Binary-lens Models Research Articles

OGLE-2019-BLG-0825: Constraints on the Source System and Effect on Binary-lens Parameters Arising from a Five-day Xallarap Effect in a Candidate Planetary Microlensing Event

We present an analysis of microlensing event OGLE-2019-BLG-0825. This event was identified as a planetary candidate by preliminary modeling. We find that significant residuals from the best-fit static binary-lens model exist and a xallarap effect can fit the residuals very well and significantly improves χ 2 values. On the other hand, by including the xallarap effect in our models, we find that binary-lens parameters such as mass ratio, q, and separation, s, cannot be constrained well. However, we also find that the parameters for the source system such as the orbital period and semimajor axis are consistent between all the models we analyzed. We therefore constrain the properties of the source system better than the properties of the lens system. The source system comprises a G-type main-sequence star orbited by a brown dwarf with a period of P ∼ 5 days. This analysis is the first to demonstrate that the xallarap effect does affect binary-lens parameters in planetary events. It would not be common for the presence or absence of the xallarap effect to affect lens parameters in events with long orbital periods of the source system or events with transits to caustics, but in other cases, such as this event, the xallarap effect can affect binary-lens parameters.

KMT-2022-BLG-0440Lb: A new q < 10−4 microlensing planet with the central-resonant caustic degeneracy broken

ABSTRACT We present the observations and analysis of a high-magnification microlensing planetary event, KMT-2022-BLG-0440, for which the weak and short-lived planetary signal was covered by both the KMTNet survey and follow-up observations. The binary-lens models with a central caustic provide the best fits, with a planet/host mass ratio, q = 0.75–1.00 × 10−4 at 1σ. The binary-lens models with a resonant caustic and a brown-dwarf mass ratio are both excluded by Δχ2 > 70. The binary-source model can fit the anomaly well but is rejected by the ‘colour argument’ on the second source. From Bayesian analyses, it is estimated that the host star is likely a K or M dwarf located in the Galactic disc, the planet probably has a Neptune-mass, and the projected planet-host separation is $1.9^{+0.6}_{-0.7}$ or $4.6^{+1.4}_{-1.7}$ au, subject to the close/wide degeneracy. This is the third q < 10−4 planet from a high-magnification planetary signal (A ≳ 65). Together with another such planet, KMT-2021-BLG-0171Lb, the ongoing follow-up program for the KMTNet high-magnification events has demonstrated its ability to detect high-magnification planetary signals for q < 10−4 planets, which are challenging for the current microlensing surveys.

MOA-2019-BLG-008Lb: A New Microlensing Detection of an Object at the Planet/Brown Dwarf Boundary

We report on the observations, analysis and interpretation of the microlensing event MOA-2019-BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite-source effects were observed. Therefore, the angular Einstein ring radius θ E cannot be measured from the light curve alone. However, the large event duration, t E ∼ 80 days, allows a precise measurement of the microlensing parallax π E. In addition to the constraints on the angular radius θ * and the apparent brightness I s of the source, we employ the Besançon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two galactic models: the companion is likely a resident of the brown dwarf desert with a mass M p ∼ 30 M Jup, and the host is a main-sequence dwarf star. The lens lies along the line of sight to the Galactic bulge, at a distance of ≤4 kpc. We estimate that in about 10 yr the lens and source will be separated by ∼55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground- or space-based observatories.

OGLE-2019-BLG-0304: Competing Interpretations between a Planet–binary Model and a Binary-source + Binary-lens Model

Abstract We analyze the microlensing event OGLE-2019-BLG-0304, whose light curve exhibits two distinctive features: a deviation in the peak region and a second bump appearing ∼61 days after the main peak. Although a binary-lens model can explain the overall features, it leaves subtle but noticeable residuals in the peak region. We find that the residuals can be explained by the presence of either a planetary companion located close to the primary of the binary lens (3L1S model) or an additional close companion to the source (2L2S model). Although the 3L1S model is favored over the 2L2S model, with Δχ 2 ∼ 8, securely resolving the degeneracy between the two models is difficult with the currently available photometric data. According to the 3L1S interpretation, the lens is a planetary system, in which a planet with a mass 0.51 − 0.23 + 0.51 M J is in an S-type orbit around a binary composed of stars with masses 0.27 − 0.12 + 0.27 M ⊙ and 0.10 − 0.04 + 0.10 M ⊙ . According to the 2L2S interpretation, however, the source is composed of G- and K-type giant stars and the lens is composed of a low-mass M dwarf and a brown dwarf with masses 0.12 − 0.05 + 0.12 M ⊙ and 0.045 − .019 + 0.045 M ⊙ , respectively. The event illustrates the need for thorough model testing in the interpretation of lensing events with complex features in light curves.

KMT-2019-BLG-1715: Planetary Microlensing Event with Three Lens Masses and Two Source Stars

Abstract We investigate the gravitational microlensing event KMT-2019-BLG-1715, the light curve of which shows two short-term anomalies from a caustic-crossing binary-lensing light curve: one with a large deviation and the other with a small deviation. We identify five pairs of solutions, in which the anomalies are explained by adding an extra lens or source component in addition to the base binary-lens model. We resolve the degeneracies by applying a method in which the measured flux ratio between the first and second source stars is compared with the flux ratio deduced from the ratio of the source radii. Applying this method leaves a single pair of viable solutions, in both of which the major anomaly is generated by a planetary-mass third body of the lens, and the minor anomaly is generated by a faint second source. A Bayesian analysis indicates that the lens comprises three masses: a planet-mass object with ∼2.6 M J and binary stars of K and M dwarfs lying in the galactic disk. We point out the possibility that the lens is the blend, and this can be verified by conducting high-resolution follow-up imaging for the resolution of the lens from the source.

KMT-2018-BLG-0748Lb: sub-Saturn microlensing planet orbiting an ultracool host

Aims. We announce the discovery of a microlensing planetary system, in which a sub-Saturn planet is orbiting an ultracool dwarf host. Methods. We detected the planetary system by analyzing the short-timescale (tE ~ 4.4 days) lensing event KMT-2018-BLG-0748. The central part of the light curve exhibits asymmetry due to negative deviations in the rising side and positive deviations in the falling side. Results. We find that the deviations are explained by a binary-lens model with a mass ratio between the lens components of q ~ 2 × 10−3. The short event timescale, together with the small angular Einstein radius, θE ~ 0.11 mas, indicate that the mass of the planet host is very small. The Bayesian analysis conducted under the assumption that the planet frequency is independent of the host mass indicates that the mass of the planet is Mp = 0.18−0.10+0.29 MJ, and the mass of the host, Mh = 0.087−0.047+0.138 M⊙, is near the star–brown dwarf boundary, but the estimated host mass is sensitive to this assumption about the planet hosting probability. High-resolution follow-up observations would lead to revealing the nature of the planet host.

Faint-source-star planetary microlensing: the discovery of the cold gas-giant planet OGLE-2014-BLG-0676Lb

We report the discovery of a planet --- OGLE-2014-BLG-0676Lb --- via gravitational microlensing. Observations for the lensing event were made by the MOA, OGLE, Wise, RoboNET/LCOGT, MiNDSTEp and $\mu$FUN groups. All analyses of the light curve data favour a lens system comprising a planetary mass orbiting a host star. The most favoured binary lens model has a mass ratio between the two lens masses of $(4.78 \pm 0.13)\times 10^{-3}$. Subject to some important assumptions, a Bayesian probability density analysis suggests the lens system comprises a $3.09_{-1.12}^{+1.02}$ M_jup planet orbiting a $0.62_{-0.22}^{+0.20}$ M_sun host star at a deprojected orbital separation of $4.40_{-1.46}^{+2.16}$ AU. The distance to the lens system is $2.22_{-0.83}^{+0.96}$ kpc. Planet OGLE-2014-BLG-0676Lb provides additional data to the growing number of cool planets discovered using gravitational microlensing against which planetary formation theories may be tested. Most of the light in the baseline of this event is expected to come from the lens and thus high-resolution imaging observations could confirm our planetary model interpretation.

A SEARCH FOR STELLAR-MASS BLACK HOLES VIA ASTROMETRIC MICROLENSING

ABSTRACT While dozens of stellar-mass black holes (BHs) have been discovered in binary systems, isolated BHs have eluded detection. Their presence can be inferred when they lens light from a background star. We attempt to detect the astrometric lensing signatures of three photometrically identified microlensing events, OGLE-2011-BLG-0022, OGLE-2011-BLG-0125, and OGLE-2012-BLG-0169 (OB110022, OB110125, and OB120169), located toward the Galactic Bulge. These events were selected because of their long durations, which statistically favors more massive lenses. Astrometric measurements were made over one to two years using laser-guided adaptive optics observations from the W. M. Keck Observatory. Lens model parameters were first constrained by the photometric light curves. The OB120169 light curve is well fit by a single-lens model, while both OB110022 and OB110125 light curves favor binary lens models. Using the photometric fits as prior information, no significant astrometric lensing signal was detected and all targets were consistent with linear motion. The significant lack of astrometric signal constrains the lens mass of OB110022 to 0.05–1.79 M ⊙ in a 99.7% confidence interval, which disfavors a BH lens. Fits to OB110125 yielded a reduced Einstein crossing time and insufficient observations during the peak, so no mass limits were obtained. Two degenerate solutions exist for OB120169, which have a lens mass between 0.2–38.8 M ⊙ and 0.4–39.8 M ⊙ for a 99.7% confidence interval. Follow-up observations of OB120169 will further constrain the lens mass. Based on our experience, we use simulations to design optimal astrometric observing strategies and show that with more typical observing conditions the detection of BHs is feasible.

REANALYSES OF ANOMALOUS GRAVITATIONAL MICROLENSING EVENTS IN THE OGLE-III EARLY WARNING SYSTEM DATABASE WITH COMBINED DATA

We reanalyze microlensing events in the published list of anomalous events that were observed from the OGLE lensing survey conducted during 2004-2008 period. In order to check the existence of possible degenerate solutions and extract extra information, we conduct analyses based on combined data from other survey and follow-up observation and consider higher-order effects. Among the analyzed events, we present analyses of 8 events for which either new solutions are identified or additional information is obtained. We find that the previous binary-source interpretations of 5 events are better interpreted by binary-lens models. These events include OGLE-2006-BLG-238, OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210. With additional data covering caustic crossings, we detect finite-source effects for 6 events including OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, OGLE-2008-BLG-143, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. Among them, we are able to measure the Einstein radii of 3 events for which multi-band data are available. These events are OGLE-2006-BLG-238, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. For OGLE-2008-BLG-143, we detect higher-order effect induced by the changes of the observer's position caused by the orbital motion of the Earth around the Sun. In addition, we present degenerate solutions resulting from the known close/wide or ecliptic degeneracy. Finally, we note that the masses of the binary companions of the lenses of OGLE-2006-BLG-450 and OGLE-2008-BLG-210 are in the brown-dwarf regime.

REANALYSIS OF THE GRAVITATIONAL MICROLENSING EVENT MACHO-97-BLG-41 BASED ON COMBINED DATA

MACHO-97-BLG-41 is a gravitational microlensing event produced by a lens composed of multiple masses detected by the first-generation lensing experiment. For the event, there exist two different interpretations of the lens from independent analyses based on two different data sets: one interpreted the event as produced by a circumbinary planetary system while the other explained the light curve with only a binary system by introducing orbital motion of the lens. According to the former interpretation, the lens would be not only the first planet detected via microlensing but also the first circumbinary planet ever detected. To resolve the issue using state-of-the-art analysis methods, we reanalyze the event based on the combined data used separately by the previous analyses. By considering various higher-order effects, we find that the orbiting binary-lens model provides a better fit than the circumbinary planet model with \Delta\chi^2 ~166. The result signifies the importance of even and dense coverage of lensing light curves in the interpretation of events.

A POSSIBLE BINARY SYSTEM OF A STELLAR REMNANT IN THE HIGH-MAGNIFICATION GRAVITATIONAL MICROLENSING EVENT OGLE-2007-BLG-514

We report the extremely high magnification (A > 1000) binary microlensing event OGLE-2007-BLG-514. We obtained good coverage around the double peak structure in the light curve via follow-up observations from different observatories. The binary lens model that includes the effects of parallax (known orbital motion of the Earth) and orbital motion of the lens yields a binary lens mass ratio of q = 0.321 +/- 0.007 and a projected separation of s = 0.072 +/- 0.001$ in units of the Einstein radius. The parallax parameters allow us to determine the lens distance D_L = 3.11 +/- 0.39 kpc and total mass M_L=1.40 +/- 0.18 M_sun; this leads to the primary and secondary components having masses of M_1 = 1.06 +/- 0.13 M_sun and M_2 = 0.34 +/- 0.04 M_sun, respectively. The parallax model indicates that the binary lens system is likely constructed by the main sequence stars. On the other hand, we used a Bayesian analysis to estimate probability distributions by the model that includes the effects of xallarap (possible orbital motion of the source around a companion) and parallax (q = 0.270 +/- 0.005, s = 0.083 +/- 0.001). The primary component of the binary lens is relatively massive with M_1 = 0.9_{-0.3}^{+4.6} M_sun and it is at a distance of D_L = 2.6_{-0.9}^{+3.8} kpc. Given the secure mass ratio measurement, the companion mass is therefore M_2 = 0.2_{-0.1}^{+1.2} M_sun. The xallarap model implies that the primary lens is likely a stellar remnant, such as a white dwarf, a neutron star or a black hole.

The Many Possible Interpretations of Microlensing Event OGLE 2002‐BLG‐055

Microlensing event OGLE 2002-BLG-055 is characterized by a smooth, slightly asymmetric single-lens curve with an isolated, secure data point that is ~0.6 mag brighter than neighboring points separated by a few days. It was previously suggested that the single deviant data point and global asymmetry were best explained by a planetary companion to the primary lens with mass ratio q = 10-3 to 10-2 and by parallax effects induced by the motion of the Earth. We revisit the interpretation of OGLE 2002-BLG-055 and show that the data can be explained by a wide variety of models. We find that the deviant data point can be fitted by a large number of qualitatively different binary-lens models whose mass ratios range, at the ~3 σ level, from q 10-4 to 10-1. This range is consistent with a planet, brown dwarf, or M dwarf companion for reasonable primary masses of M 0.8 M☉. A subset of these binary-lens fits consists of a family of continuously degenerate models whose mass ratios differ by an order of magnitude, but whose light curves differ by 2% for the majority of the perturbation. The deviant data point can also be explained by a binary companion to the source, with a secondary/primary flux ratio of ~1%. This model has the added appeal that the global asymmetry is naturally explained by the acceleration of the primary induced by the secondary. The binary-source model yields a measurement of the Einstein ring radius projected onto the source plane of E = 1.87 ± 0.40 AU. OGLE 2002-BLG-055 is an extreme example that illustrates the difficulties and degeneracies inherent in the interpretation of weakly perturbed and/or poorly sampled microlensing light curves.

Optical gravitational lensing experiment: OGLE-1999-BUL-19 – the first multipeak parallax event

We describe a highly unusual microlensing event, OGLE-1999-BUL-19. Unlike most standard microlensing events, this event exhibits multiple peaks in its light curve. The Einstein radius crossing time for this event is approximately 1 yr, which is unusually long. We show that the additional peaks in the light curve can be caused by the very small value for the relative transverse velocity of the lens projected on to the observer plane (). Since this value is significantly less than the speed of the orbit of the Earth around the Sun (v⊕∼ 30km s−1), the motion of the Earth induces these multiple peaks in the light curve. This value for is the lowest velocity so far published and we believe that this is the first multiple-peak parallax event ever observed. We also found that the event can be somewhat better fitted by a rotating binary-source model, although this is to be expected since every parallax microlensing event can be exactly reproduced by a suitable binary-source model. A face-on rotating binary-lens model was also identified, but this provides a significantly worse fit. We conclude that the most likely cause for this multipeak behaviour is parallax microlensing rather than microlensing by a binary source. However, this event may be exhibiting a slight binary-source signature in addition to these parallax-induced multiple peaks. With spectroscopic observations it is possible to test this ‘parallax plus binary-source’ hypothesis and (in the instance that the hypothesis turns out to be correct) to simultaneously fit both models and obtain a measurement of the lens mass. Furthermore, spectroscopic observations could also supply information regarding the lens properties, possibly providing another avenue for determining the lens mass. We also investigated the nature of the blending for this event, and found that the majority of the I-band blending is contributed by a source roughly aligned with the lensed source. This implies that most of the I-band blending is caused by light from the lens or a binary companion to the source. However, in the V band, there appears to be a second blended source 0.35 arcsec away from the lensed source. Hubble Space Telescope observations will be very useful for understanding the nature of the blends. We also suggest that a radial velocity survey of all parallax events will be very useful for further constraining the lensing kinematics and understanding the origins of these events and the excess of long events toward the bulge.

Predicting the second caustic crossing in binary microlensing events

We fit binary lens models to the data covering the initial part of real microlensing events in an attempt to predict the time of the second caustic crossing. We use approximations during the initial search through the parameter space for light curves that roughly match the observed ones. Exact methods for calculating the lens magnification of an extended source are used when we refine our best initial models. Our calculations show that the reliable prediction of the second crossing can only be made very late, when the light curve has risen appreciably after the minimum between the two caustic crossings. The best observational strategy is therefore to sample as frequently as possible once the light curve starts to rise after the minimum.

The Relative Lens‐Source Proper Motion in MACHO 98‐SMC‐1

We present photometric and spectroscopic data for the second microlensing event seen toward the Small Magellanic Cloud (SMC), MACHO 98-SMC-1. The lens is a binary. We resolve the caustic crossing and find that the source took 2 Δt=8.5 hr to transit the caustic. We measure the source temperature Teff=8000 K both spectroscopically and from the color, (V-I)0~0.22. We find two acceptable binary-lens models. In the first, the source crosses the caustic at =432 and the unmagnified source magnitude is Is=22.15. The angle implies that the lens crosses the source radius in time t*=Δt=2.92 hr. The magnitude (together with the temperature) implies that the angular radius of the source is θ*=0.089 μas. Hence, the proper motion is μ=θ*/t*=1.26 km s-1 kpc-1. For the second solution, the corresponding parameters are =306, Is=21.81, t*=2.15 hr, θ*=0.104 μas, and μ=θ*/t*=2.00 km s-1 kpc-1. Both proper-motion estimates are slower than 99.5% of the proper motions expected for halo lenses. Both are consistent with an ordinary binary lens moving at ~75-120 km s-1 within the SMC itself. We conclude that the lens is most likely in the SMC proper.

Galactic Microlensing beyond the Standard Model

For most of the Galactic microlensing events as well as for the analysis of the results from microlensing surveys, a simplified model of pointlike source objects (observed stars) and lens objects (matter between source and observer that causes a light deflection) is being used. Here I discuss effects beyond this approximation, using observed events as examples if they exhibit such effects, prospects of observing such effects, and the influence of these effects on the interpretation of the data. Moreover, I investigate whether ambiguities show up in modeling the observed events, how well model parameters are constrained by the observations, and what implications follow for the physical quantities of the lens system, which are lens mass, distance, and velocity as well as rotation period and semimajor axis for binary lenses. The effects discussed include light from other sources (blending), extended and binary lenses and sources, and rotation effects in the observer (Earth around Sun), the lens, and the source. Taking into account these “nonstandard” effects, I discuss fits for the Galactic microlensing events MACHO LMC 1, EROS 1, OGLE 1–7, and DUO 2. For fitting model parameters of microlensing light curves to the observed data, I discuss an efficient numerical approach that has been used for the fits presented in this dissertation. I argue that some of the observed events that are claimed as being due to point sources and lenses are better explained by source or lens binaries, which are more general models and include the pointlike objects as a limit. In particular, MACHO LMC 1 is best explained by a binary lens. Several different binary lens models are presented for OGLE 7 and DUO 2, which are all consistent with the observed data. I show that the inclusion of blending in fits for the OGLE 1–6 events yields large uncertainties for the event timescales and therefore for the lens masses. Since “nonstandard” events show different statistics than point source–point lens events, one has to be careful with the interpretation of the results of ongoing microlensing searches. Since the Galactic halo is an unknown population, it is difficult to make assumptions about statistics of binary objects. Binarity of objects makes it difficult to obtain the mass spectrum of the lens objects. Since the distance and velocity of the lens are not known in general, the lens mass cannot be determined directly. I derive the probability density of the lens mass for a given observed event from assumed mass densities and velocity distributions. The inclusion of the revolution of the Earth around the Sun, the source size, and the lens rotation each give an additional constraint on the lens distance and velocity, so that the lens mass can be determined (up to a twofold degeneracy) if at least two of these effects are observed. If the lens consists of a star and a planetary companion, the presented methods of estimating physical quantities of the lens system and determining the uncertainties of the fit parameters as well as the discussion of ambiguities of the fit parameters are a necessary prerequisite to draw the right conclusions from an observed light curve.

A Statistical Investigation of the Contamination of Binary Gravitational Lens Candidates by Cataclysmic Variables

A common remark at conferences and meetings has been: One can fit any light curve with binary lens models because of the large number of parameters! It is especially tempting to claim that some of the possible binary events in the Galactic microlensing searches could be caused by cataclysmic variables since both phenomena exhibits asymmetric light curves. This paper presents a statistical analysis comparing the light curves of cataclysmic variable stars to the light curves generated from binary lens models. It is shown that the light curves of high amplitude cataclysmic variables are one example of light curves that can not be explained with binary lens models. It is, therefore, not only unlikely, but also impossible that cataclysmic variables can contaminate the binary microlens candidates.