Lens-source Relative Proper Motion Research Articles

Kepler K2Campaign 9 – II. First space-based discovery of an exoplanet using microlensing

ABSTRACTWe present K2-2016-BLG-0005Lb, a densely sampled, planetary binary caustic-crossing microlensing event found from a blind search of data gathered from Campaign 9 of the Kepler K2 mission (K2C9). K2-2016-BLG-0005Lb is the first bound microlensing exoplanet discovered from space-based data. The event has caustic entry and exit points that are resolved in the K2C9 data, enabling the lens-source relative proper motion to be measured. We have fitted a binary microlens model to the Kepler data and to simultaneous observations from multiple ground-based surveys. Whilst the ground-based data only sparsely sample the binary caustic, they provide a clear detection of parallax that allows us to break completely the microlensing mass-position-velocity degeneracy and measure the planet’s mass directly. We find a host mass of 0.58 ± 0.04 M⊙ and a planetary mass of 1.1 ± 0.1 MJ. The system lies at a distance of 5.2 ± 0.2 kpc from Earth towards the Galactic bulge, more than twice the distance of the previous most distant planet found by Kepler. The sky-projected separation of the planet from its host is found to be 4.2 ± 0.3 au which, for circular orbits, deprojects to a host separation $a = 4.4^{+1.9}_{-0.4}$ au and orbital period $P = 13^{+9}_{-2}$ yr. This makes K2-2016-BLG-0005Lb a close Jupiter analogue orbiting a low-mass host star. According to current planet formation models, this system is very close to the host mass threshold below which Jupiters are not expected to form. Upcoming space-based exoplanet microlensing surveys by NASA’s Nancy Grace Roman Space Telescope and, possibly, ESA’s Euclid mission, will provide demanding tests of current planet formation models.

Using Source Proper Motion to Validate Terrestrial Parallax: OGLE-2019-BLG-1058

Abstract We show that because the conditions for producing terrestrial microlens parallax (TPRX; i.e., a nearby disk lens) will also tend to produce a large lens-source relative proper motion (μ rel), source proper motion ( μ S) measurements in general provide a strong test of TPRX signals, which Gould & Yee (2013) showed were an important probe of free-floating planet (FFP) candidates. As a case study, we report a single-lens/single-source microlensing event designated as OGLE-2019-BLG-1058. For this event, the short timescale (∼2.5 days) and very fast μ rel (∼17.6 mas yr−1) suggest that this isolated lens is an FFP candidate located in the disk of our Galaxy. For this event, we find a TPRX signal consistent with a disk FFP, but at low significance. A direct measurement of the μ S shows that the large μ rel is due to an extreme μ S, and thus, the lens is consistent with being a very-low-mass star in the bulge and the TPRX measurement is likely spurious. By contrast, we show how a precise measurement of μ S with the mean properties of the bulge proper motion distribution would have given the opposite result; i.e., provided supporting evidence for an FFP in the disk and the TPRX measurement.

KMT-2017-BLG-2820 and the Nature of the Free-floating Planet Population

Abstract We report a new free-floating planet (FFP) candidate, KMT-2017-BLG-2820, with Einstein radius θ E ≃ 6 μas, lens-source relative proper motion μ rel ≃ 8 mas yr−1, and Einstein timescale t E = 6.5 hr. It is the third FFP candidate found in an ongoing study of giant-source finite-source point-lens (FSPL) events in the KMTNet database and the sixth FSPL FFP candidate overall. We find no significant evidence for a host. Based on their timescale distributions and detection rates, we argue that five of these six FSPL FFP candidates are drawn from the same population as the six point-source point-lens (PSPL) FFP candidates found by Mróz et al. in the OGLE-IV database. The θ E distribution of the FSPL FFPs implies that they are either sub-Jovian planets in the bulge or super-Earths in the disk. However, the apparent “Einstein desert” (10 ≲ θ E/μas ≲ 30) would argue for the latter. Whether each of the 12 (six FSPL and six PSPL) FFP candidates is truly an FFP or simply a very wide-separation planet can be determined at first adaptive optics (AO) light on 30 m telescopes, and earlier for some. If the latter, a second epoch of AO observations could measure the projected planet–host separation with a precision of . At the present time, the balance of evidence favors the unbound-planet hypothesis.

MaBμlS-2: high-precision microlensing modelling for the large-scale survey era

ABSTRACT Galactic microlensing datasets now comprise in excess of 104 events and, with the advent of next-generation microlensing surveys that may be undertaken with facilities such as the Rubin Observatory (formerly LSST) and Roman Space Telescope (formerly WFIRST), this number will increase significantly. So too will the fraction of events with measurable higher order information, such as finite-source effects and lens–source relative proper motion. Analysing such data requires a more sophisticated Galactic microlens modelling approach. We present a new second-generation Manchester–Besançon Microlensing Simulator (MaBμlS-2), which uses a version of the Besançon population synthesis Galactic model that provides good agreement with stellar kinematics observed by the Hubble Space Telescope (HST) towards the bulge. MaBμlS-2 provides high-fidelity signal-to-noise limited maps of the microlensing optical depth, rate and average time-scale towards a 400 deg2 region of the Galactic bulge in several optical to near-infrared pass-bands. The maps take full account of the unresolved stellar background, as well as limb-darkened source profiles. Comparing MaBμlS-2 with the efficiency-corrected OGLE-IV 8000 event sample shows a much improved agreement over the previous version of MaBμlS and succeeds in matching even small-scale structural features in the OGLE-IV event rate map. However, evidence remains for a small underprediction of the event rate per source and overprediction of the time-scale. MaBμlS-2 is available online (www.mabuls.net, Specht & Kerins) to provide on-the-fly maps for user-supplied cuts in survey magnitude, event time-scale and relative proper motion.

Spitzer + VLTI-GRAVITY Measure the Lens Mass of a Nearby Microlensing Event

Abstract We report the lens mass and distance measurements of the nearby microlensing event TCP J05074264+2447555 (Kojima-1). We measure the microlens parallax vector using Spitzer and ground-based light curves with constraints on the direction of lens-source relative proper motion derived from Very Large Telescope Interferometer (VLTI) GRAVITY observations. Combining this determination with the angular Einstein radius measured by VLTI-GRAVITY observations, we find that the lens is a star with mass at a distance D L = 429 ± 21 pc. We find that the blended light basically all comes from the lens. The lens-source proper motion is , so with currently available adaptive-optics instruments, the lens and source can be resolved in 2021. This is the first microlensing event whose lens mass is unambiguously measured by interferometry + satellite-parallax observations, which opens a new window for mass measurements of isolated objects such as stellar-mass black holes.

Keck Observations Confirm a Super-Jupiter Planet Orbiting M Dwarf OGLE-2005-BLG-071L

Abstract We present adaptive optics imaging from the NIRC2 instrument on the Keck II telescope that resolves the exoplanet host (and lens) star as it separates from the brighter source star. These observations yield the K-band brightness of the lens and planetary host star, as well as the lens-source relative proper motion, , in the heliocentric reference frame. The measurement allows for the determination of the microlensing parallax vector, , which had only a single component determined by the microlensing light curve. The combined measurements of and K L provide the masses of the host star, , and planet, m p = 3.27 ± 0.32M Jupiter with a projected separation of 3.4 ± 0.5 au. This confirms the tentative conclusion of a previous paper that this super-Jupiter mass planet, OGLE-2005-BLG-071Lb, orbits an M dwarf. Such planets are predicted to be rare by the core accretion theory and have been difficult to find with other methods, but there are two such planets with firm mass measurements from microlensing, and an additional 11 planetary microlens events with host mass estimates and planet mass estimates >2 Jupiter masses that could be confirmed by high angular follow-up observations. We also point out that OGLE-2005-BLG-071L has separated far enough from its host star that it should be possible to measure the host-star metallicity with spectra from a high angular resolution telescope such as Keck, the Very Large Telescope, the Hubble Space Telescope, or the James Webb Space Telescope.

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

Abstract 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).

OGLE-2018-BLG-0022: First Prediction of an Astrometric Microlensing Signal from a Photometric Microlensing Event

Abstract In this work, we present the analysis of the binary microlensing event OGLE-2018-BLG-0022 that is detected toward the Galactic bulge field. The dense and continuous coverage with the high-quality photometry data from ground-based observations combined with the space-based Spitzer observations of this long timescale event enables us to uniquely determine the masses M 1 = 0.40 ± 0.05 M ⊙ and M 2 = 0.13 ± 0.01 M ⊙ of the individual lens components. Because the lens-source relative parallax and the vector lens-source relative proper motion are unambiguously determined, we can likewise unambiguously predict the astrometric offset between the light centroid of the magnified images (as observed by the Gaia satellite) and the true position of the source. This prediction can be tested when the individual-epoch Gaia astrometric measurements are released.

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-1522: A Giant Planet around a Brown Dwarf Located in the Galactic Bulge

Abstract We report the discovery of a giant planet in the OGLE-2017-BLG-1522 microlensing event. The planetary perturbations were clearly identified by high-cadence survey experiments despite the relatively short event timescale of t E ∼ 7.5 days. The Einstein radius is unusually small, θ E = 0.065 mas, implying that the lens system either has very low mass or lies much closer to the microlensed source than the Sun, or both. A Bayesian analysis yields component masses and source-lens distance , implying that this is a brown-dwarf/Jupiter system that probably lies in the Galactic bulge, a location that is also consistent with the relatively low lens-source relative proper motion μ = 3.2 ± 0.5 mas yr−1. The projected companion-host separation is , indicating that the planet is placed beyond the snow line of the host, i.e., a sl ∼ 0.12 au. Planet formation scenarios combined with the small companion-host mass ratio q ∼ 0.016 and separation suggest that the companion could be the first discovery of a giant planet that formed in a protoplanetary disk around a brown-dwarf host.

OGLE-2016-BLG-0613LABb: A Microlensing Planet in a Binary System

Abstract We present the analysis of OGLE-2016-BLG-0613, for which the lensing light curve appears to be that of a typical binary-lens event with two caustic spikes but with a discontinuous feature on the trough between the spikes. We find that the discontinuous feature was produced by a planetary companion to the binary lens. We find four degenerate triple-lens solution classes, each composed of a pair of solutions according to the well-known wide/close planetary degeneracy. One of these solution classes is excluded due to its relatively poor fit. For the remaining three pairs of solutions, the most-likely primary mass is about , while the planet is a super Jupiter. In all cases, the system lies in the Galactic disk, about halfway toward the Galactic bulge. However, in one of these three solution classes, the secondary of the binary system is a low-mass brown dwarf, with relative mass ratios (1:0.03:0.003), while in the two others the masses of the binary components are comparable. These two possibilities can be distinguished in about 2024 when the measured lens-source relative proper motion will permit separate resolution of the lens and source.

MOA Data Reveal a New Mass, Distance, and Relative Proper Motion for Planetary System OGLE-2015-BLG-0954L

Abstract We present the MOA Collaboration light-curve data for the planetary microlensing event OGLE-2015-BLG-0954, which was previously announced in a paper by the KMTNet and OGLE Collaborations. The MOA data cover the caustic exit, which was not covered by the KMTNet or Optical Gravitational Lensing Experiment (OGLE) data, and they provide a more reliable measurement of the finite source effect. The MOA data also provide a new source color measurement that reveals a lens-source relative proper motion of μ rel = 11.8 ± 0.8 mas yr−1, which compares to the value of μ rel = 18.4 ± 1.7 mas yr−1 reported in the KMTNet-OGLE paper. This new MOA value for μ rel has an a priori probability that is a factor of ≳100 times larger than the previous value, and it does not require a lens system distance of D L < 1 kpc. Based on the corrected source color, we find that the lens system consists of a planet of mass orbiting a star at an orbital separation of and a distance of .

OGLE-2012-BLG-0724LB: A SATURN-MASS PLANET AROUND AN M DWARF

ABSTRACT We report the discovery of a planet by the microlensing method, OGLE-2012-BLG-0724Lb. Although the duration of the planetary signal for this event was one of the shortest seen for a planetary event, the anomaly was well covered thanks to high-cadence observations taken by the survey groups OGLE and MOA. By analyzing the light curve, this planetary system is found to have a mass ratio q = ( 1.58 ± 0.15 ) × 10 − 3 . By conducting a Bayesian analysis, we estimate that the host star is an M dwarf with a mass of M L = 0.29 − 0.16 + 0.33 M ☉ located at D L = 6.7 − 1.2 + 1.1 kpc away from the Earth and the companion’s mass is m P = 0.47 − 0.26 + 0.54 M Jup . The projected planet–host separation is a ⊥ = 1.6 − 0.3 + 0.4 AU . Because the lens–source relative proper motion is relatively high, future high-resolution images would detect the lens host star and determine the lens properties uniquely. This system is likely a Saturn-mass exoplanet around an M dwarf, and such systems are commonly detected by gravitational microlensing. This adds another example of a possible pileup of sub-Jupiters ( 0.2 < m P / M Jup < 1 ) in contrast to a lack of Jupiters ( ∼ 1 – 2 M Jup ) around M dwarfs, supporting the prediction by core accretion models that Jupiter-mass or more massive planets are unlikely to form around M dwarfs.

MICROLENS MASSES FROM 1-D PARALLAXES AND HELIOCENTRIC PROPER MOTIONS

One-dimensional (1-D) microlens parallaxes can be combined with heliocentric lens-source relative proper motion measurements to derive the lens mass and distance, as suggested by Ghosh et al. (2004). Here I present the first mathematical anlysis of this procedure, which I show can be represented as a quadratic equation. Hence, it is formally subject to a two-fold degeneracy. I show that this degeneracy can be broken in many cases using the relatively crude 2-D parallax information that is often available for microlensing events. I also develop an explicit formula for the region of parameter space where it is more difficult to break this degeneracy. Although no mass/distance measurements have yet been made using this technique, it is likely to become quite common over the next decade.

NEW METHOD TO MEASURE PROPER MOTIONS OF MICROLENSED SOURCES: APPLICATION TO CANDIDATE FREE-FLOATING-PLANET EVENT MOA-2011-BLG-262

We develop a new method to measure source proper motions in microlensing events, which can partially overcome problems due to blending. It takes advantage of the fact that the source position is known precisely from the microlensing event itself. We apply this method to the event MOA-2011-BLG-262, which has a short timescale t_E=3.8 day, a companion mass ratio q=0.0047 and a very high or high lens-source relative proper motion mu_rel=20 mas/yr or 12 mas/yr (for two possible models). These three characteristics imply that the lens could be a brown dwarf or a massive planet with a roughly Earth-mass "moon". The probability of such an interpretation would be greatly increased if it could be shown that the high lens-source relative proper motion was primarily due to the lens rather than the source. Based on the long-term monitoring data of the Galactic bulge from the Optical Gravitational Lensing Experiment (OGLE), we measure the source proper motion that is small, mu_s = (-2.3, -0.9) +- (2.8,2.6) mas/yr in a (North, East) Galactic coordinate frame. These values are then important input into a Bayesian analysis of the event presented in a companion paper by Bennett et al.

MOA-2011-BLG-262Lb: A SUB-EARTH-MASS MOON ORBITING A GAS GIANT PRIMARY OR A HIGH VELOCITY PLANETARY SYSTEM IN THE GALACTIC BULGE

We present the first microlensing candidate for a free-floating exoplanet-exomoon system, MOA-2011-BLG-262, with a primary lens mass of M_host ~ 4 Jupiter masses hosting a sub-Earth mass moon. The data are well fit by this exomoon model, but an alternate star+planet model fits the data almost as well. Nevertheless, these results indicate the potential of microlensing to detect exomoons, albeit ones that are different from the giant planet moons in our solar system. The argument for an exomoon hinges on the system being relatively close to the Sun. The data constrain the product M pi_rel, where M is the lens system mass and pi_rel is the lens-source relative parallax. If the lens system is nearby (large pi_rel), then M is small (a few Jupiter masses) and the companion is a sub-Earth-mass exomoon. The best-fit solution has a large lens-source relative proper motion, mu_rel = 19.6 +- 1.6 mas/yr, which would rule out a distant lens system unless the source star has an unusually high proper motion. However, data from the OGLE collaboration nearly rule out a high source proper motion, so the exoplanet+exomoon model is the favored interpretation for the best fit model. However, the alternate solution has a lower proper motion, which is compatible with a distant (so stellar) host. A Bayesian analysis does not favor the exoplanet+exomoon interpretation, so Occam's razor favors a lens system in the bulge with host and companion masses of M_host = 0.12 (+0.19 -0.06) M_solar and m_comp = 18 (+28 -100 M_earth, at a projected separation of a_perp ~ 0.84 AU. The existence of this degeneracy is an unlucky accident, so current microlensing experiments are in principle sensitive to exomoons. In some circumstances, it will be possible to definitively establish the low mass of such lens systems through the microlensing parallax effect. Future experiments will be sensitive to less extreme exomoons.

MOA-2008-BLG-379Lb: A MASSIVE PLANET FROM A HIGH MAGNIFICATION EVENT WITH A FAINT SOURCE

We report analysis of high microlensing event MOA-2008-BLG-379, which has a strong microlensing anomaly at its peak, due to a massive planet with a mass ratio of q = 6.9 x 10^{-3}. Because the faint source star crosses the large resonant caustic, the planetary signal dominates the light curve. This is unusual for planetary microlensing events, and as a result, the planetary nature of this light curve was not immediately noticed. The planetary nature of the event was found when the MOA Collaboration conducted a systematic study of binary microlensing events previously identified by the MOA alert system. We have conducted a Bayesian analysis based on a standard Galactic model to estimate the physical parameters of the lens system. This yields a host star mass of M_L = 0.66_{-0.33}^{+0.29} M_Sun orbited by a planet of mass m_P = 4.8_{-2.4}^{+2.1} M_Jup at an orbital separation of a = 4.1_{-1.5}^{+1.9} AU at a distance of D_L = 3.6 +/- 1.3 kpc. The faint source magnitude of I_S = 21.30 and relatively high lens-source relative proper motion of mu_rel = 7.6 +/- 1.6 mas/yr implies that high angular resolution adaptive optics or Hubble Space Telescope observations are likely to be able to detect the source star, which would determine the masses and distance of the planet and its host star.

Characterization of Gravitational Microlensing Planetary Host Stars

The gravitational microlensing light curves that reveal the presence of extrasolar planets generally yield the planet-star mass ratio and separation in units of the Einstein ring radius. The microlensing method does not require the detection of light from the planetary host star. This allows the detection of planets orbiting very faint stars, but it also makes it difficult to convert the planet-star mass ratio to a value for the planet mass. We show that in many cases, the lens stars are readily detectable with high resolution space-based follow-up observations in a single passband. When the lens star is detected, the lens-source relative proper motion can also be measured, and this allows the masses of the planet and its host star to be determined and the star-planet separation can be converted to physical units. Observations in multiple passbands provide redundant information, which can be used to confirm this interpretation. For the recently detected super-Earth planet, OGLE-2005-BLG-169Lb, we show that the lens star will definitely be detectable with observations by the Hubble Space Telescope (HST) unless it is a stellar remnant. Finally, we show that most planets detected by a space-based microlensing survey are likely to orbit host stars that will be detected and characterized by the same survey.

Microlens OGLE-2005-BLG-169 Implies That Cool Neptune-like Planets Are Common

We detect a Neptune mass ratio (q 8 ? 10-5) planetary companion to the lens star in the extremely high magnification (A ~ 800) microlensing event OGLE-2005-BLG-169. If the parent is a main-sequence star, it has mass M ~ 0.5 M?, implying a planet mass of ~13 M? and projected separation of ~2.7 AU. When intensely monitored over their peak, high-magnification events similar to OGLE-2005-BLG-169 have nearly complete sensitivity to Neptune mass ratio planets with projected separations of 0.6-1.6 Einstein radii, corresponding to 1.6-4.3 AU in the present case. Only two other such events were monitored well enough to detect Neptunes, and so this detection by itself suggests that Neptune mass ratio planets are common. Moreover, another Neptune was recently discovered at a similar distance from its parent star in a low-magnification event, which are more common but are individually much less sensitive to planets. Combining the two detections yields 90% upper and lower frequency limits f = 0.38 over just 0.4 decades of planet-star separation. In particular, f > 16% at 90% confidence. The parent star hosts no Jupiter-mass companions with projected separations within a factor 5 of that of the detected planet. The lens-source relative proper motion is ? ~ 7-10 mas yr-1, implying that if the lens is sufficiently bright, I 23.8, it will be detectable by the Hubble Space Telescope by 3 years after peak. This would permit a more precise estimate of the lens mass and distance and, so, the mass and projected separation of the planet. Analogs of OGLE-2005-BLG-169Lb orbiting nearby stars would be difficult to detect by other methods of planet detection, including radial velocities, transits, and astrometry.

Potential Direct Single‐Star Mass Measurement

We analyze the light curve of the microlensing event OGLE-2003-BLG-175/MOA-2003-BLG-45 and show that it has two properties that, when combined with future high-resolution astrometry, could lead to a direct, accurate measurement of the lens mass. First, the light curve shows clear signs of distortion due to the Earth's accelerated motion, which yields a measurement of the projected Einstein radius E. Second, from precise astrometric measurements, we show that the blended light in the event is coincident with the microlensed source to within about 15 mas. This argues strongly that this blended light is the lens and hence opens the possibility of directly measuring the lens-source relative proper motion μrel and so the mass M = (c2/4G)μreltEE, where tE is the measured Einstein timescale. While the light-curve-based measurement of E is, by itself, severely degenerate, we show that this degeneracy can be completely resolved by measuring the direction of proper motion μrel.