arrival times is random when the microobjects responsible for the lensing are randomly distributed. If the microobjects are clustered in space, then microimages are clustered in time. In some models there are many pairs of microimages with a very small time separation. It is proposed that the recently discovered recurrent soft gamma-ray burster GB 790107, for which more than 50 bursts were detected, is a single event multiply imaged due to gravitational microlensing by an ensemble of nonrandomly distributed microobjects, perhaps a rich cluster of galaxies. Some observational tests of this hypothesis are proposed. If correct, the hypothesis requires the burster to be at a cosmological distance, perhaps farther away than the most distant quasars.

Paczynski, Bohdan↗
NASA NTRS1990

A microlensing model for QSO 2237 + 0305

Models of microlensing are presented for the four images of QSO 2237 + 0305, with the surface mass density and shear for each image based on the macrolensing model developed by Schneider et al. (1988). The computations were done with a new code that makes use of the hierarchical tree method. The high efficiency of this approach makes it possible to include up to 60,000 lensing stars with different masses. Examples are given of amplification maps, light curves, correlation functions, and amplification probabilities. All these are very strongly affected by the shear due to macrolensing. The observed changes in the luminosity of the four images of QSO 2237 + 0305 are most likely induced by microlensing.

Wambsganss, J.↗
NASA NTRS1991

Gravitational microlensing of the Galactic bulge stars

The optical depth to microlensing on the ordinary disk stars is about 4 x 10 to the -7th for the Galactic bulge stars visible in Baade's window. This means that at any given time one out of about 2.5 x 10 to the 6th bulge stars must be brightened by at least 0.3 mag. The duration of events is proportional to the square root of mass of the lensing star, and it is in the range of 1 week to 1 month for the lensing stars of 0.1-1.0 solar mass. The average number of events with the amplitude exceeding 0.3 mag is expected to be about 4 per year per million bulge stars. If there are brown dwarfs in the Galactic disk with masses in the range 0.01-0.1 solar mass, with the total mass density equal to the total mass density of the ordinary stars, then the combined optical depth to microlensing of the bulge stars is about 8 x 10 to the -7th, the average number of events with the amplitude exceeding 0.3 mag is expected to be about 17 per year per million bulge stars, and the time scales of events are in the range of 3-20 days.

Paczynski, B.↗
NASA NTRS1991

Microlensing and the structure of active galactic nucleus accretion disks

Rapid variability has been reported in two of the four gravitationally lensed images of Q2237 + 0305, and this is attributed to microlensing caused by the intervening stars. The associated constraints on the source size and properties are studied and compared with a variety of stationary accretion disk models. The reported microlensing variation in Q2237 + 0305 requires the disk size to be over 3 times smaller than a blackbody disk of similar luminosity, implying that the optical emission is either nonthermal or optically tin. An exploration of nonstationary disk models including orbiting, transient hot spots leads to a similar conclusion. Implications for models of active galactic nucleus optical continua are briefly discussed.

Rauch, Kevin P.↗
NASA NTRS1992

Gravitational microlensing by a single star plus external shear

Gravitational microlensing by a single star plus external shear is considered. It is shown that for a general cusp the magnification probability distribution follows pc(A)dA of about (A exp -7/2)dA for sufficiently large magnifications. An adaptive grid technique is developed to calculate the magnification probability distributions. The results could be useful for cases of microlensing where the surface-mass density is low.

Mao, Shude↗
NASA NTRS1992

Microlensed light curves for thin accretion disks around Schwarzschild and Kerr black holes

Surface brightness maps for thin accretion disks around Schwarzschild and Kerr black holes are presented. These disks are a few times smaller than those used by Rauch and Blandford (1991), and some of the present models are slightly less luminous than theirs. Example of microlensed light curves are calculated by convolving these accretion disk maps with the magnification patterns obtained from microlensing calculations. The light curves exhibit eventlike variations with amplitudes and time scales comparable to those observed in QSO 2237 + 0305. It is concluded that thin thermal accretion disk models are not in contradiction with the observed microlens-induced variations of QSO 2237 + 0305.

Jaroszynski, M.↗
NASA NTRS1993

Gravitational microlensing of gamma-ray bursts

A Monte Carlo code is developed to calculate gravitational microlensing in three dimensions when the lensing optical depth is low or moderate (not greater than 0.25). The code calculates positions of microimages and time delays between the microimages. The majority of lensed gamma-ray bursts should show a simple double-burst structure, as predicted by a single point mass lens model. A small fraction should show complicated multiple events due to the collective effects of several point masses (black holes). Cosmological models with a significant fraction of mass density in massive compact objects can be tested by searching for microlensing events in the current BATSE data. Our catalog generated by 10,000 Monte Carlo models is accessible through the computer network. The catalog can be used to take realistic selection effects into account.

Mao, Shude↗
NASA NTRS1993

An efficient method to compute microlensed light curves for point sources

We present a method to compute microlensed light curves for point sources. This method has the general advantage that all microimages contributing to the light curve are found. While a source moves along a straight line, all micro images are located either on the primary image track or on the secondary image tracks (loops). The primary image track extends from - infinity to + infinity and is made of many sequents which are continuously connected. All the secondary image tracks (loops) begin and end on the lensing point masses. The method can be applied to any microlensing situation with point masses in the deflector plane, even for the overcritical case and surface densities close to the critical. Furthermore, we present general rules to evaluate the light curve for a straight track arbitrary placed in the caustic network of a sample of many point masses.

Witt, Hans J.↗
NASA NTRS1993

Theory of dispersive microlenses

A dispersive microlens is a miniature optical element which simultaneously focuses and disperses light. Arrays of dispersive mircolenses have potential applications in multicolor focal planes. They have a 100 percent optical fill factor and can focus light down to detectors of diffraction spot size, freeing up areas on the focal plane for on-chip analog signal processing. Use of dispersive microlenses allows inband color separation within a pixel and perfect scene registration. A dual-color separation has the potential for temperature discrimination. We discuss the design of dispersive microlenses and present sample results for efficient designs.

Herman, B.↗
NASA NTRS1994

M dwarfs, microlensing, and the mass budget of the Galaxy

We show that faint red stars do not contribute significantly to the mass budget of the Galaxy or to microlensing statistics. Our results are obtained by analyzing two long exposures of a high-latitude field taken with the Wide Field Camera (WFC) on the newly repaired Hubble Space Telescope (HST). Stars are easily distinguished from galaxies essentially to the limiting magnitudes of the images. We find five stars with 2.0 less than V - I less than 3.0 and I less than 25.3 and no stars with V - I greater than 3.0. Therefore, main-sequence stars with M(sub I) greater than 10 that are above the hydrogen-burning limit in the dark halo or the spheroid contribute less than 6% of the unseen matter. Faint red disk stars, M-dwarfs, contribute at most 15% to the mass of the disk. We parameterize the faint end of the cumulative distribution of stars, Phi, as a function of luminosity L(sub V), d Phi/d ln L(sub V) proportional to L(sub V exp -gamma). For spheroid stars, gamma less than 0.32 over the range 6 less than M(sub V) less than 17, with 98% confidence. The disk luminosity function falls, gamma less than 0, for 15 approximately less than M(sub V) approximately less than 19. Faint red stars in the disk or thick disk, and stars with M(sub V) less than 16 in the spheroid contribute tau less than 10(exp -8) to the optical depth to microlensing toward the Large Magellanic Cloud.

Bahcall, John N.↗
NASA NTRS1995

Microlensing by the galactic bar

We compute the optical depth and duration distribution of microlensing events towrd Baade's window in a model composed of a Galactic disk and a bar. The bar model is a self-consistent dynamical model built out of individual orbits that has been populated to be consistent with the COBE maps of the Galaxy and kinematic observations of the Galactic bulge. We find that most of the lenses are in the bulge with a line-of-sight distance 6.25 kpc (adopting R(sub 0) = 8 kpc). The microlensing optical depth of a 2 x 10(exp 10) solar mass bar plus a truncated disk is (2.2 +/- 0.45) x 10(exp -6), consistent with the large optical depth (3.2 +/- 1.2) x 10(exp -6) found by Udalski et al. (1994). This model optical depth is enhanced over the predictions of axisymmetric models by Kiraga & Paczynski (1994) by slightly more than a factor of 2, since the bar is elongated along the line of sight. The large Einstein radius and small transverse velocity dispersion also predict a longer event duration in the self-consistent bar model than in the Kiraga-Paczynski model. The event rate and duration distribution also depend on the lower mass cutoff of the lens mass function. With a 0.1 solar mass cutoff, five to seven events (depending on the contribution of disk lenses) with a logarithmic mean duration of 20 days are expected for the Optical Gravitational Lensing Experiment (OGLE) according to our model, while Udalski et al. (1994) observed nine events with durations from 8 to 62 days. On the other hand, if most of the lenses are brown dwarfs, our model predicts too many short-duration events. A Kolmogorov-Smirnov test finds only 7% probability for the model with 0.01 solar mass cutoff to be consistent with current data.

Zhao, Hongsheng↗
NASA NTRS2012

The Exoplanet Microlensing Survey by the Proposed WFIRST Observatory

The New Worlds, New Horizons report released by the Astronomy and Astrophysics Decadal Survey Board in 2010 listed the Wide Field Infrared Survey Telescope (WFIRST) as the highest-priority large space mission for the . coming decade. This observatory will provide wide-field imaging and slitless spectroscopy at near infrared wavelengths. The scientific goals are to obtain a statistical census of exoplanets using gravitational microlensing. measure the expansion history of and the growth of structure in the Universe by multiple methods, and perform other astronomical surveys to be selected through a guest observer program. A Science Definition Team has been established to assist NASA in the development of a Design Reference Mission that accomplishes this diverse array of science programs with a single observatory. In this paper we present the current WFIRST payload concept and the expected capabilities for planet detection. The observatory. with science goals that are complimentary to the Kepler exoplanet transit mission, is designed to complete the statistical census of planetary systems in the Galaxy, from habitable Earth-mass planets to free floating planets, including analogs to all of the planets in our Solar System except Mercury. The exoplanet microlensing survey will observe for 500 days spanning 5 years. This long temporal baseline will enable the determination of the masses for most detected exoplanets down to 0.1 Earth masses.

Barry, Richard↗
NASA NTRS2019

The 2L1S/1L2S Degeneracy for Two Microlensing Planet Candidates Discovered by the KMTNet Survey in 2017

We report two microlensing planet candidates discovered by the Korea Microlensing Telescope Network (KMTNet) survey in 2017. However, both events have the 2L1S/1L2S degeneracy, which is an obstacle to claiming the discovery of the planets with certainty unless the degeneracy can be resolved. For KMT-2017-BLG-0962, the degeneracy cannot be resolved. If the 2L1S solution is correct, KMT-2017-BLG-0962 might be produced by a super Jupiter-mass planet orbiting a mid-M-dwarf host star. For KMT-2017-BLG-1119, the light-curve modeling favors the 2L1S solution but higher-resolution observations of the baseline object tend to support the 1L2S interpretation rather than the planetary interpretation. This degeneracy might be resolved by a future measurement of the lens-source relative proper motion. This study shows that the problem of resolving 2L1S/1L2S degeneracy exists over a much wider range of conditions than those considered by the theoretical study of Gaudi (1998).

I.-G. Shin↗
NASA NTRS2019

OGLE-2018-BLG-1011Lb,c: Microlensing Planetary System with Two Giant Planets Orbiting a Low-mass Star

We report a multiplanetary system found from the analysis of microlensing event OGLE-2018-BLG-1011, for which the light curve exhibits a double-bump anomaly around the peak. We find that the anomaly cannot be fully explained by the binary-lens or binary-source interpretations and its description requires the introduction of an additional lens component. The 3L1S (three lens components and a single source) modeling yields three sets of solutions, in which one set of solutions indicates that the lens is a planetary system in a binary, while the other two sets imply that the lens is a multiplanetary system. By investigating the fits of the individual models to the detailed light curve structure, we find that the multiple-planet solution with planet-to-host mass ratios ∼9.5 X 10(exp −3) and ∼15 X 10(eap −3) are favored over the other solutions. From the Bayesian analysis, we find that the lens is composed of two planets with masses 1.8 (sup +3.4, sub -1.1) M(J) and 2.8 (sup +5.8, sub -1.7) M(J) around a host with a mass 0.18 (sup +0.33,sub - 0.10) M(ʘ) and located at a distance 7.1(sup +1.1, sub -1.5) kpc. The estimated distance indicates that the lens is the farthest system among the known multiplanetary systems. The projected planet–host separations are a(⊥,2) = 1.8 (sup +2.1, sub -1.5)au (0.8 (sup +0.9,sub -0.6 au) and a(⊥,3) = 0.8 (sup +0.9, sub -0.6)au , where the values of a(⊥,2) inside and outside the parenthesis are the separations corresponding to the two degenerate solutions, indicating that both planets are located beyond the snow line of the host, as with the other four multiplanetary systems previously found by microlensing.

Cheongho Han↗
NASA NTRS2019

Spitzer Microlensing of MOA-2016-BLG-231L: A Counter-rotating Brown Dwarf Binary in the Galactic Disk

We analyze the binary microlensing event MOA-2016-BLG-231, which was observed from the ground and from Spitzer. The lens is composed of very-low-mass brown dwarfs (BDs) with M(1)= 21(+12, -5) M(J) and M(2)=9(+5. -2) M(J), and it is located in the Galactic disk D(L)=2.85(+0.88, -0.50) kpc. This is the fifth binary brown dwarf discovered by microlensing, and the BD binary is moving counter to the orbital motion of disk stars. Constraints on the lens physical properties come from late-time, non-caustic-crossing features of the Spitzer light curve. Thus, MOA-2016-BLG-231 shows how Spitzer plays a crucial role in resolving the nature of BDs in binary BD events with short timescales (≲10 days).

Sun-Ju Chung↗
NASA NTRS2019

An analysis of binary microlensing event OGLE-2015-BLG-0060

We present the analysis of stellar binary microlensing event OGLE-2015-BLG-0060 based on observations obtained from 13 different telescopes. Intensive coverage of the anomalous parts of the light curve was achieved by automated follow-up observations from the robotic telescopes of the Las Cumbres Observatory. We show that, for the first time, all main features of an anomalous microlensing event are well covered by follow-up data, allowing us to estimate the physical parameters of the lens. The strong detection of second-order effects in the event light curve necessitates the inclusion of longer-baseline survey data in order to constrain the parallax vector. We find that the event was most likely caused by a stellar binary-lens with masses M ͙(1) = 0.87 ± 0.12M(☉) and M ͙(2)= 0.77 ± 0.11M(☉). The distance to the lensing system is 6.41 ± 0.14 kpc and the projected separation between the two components is 13.85 ± 0.16 au. Alternative interpretations are also considered.

Y. Tsapras↗
NASA NTRS2022

KMT-2021-BLG-0912Lb: A Microlensing Super Earth Around A K-Type Star

Aims . The light curve of the microlensing event KMT-2021-BLG-0912 exhibits a very short anomaly relative to a single-lens single-source form. We investigate the light curve for the purpose of identifying the origin of the anomaly. Methods . We model the light curve under various interpretations. From this, we find four solutions, in which three solutions are found under the assumption that the lens is composed of two masses (2L1S models), and the other solution is found under the assumption that the source is comprised of binary stars (1L2S model). The 1L2S model is ruled out based on the contradiction that the faint source companion is bigger than its primary, and one of the 2L1S solutions is excluded from the combination of the poorer fit, blending constraint, and lower overall probability, leaving two surviving solutions with the planet/host mass ratios of q ∼ 2.8 × 10 −5 and ∼1.1 × 10 −5 . A subtle central deviation supports the possibility of a tertiary lens component, either a binary companion to the host with a very large or small separation, or a second planet lying near the Einstein ring, but it is difficult to claim a secure detection due to the marginal improvement of the fit, lack of consistency among different data sets, and difficulty in uniquely specifying the nature of the tertiary component. Results . With the observables of the event, it is estimated that the masses of the planet and host are ∼(6.9 M ⊕ , 0.75 M ⊙ ) according to one solution and ∼(2.8 M ⊕ , 0.80 M ⊙ ) according to the other, indicating that the planet is a super Earth around a K-type star, regardless of the solution. The fact that 16 (including the one reported in this work) out of 19 microlensing planets with M ≲ 10 M ⊕ were detected during the last 6 yr nicely demonstrates the importance of high-cadence global surveys in detecting very low-mass planets.

gravitational lensing↗