Angular Einstein Radius Research Articles

A Free-floating or Wide-orbit Planet in the Microlensing Event OGLE-2019-BLG-0551

Abstract High-cadence observations of the Galactic bulge by the microlensing surveys led to the discovery of a handful of extremely short-timescale microlensing events that can be attributed to free-floating or wide-orbit planets. Here, we report the discovery of another strong free-floating planet candidate, which was found from the analysis of the gravitational microlensing event OGLE-2019-BLG-0551. The light curve of the event is characterized by a very short duration (≲3 days) and a very small amplitude (≲0.1 mag). From modeling of the light curve, we find that the Einstein timescale, day, is much shorter, and the angular Einstein radius, μas, is much smaller than those of typical lensing events produced by stellar-mass lenses ( days, mas), indicating that the lens is very likely to be a planetary-mass object. We conduct an extensive search for possible signatures of a companion star in the light curve of the event, finding no significant evidence for the putative host star. For the first time, we also demonstrate that the angular Einstein radius of the lens does not depend on blending in the low-magnification events with strong finite source effects.

OGLE-2016-BLG-1227L: A Wide-separation Planet from a Very Short-timescale Microlensing Event

Abstract We present the analysis of the microlensing event OGLE-2016-BLG-1227. The light curve of this short-duration event appears to be a single-lens event affected by severe finite-source effects. Analysis of the light curve based on a single-lens single-source (1L1S) model yields very small values of the event timescale, days, and the angular Einstein radius, mas, making the lens a candidate of a free-floating planet. Close inspection reveals that the 1L1S solution leaves small residuals with an amplitude of ΔI ≲ 0.03 mag. We find that the residuals are explained by the existence of an additional widely separated heavier lens component, indicating that the lens is a wide-separation planetary system rather than a free-floating planet. From Bayesian analysis, it is estimated that the planet has a mass of and it is orbiting a low-mass host star with a mass of located with a projected separation of au. The planetary system is located in the Galactic bulge with a line-of-sight separation from the source star of kpc. The event shows that there is a range of deviations in the signatures of host stars for apparently isolated planetary lensing events and that it is possible to identify a host even when a deviation is subtle.

OGLE-2018-BLG-1700L: Microlensing Planet in Binary Stellar System

Abstract We report a planet in a binary that was discovered from the analysis of the microlensing event OGLE-2018-BLG-1700. We identify the triple nature of the lens from the fact that the anomaly pattern can be decomposed into two parts produced by two binary-lens events, in which one binary pair has a mass ratio of ∼0.01 between the lens components and the other pair has a mass ratio of ∼0.3. We find two sets of degenerate solutions, in which one solution has a projected separation between the primary and its stellar companion less than the angular Einstein radius (close solution), while the other solution has a separation greater than (wide solution). From the Bayesian analysis with the constraints of the event timescale and angular Einstein radius, we find that the planet has a mass of and the stellar binary components have masses of and , respectively, and the distance to the lens is . The planet is a circumstellar planet according to the wide solution, while it is a circumbinary planet according to the close solution.

OGLE-2015-BLG-1649Lb: A Gas Giant Planet around a Low-mass Dwarf

Abstract We report the discovery of an exoplanet from the analysis of the gravitational microlensing event OGLE-2015-BLG-1649 that challenges the core accretion model of planet formation and appears to support the disk instability model. The planet/host-star mass ratio is q = 7.2 × 10−3 and the projected separation normalized to the angular Einstein radius is s = 0.9. We conducted high-resolution follow-up observations using the Infrared Camera and Spectrograph (IRCS) camera on the Subaru telescope and are able to place an upper limit on the lens flux. From these measurements we are able to exclude all host stars greater than or equal in mass to a G-type dwarf. We conducted a Bayesian analysis with these new flux constraints included as priors resulting in estimates of the masses of the host star and planet. These are M L = 0.34 ± 0.19 M ⊙ and , respectively. The distance to the system is . The projected star–planet separation is . The estimated relative lens-source proper motion, ∼7.1 mas yr−1, is fairly high and thus the lens can be better constrained if additional follow-up observations are conducted several years after the event.

OGLE-2016-BLG-0156: Microlensing Event with Pronounced Microlens-parallax Effects Yielding a Precise Lens Mass Measurement

Abstract We analyze the gravitational binary-lensing event OGLE-2016-BLG-0156, for which the lensing light curve displays pronounced deviations induced by microlens-parallax effects. The light curve exhibits three distinctive widely separated peaks and we find that the multiple-peak feature provides a very tight constraint on the microlens-parallax effect, enabling us to precisely measure the microlens parallax . All the peaks are densely and continuously covered from high-cadence survey observations using globally located telescopes and the analysis of the peaks leads to the precise measurement of the angular Einstein radius . From the combination of the measured and , we determine the physical parameters of the lens. It is found that the lens is a binary composed of two M dwarfs with masses M 1 = 0.18 ± 0.01 M ⊙ and M 2 = 0.16 ± 0.01 M ⊙ located at a distance . According to the estimated lens mass and distance, the flux from the lens comprises an important fraction, ∼25%, of the blended flux. The bright nature of the lens combined with the high relative lens-source motion, μ = 6.94 ± 0.50 mas yr−1, suggests that the lens can be directly observed from future high-resolution follow-up observations.

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.

KMT-2016-BLG-2052L: Microlensing Binary Composed of M Dwarfs Revealed from a Very Long Timescale Event

Abstract We present the analysis of a binary microlensing event, KMT-2016-BLG-2052, for which the lensing-induced brightening of the source star lasted for two seasons. We determine the lens mass from the combined measurements of the microlens parallax, π E, and angular Einstein radius, θ E. The measured mass indicates that the lens is a binary composed of M dwarfs with masses of M 1 ∼ 0.34 M ⊙ and M 2 ∼ 0.17 M ⊙. The measured relative lens-source proper motion of μ ∼ 3.9 mas yr−1 is smaller than ∼5 mas yr−1 of typical Galactic lensing events, while the estimated angular Einstein radius of θ E ∼ 1.2 mas is substantially greater than the typical value of ∼0.5 mas. Therefore, it turns out that the long timescale of the event is caused by the combination of the slow μ and large θ E rather than the heavy mass of the lens. From the simulation of Galactic lensing events with very long timescales (t E ≳ 100 days), we find that the probabilities that long timescale events are produced by lenses with masses ≥1.0 M ⊙ and ≥3.0 M ⊙ are ∼19% and 2.6%, respectively, indicating that events produced by heavy lenses comprise a minor fraction of long timescale events. The results indicate that it is essential to determine lens masses by measuring both π E and θ E in order to firmly identify heavy stellar remnants, such as neutron stars and black holes.

MOA-2015-BLG-337: A Planetary System with a Low-mass Brown Dwarf/Planetary Boundary Host, or a Brown Dwarf Binary

Abstract We report on the discovery and analysis of the short-timescale binary-lens microlensing event, MOA-2015-BLG-337. The lens system could be a planetary system with a very low-mass host, around the brown dwarf (BD)/planetary-mass boundary, or a BD binary. We found two competing models that explain the observed light curves with companion/host mass ratios of q ∼ 0.01 and ∼0.17, respectively. A significant finite source effect in the best-fit planetary model (q ∼ 0.01) reveals a small angular Einstein radius of θ E ≃ 0.03 mas, which favors a low-mass lens. We obtain the posterior probability distribution of the lens properties from a Bayesian analysis. The results for the planetary models strongly depend on a power-law index in planetary-mass regime, α pl, in the assumed mass function. In summary, there are two solutions of the lens system: (1) a BD/planetary-mass boundary object orbited by a super-Neptune (the planetary model with α pl = 0.49) and (2) a BD binary (the binary model). If the planetary models are correct, this system can be one of a new class of planetary system, having a low host mass and also a planetary-mass ratio (q < 0.03) between the companion and its host. The discovery of the event is important for the study of planetary formation in very low-mass objects. In addition, it is important to consider all viable solutions in these kinds of ambiguous events in order for the future comprehensive statistical analyses of planetary/binary microlensing events.

OGLE-2017-BLG-0537: A Microlensing Event with a Resolvable Lens in ≲5 years from High-resolution Follow-up Observations

Abstract We present an analysis of the binary-lens microlensing event OGLE-2017-BLG-0537. The light curve of the event exhibits two strong caustic-crossing spikes among which the second caustic crossing was resolved by high-cadence surveys. It is found that the lens components with a mass ratio ∼0.5 are separated in projection by , where θ E is the angular Einstein radius. Analysis of the caustic-crossing part yields mas and a lens-source relative proper motion of μ = 12.4 ± 1.1 mas yr−1. The measured μ is the third highest value among the events with measured proper motions and is ∼3 times higher than the value of typical Galactic bulge events, making the event a strong candidate for follow-up observations to directly image the lens by separating it from the source. From the angular Einstein radius combined with the microlens parallax, it is estimated that the lens is composed of two main-sequence stars with masses M 1 ∼ 0.4 M ⊙ and M 2 ∼ 0.2 M ⊙ located at a distance of D L ∼ 1.2 kpc. However, the physical lens parameters are not very secure due to the weak microlens-parallax signal, thus we cross-check the parameters by conducting a Bayesian analysis based on the measured Einstein radius and event timescale, combined with the blending constraint. From this, we find that the physical parameters estimated from the Bayesian analysis are consistent with those based on the measured microlens parallax. Resolving the lens from the source can be done in about 5 years from high-resolution follow-up observations and this will provide a rare opportunity to test and refine the microlensing model.

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.

UKIRT-2017-BLG-001Lb: A Giant Planet Detected through the Dust

Abstract We report the discovery of a giant planet in event UKIRT-2017-BLG-001, detected by the United Kingdom Infrared Telescope (UKIRT) microlensing survey. The mass ratio between the planet and its host is , about 1.5 times the Jupiter/Sun mass ratio. The event lies 0.°35 from the Galactic center and suffers from high extinction of A K = 1.68. Therefore, it could be detected only by a near-infrared (NIR) survey. The field also suffers from large spatial differential extinction, which makes it difficult to estimate the source properties required to derive the angular Einstein radius. Nevertheless, we find evidence suggesting that the source is located in the far disk. If correct, this would be the first source star of a microlensing event to be identified as belonging to the far disk. We estimate the lens mass and distance using a Bayesian analysis to find that the planet’s mass is , and it orbits a star at an instantaneous projected separation of au. The system is at a distance of kpc, and so likely resides in the Galactic bulge. In addition, we find a non-standard extinction curve in this field, in agreement with previous results toward high-extinction fields near the Galactic center.

Weak deflection gravitational lensing for photons coupled to Weyl tensor in a Schwarzschild black hole

Beyond the Einstein–Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of varepsilon which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.

A Neptune-mass Free-floating Planet Candidate Discovered by Microlensing Surveys

Abstract Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (below two days), but lacked an angular Einstein radius measurement (and hence lacked a significant constraint on the lens mass). Here, we present the discovery of a Neptune-mass free-floating planet candidate in the ultrashort (t E = 0.320 ± 0.003 days) microlensing event OGLE-2016-BLG-1540. The event exhibited strong finite-source effects, which allowed us to measure its angular Einstein radius of θ E = 9.2 ± 0.5 μas. There remains, however, a degeneracy between the lens mass and distance. The combination of the source proper motion and source-lens relative proper motion measurements favors a Neptune-mass lens located in the Galactic disk. However, we cannot rule out that the lens is a Saturn-mass object belonging to the bulge population. We exclude stellar companions up to ∼15 au.

Ground-based Parallax Confirmed by Spitzer: Binary Microlensing Event MOA-2015-BLG-020

Abstract We present the analysis of the binary gravitational microlensing event MOA-2015-BLG-020. The event has a fairly long timescale (∼63 days) and thus the light curve deviates significantly from the lensing model that is based on the rectilinear lens-source relative motion. This enables us to measure the microlensing parallax through the annual parallax effect. The microlensing parallax parameters constrained by the ground-based data are confirmed by the Spitzer observations through the satellite parallax method. By additionally measuring the angular Einstein radius from the analysis of the resolved caustic crossing, the physical parameters of the lens are determined. It is found that the binary lens is composed of two dwarf stars with masses and in the Galactic disk. Assuming that the source star is at the same distance as the bulge red clump stars, we find the lens is at a distance . We also provide a summary and short discussion of all of the published microlensing events in which the annual parallax effect is confirmed by other independent observations.

MOA-2012-BLG-505Lb: A Super-Earth-mass Planet That Probably Resides in the Galactic Bulge

Abstract We report the discovery of a super-Earth-mass planet in the microlensing event MOA-2012-BLG-505. This event has the second shortest event timescale of t E = 10 ± 1 days where the observed data show evidence of a planetary companion. Our 15 minute high cadence survey observation schedule revealed the short subtle planetary signature. The system shows the well known close/wide degeneracy. The planet/host-star mass ratio is q = 2.1 × 10−4 and the projected separation normalized by the Einstein radius is s = 1.1 or 0.9 for the wide and close solutions, respectively. We estimate the physical parameters of the system by using a Bayesian analysis and find that the lens consists of a super-Earth with a mass of orbiting around a brown dwarf or late-M-dwarf host with a mass of with a projected star–planet separation of . The system is at a distance of 7.2 ± 1.1 kpc, i.e., it is likely to be in the Galactic bulge. The small angular Einstein radius (θ E = 0.12 ± 0.02 mas) and short event timescale are typical for a low-mass lens in the Galactic bulge. Such low-mass planetary systems in the Bulge are rare because the detection efficiency of planets in short microlensing events is relatively low. This discovery may suggest that such low-mass planetary systems are abundant in the Bulge and currently on-going high cadence survey programs will detect more such events and may reveal an abundance of such planetary systems.

OGLE-2015-BLG-1482L: The First Isolated Low-mass Microlens in the Galactic Bulge

Abstract We analyze the single microlensing event OGLE-2015-BLG-1482 simultaneously observed from two ground-based surveys and from Spitzer. The Spitzer data exhibit finite-source effects that are due to the passage of the lens close to or directly over the surface of the source star as seen from Spitzer. Such finite-source effects generally yield measurements of the angular Einstein radius, which when combined with the microlens parallax derived from a comparison between the ground-based and the Spitzer light curves yields the lens mass and lens-source relative parallax. From this analysis, we find that the lens of OGLE-2015-BLG-1482 is a very low-mass star with a mass or a brown dwarf with a mass , which are located at and , respectively, where is the distance between the lens and the source, and thus it is the first isolated low-mass microlens that has been decisively located in the Galactic bulge. The degeneracy between the two solutions is severe ( ). The fundamental reason for the degeneracy is that the finite-source effect is seen only in a single data point from Spitzer, and this single data point gives rise to two solutions for ρ, the angular size of the source in units of the angular Einstein ring radius. Because the ρ degeneracy can be resolved only by relatively high-cadence observations around the peak, while the Spitzer cadence is typically , we expect that events for which the finite-source effect is seen only in the Spitzer data may frequently exhibit this ρ degeneracy. For OGLE-2015-BLG-1482, the relative proper motion of the lens and source for the low-mass star is , while for the brown dwarf it is . Hence, the degeneracy can be resolved within from direct-lens imaging by using next-generation instruments with high spatial resolution.

Predictions for the Detection and Characterization of a Population of Free-floating Planets with K2 Campaign 9

Abstract K2 Campaign 9 (K2C9) offers the first chance to measure parallaxes and masses of members of the large population of free-floating planets (FFPs) that has previously been inferred from measurements of the rate of short-timescale microlensing events. Using detailed simulations of the nominal campaign (ignoring the loss of events due to Kepler’s emergency mode) and ground-based microlensing surveys, we predict the number of events that can be detected if there is a population of 1 FFPs matching current observational constraints. Using a Fisher matrix analysis, we also estimate the number of detections for which it will be possible to measure the microlensing parallax, angular Einstein radius, and FFP mass. We predict that between 1.4 and 7.9 events will be detected in the K2 data, depending on the noise floor that can be reached, but with the optimistic scenario being more likely. For nearly all of these, it will be possible to either measure the parallax or constrain it to be probabilistically consistent with only planetary-mass lenses. We expect that for between 0.42 and 0.98 events it will be possible to gain a complete solution and measure the FFP mass. For the emergency-mode truncated campaign, these numbers are reduced by 20 percent. We argue that when combined with prompt high-resolution imaging of a larger sample of short-timescale events, K2C9 will conclusively determine if the putative FFP population is indeed both planetary and free-floating.

OGLE-2015-BLG-0196: GROUND-BASED GRAVITATIONAL MICROLENS PARALLAX CONFIRMED BY SPACE-BASED OBSERVATION

ABSTRACT In this paper, we present an analysis of the binary gravitational microlensing event OGLE-2015-BLG-0196. The event lasted for almost a year, and the light curve exhibited significant deviations from the lensing model based on the rectilinear lens-source relative motion, enabling us to measure the microlens parallax. The ground-based microlens parallax is confirmed by the data obtained from space-based microlens observations using the Spitzer telescope. By additionally measuring the angular Einstein radius from the analysis of the resolved caustic crossing, the physical parameters of the lens are determined up to the twofold degeneracy, u 0 < 0 and u 0 > 0, solutions caused by the well-known “ecliptic” degeneracy. It is found that the binary lens is composed of two M dwarf stars with similar masses, M 1 = 0.38 ± 0.04 M ⊙ (0.50 ± 0.05 M ⊙) and M 2 = 0.38 ± 0.04 M ⊙ (0.55 ± 0.06 M ⊙), and the distance to the lens is D L = 2.77 ± 0.23 kpc (3.30 ± 0.29 kpc). Here the physical parameters outside and inside the parentheses are for the u 0 < 0 and u 0 > 0 solutions, respectively.

OGLE-2015-BLG-0051/KMT-2015-BLG-0048LB: A GIANT PLANET ORBITING A LOW-MASS BULGE STAR DISCOVERED BY HIGH-CADENCE MICROLENSING SURVEYS

ABSTRACT We report the discovery of an extrasolar planet detected from the combined data of a microlensing event OGLE-2015-BLG-0051/KMT-2015-BLG-0048 acquired by two microlensing surveys. Despite the fact that the short planetary signal occurred in the very early Bulge season during which the lensing event could be seen for just about an hour, the signal was continuously and densely covered. From the Bayesian analysis using models of the mass function, and matter and velocity distributions, combined with information on the angular Einstein radius, it is found that the host of the planet is located in the Galactic bulge. The planet has a mass and it is orbiting a low-mass M-dwarf host with a projected separation . The discovery of the planet demonstrates the capability of the current high-cadence microlensing lensing surveys in detecting and characterizing planets.