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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

ON THE FEASIBILITY OF CHARACTERIZING FREE-FLOATING PLANETS WITH CURRENT AND FUTURE SPACE-BASED MICROLENSING SURVEYS

Simultaneous space- and ground-based microlensing surveys, such as K2's Campaign 9 (K2C9) and WFIRST, facilitate measuring the masses and distances of free-floating planet (FFP) candidates, which are identified as single-lens events with timescales that are of the order of 1 day. Measuring the mass and distance of an FFP lens requires determining the size of the source star ρ, measuring the microlens parallax π{sub E}, and using high-resolution imaging to search for the lens flux F{sub ℓ} from a possible host star. Here we investigate the accessible parameter space for each of these components considering different satellites for a range of FFP masses, Galactic distances, and source star properties. We find that at the beginning of K2C9, when its projected separation D{sub ⊥} from the Earth is ≲0.2 au, it will be able to measure π{sub E} for Jupiter-mass FFP candidates at distances larger than ∼2 kpc and to Earth-mass lenses at ∼8 kpc. At the end of K2C9, when D{sub ⊥} = 0.81 au, it is sensitive to planetary-mass lenses for distances ≳3.5 kpc, and even then only to those with mass ≳M {sub Jup}. From lens flux constraints we find that it will be possible to exclude hosts down to the deuterium-burning limit for events within ∼2 kpc. This indicates that the ability to characterize FFPs detected during K2C9 is optimized for events occurring toward the beginning of the campaign. WFIRST, on the other hand, will be able to detect and characterize FFP masses down to or below super-Earths throughout the Galaxy during its entire microlensing survey.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE FIRST CIRCUMBINARY PLANET FOUND BY MICROLENSING: OGLE-2007-BLG-349L(AB)c

We present the analysis of the first circumbinary planet microlensing event, OGLE-2007-BLG-349. This event has a strong planetary signal that is best fit with a mass ratio of q ≈ 3.4 × 10{sup −4}, but there is an additional signal due to an additional lens mass, either another planet or another star. We find acceptable light-curve fits with two classes of models: two-planet models (with a single host star) and circumbinary planet models. The light curve also reveals a significant microlensing parallax effect, which constrains the mass of the lens system to be M {sub L} ≈ 0.7 M{sub ⊙}. Hubble Space Telescope (HST) images resolve the lens and source stars from their neighbors and indicate excess flux due to the star(s) in the lens system. This is consistent with the predicted flux from the circumbinary models, where the lens mass is shared between two stars, but there is not enough flux to be consistent with the two-planet, one-star models. So, only the circumbinary models are consistent with the HST data. They indicate a planet of mass m {sub c} = 80 ± 13 M{sub ⊕}, orbiting a pair of M dwarfs with masses of M {sub A} = 0.41 ± 0.07 and M {sub B} = 0.30 ± 0.07, which makes this the lowest-mass circumbinary planet system known. The ratio of the separation between the planet and the center of mass to the separation of the two stars is ∼40, so unlike most of the circumbinary planets found by Kepler, the planet does not orbit near the stability limit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Size of the accretion disk in the graviationally lensed quasar SDSS J1004+4112 from the statistics of microlensing magnifications

We present eight monitoring seasons of the four brightest images of the gravitational lens SDSS J1004+4112 observed between 2003 December and 2010 October. Using measured time delays for the images A, B, and C and the model predicted time delay for image D we have removed the intrinsic quasar variability, finding microlensing events of about 0.5 and 0.7 mag of amplitude in the images C and D. From the statistics of microlensing amplitudes in images A, C, and D, we have inferred the half-light radius (at λ{sub rest}=2407 A-ring ) for the accretion disk using two different methods, R{sub 1/2}=8.7{sub −5.5}{sup +18.5}√(M/0.3M{sub ⊙}) (histogram product) and R{sub 1/2}=4.2{sub −2.2}{sup +3.2}√(M/0.3M{sub ⊙}) lt-days (χ{sup 2}). The results are in agreement within uncertainties with the size predicted from the black hole mass in SDSS J1004+4112 using thin disk theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Spitzer Opens New Path to Break Classic Degeneracy for Jupiter-mass Microlensing Planet OGLE-2017-BLG-1140Lb

We analyze the combined Spitzer and ground-based data for OGLE-2017-BLG-1140 and show that the event was generated by a Jupiter-class (m{sub p}≃1.6 M{sub Jup}) planet orbiting a mid-late M dwarf (M≃0.2 M{sub ⊙}) that lies D{sub LS}≃1.0 kpc in the foreground of the microlensed Galactic-bar source star. The planet–host projected separation is a{sub ⊥}≃1.0 au, i.e., well beyond the snow line. By measuring the source proper motion μ{sub s} from ongoing long-term OGLE imaging and combining this with the lens-source relative proper motion μ{sub rel} derived from the microlensing solution, we show that the lens proper motion μ{sub l}=μ{sub rel}+μ{sub s} is consistent with the lens lying in the Galactic disk, although a bulge lens is not ruled out. We show that while the Spitzer and ground-based data are comparably well fitted by planetary (i.e., binary-lens (2L1S)) and binary-source (1L2S) models, the combination of Spitzer and ground-based data decisively favors the planetary model. This is a new channel to resolve the 2L1S/1L2S degeneracy, which can be difficult to break in some cases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

KMT-2016-BLG-1836Lb: A Super-Jovian Planet from a High-cadence Microlensing Field

We report the discovery of a super-Jovian planet in the microlensing event KMT-2016-BLG-1836, which was found by the Korea Microlensing Telescope Network (KMTNet) high-cadence observations (Γ~4 hr -1 ). The planet–host mass ratio q ~ 0.004. A Bayesian analysis indicates that the planetary system is composed of a super-Jovian M{ planet =2.2 -1.1 +1.9 M J planet orbiting an M or K dwarf, M{ host =0.49 -0.25 0.38 M ⊙ , at a distance of D L =7.1 -2.4} +0.8 kpc. The projected planet–host separation is 3.5 -0.9 +1.1 au, implying that the planet is located beyond the snow line of the host star. Future high-resolution images can potentially strongly constrain the lens brightness and thus the mass and distance of the planetary system. Without considering detailed detection efficiency, selection, or publication biases, we find a potential mass-ratio desert at -3.7 ≲ log q ≲ -3.0 for the 31 published KMTNet planets.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Gravitational microlensing by the galactic halo

A simple model of microlensing by massive objects that might be present in the halo of the Galaxy is presented. It is shown that in any nearby galaxy one star out of a million is strongly microlensed by a 'dark' object located in the Galactic halo, if the halo is made up of objects more massive than about 10 to the -8th solar mass. Monitoring the brightness of a few million stars in the Magellanic Clouds over a time scale between two hours and two years may lead to a discovery of 'dark halo' objects between 10 to the -6th and 10 to the -2nd solar mass, or it may put strong upper limits on the number of such objects.

Paczynski, B.↗
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↗