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In the pursuit of understanding the population of stellar remnants within the Milky Way, we analyze the sample of ∼950 microlensing events observed by the Spitzer Space Telescope between 2014 and 2019. In this study we focus on a subsample of nine microlensing events, selected based on their long timescales, small microlensing parallaxes, and joint observations by the Gaia mission, to increase the probability that the chosen lenses are massive and the mass is measurable. Among the selected events we identify lensing black holes and neutron star candidates, with potential confirmation through forthcoming release of the Gaia time-series astrometry in 2026. Utilizing Bayesian analysis and Galactic models, along with the Gaia Data Release 3 proper-motion data, four good candidates for dark remnants were identified: OGLE-2016-BLG-0293, OGLE-2018-BLG-0483, OGLE-2018-BLG-0662, and OGLE-2015-BLG-0149, with lens masses of ${3.0}_{-1.3}^{+1.8}\,{M}_{\odot }$ , ${4.7}_{-2.1}^{+3.2}\,{M}_{\odot }$ , ${3.15}_{-0.64}^{+0.66}\,{M}_{\odot }$ and ${1.40}_{-0.55}^{+0.75}\,{M}_{\odot }$ , respectively. Notably, the first two candidates are expected to exhibit astrometric microlensing signals detectable by Gaia, offering the prospect of validating the lens masses. The methodologies developed in this work will be applied to the full Spitzer microlensing sample, populating and analyzing the timescale ( t _E ) versus parallax ( π _E ) diagram to derive constraints on the population of lenses in general and massive remnants in particular.

We present pyLIMASS, a novel algorithm for estimating the physical properties of the lensing system in microlensing events. The main idea of pyLIMASS is to combine all available information regarding the microlensing event, defined as observables , and to estimate the parameter distributions of the system, such as the lens mass and distance. The algorithm is based on isochrones for the stars model and combines the observables using a Gaussian mixture approach. After describing the mathematical formalism and its implementation, we discuss the algorithm’s performance on simulated and published events. Generally, the pyLIMASS estimations are in good agreement (i.e., within 1 σ ) with the results of the selected published events, making it an effective tool to estimate the lens properties and their distribution. The applicability of the method was tested by using a catalog of realistically simulated events that could be observed by the future Galactic Bulge Time Domain Survey of the Nancy Grace Roman Space Telescope. By solely using constraints from the Roman lightcurves and images, pyLIMASS estimates the masses of the lens of the Roman catalog with a median precision of 20% with almost no bias.

We complete the analysis of planetary candidates found by the KMT AnomalyFinder for the 2017 prime fields that cover ∼13 deg ^2 . We report three unambiguous planets: OGLE-2017-BLG-0640, OGLE-2017-BLG-1275, and OGLE-2017-BLG-1237. The first two of these were not previously identified, while the last was not previously published due to technical complications induced by a nearby variable. We further report that a fourth anomalous event, the previously recognized OGLE-2017-BLG-1777, is very likely to be planetary, although its light curve requires unusually complex modeling because the lens and source both have orbiting companions. One of the three unambiguous planets, OGLE-2017-BLG-1275, is the first AnomalyFinder discovery that has a Spitzer microlens parallax measurement, π _E ≃ 0.045 ± 0.015, implying that this planetary system almost certainly lies in the Galactic bulge. In the order listed, the four planetary events have planet-host mass ratios q and normalized projected separations s of $(\mathrm{log}q,s)=(-2.31,0.61)$ , (−2.06, 0.63/1.09), (−2.10, 1.04), and (−2.86, 0.72). Combined with previously published events, the 2017 prime fields contain 11 unambiguous planets with well-measured q and one very likely candidate, of which three are AnomalyFinder discoveries. In addition to these 12, there are three other unambiguous planets with large uncertainties in q .

We systematically investigate Vandorou et al.’s claim to have detected the host star of the low-mass-ratio ( q < 10 ^−4 ) microlensing planet OGLE-2016-BLG-1195Lb, via Keck adaptive optics (AO) measurements Δ t = 4.12 yr after the event’s peak ( t _0 ). If correct, this measurement would contradict the microlens-parallax measurement derived from Spitzer observations taken near t _0 . We show that this host identification would be in 4 σ conflict with the original ground-based relative lens–source proper-motion measurements. By contrast, Gould estimated a probability p = 10% that the “other star” resolved by single-epoch late-time AO would be a companion to the host or the microlensed source, which is much more probable than a 4 σ statistical fluctuation. Independent of this proper-motion discrepancy, the kinematics of this host identification are substantially less probable than those of the Spitzer solution. Hence, this identification should not be accepted, pending additional observations that would either confirm or contradict it, which could be taken in 2023. Motivated by this tension, we present two additional investigations. We explore the possibility that Vandorou et al. identified the wrong “star” for their analysis. Astrometry of KMT and Keck images favors a star (or asterism) lying about 175 mas northwest of Vandorou et al.’s star. We also present event parameters from a combined fit to all survey data, which yields a more precise mass ratio, q = (4.6 ± 0.4) × 10 ^−5 . Finally, we discuss the broader implications of minimizing such false positives for the first measurement of the planet mass function, which will become possible when AO on next-generation telescopes are applied to microlensing planets.

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 DL = 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. [ABSTRACT FROM AUTHOR]

We report the mass and distance measurements of two single-lens events from the 2017 Spitzer microlensing campaign. The ground-based observations yield the detection of finite-source effects, and the microlens parallaxes are derived from the joint analysis of ground-based observations and Spitzer observations. We find that the lens of OGLE-2017-BLG-1254 is a 0.60 ± 0.03 M⊙ star with DLS = 0.53 ± 0.11 kpc, where DLS is the distance between the lens and the source. The second event, OGLE-2017-BLG-1161, is subject to the known satellite parallax degeneracy, and thus is either a star with DLS = 0.40 ± 0.12 kpc or a star with DLS = 0.53 ± 0.19 kpc. Both of the lenses are therefore isolated stars in the Galactic bulge. By comparing the mass and distance distributions of the eight published Spitzer finite-source events with the expectations from a Galactic model, we find that the Spitzer sample is in agreement with the probability of finite-source effects occurring in single-lens events. [ABSTRACT FROM AUTHOR]

OGLE-2014-BLG-0962 (OB140962) is a stellar binary microlensing event that was well covered by observations from the Spitzer satellite as well as ground-based surveys. Modeling yields a unique physical solution: a mid-M+M-dwarf binary with Mprim = 0.20 ± 0.01 M☉ and Msec = 0.16 ± 0.01 M☉, with projected separation of 2.0 ± 0.3 au. The lens is only DLS = 0.41 ± 0.06 kpc in front of the source, making OB140962 a bulge lens and the most distant Spitzer binary lens to date. In contrast, because the Einstein radius (θE = 0.143 ± 0.007 mas) is unusually small, a standard Bayesian analysis, conducted in the absence of parallax information, would predict a brown dwarf binary. We compare the results of Bayesian analysis using two commonly used Galactic model priors to the measured values for a set of Spitzer lenses. We find all models tested predict lens properties consistent with the Spitzer data. Furthermore, we illustrate the methodology for probing the Galactic distribution of planets by comparing the cumulative distance distribution of the Spitzer two-body lenses to that of the Spitzer single lenses. [ABSTRACT FROM AUTHOR]

Microlensing is a powerful and unique technique to probe isolated objects in the Galaxy. To study the characteristics of these interesting objects based on the microlensing method, measurement of the microlens parallax is required to determine the properties of the lens. Of the various methods to measure microlens parallax, the most routine way is to make simultaneous ground- and space-based observations, i.e., by measuring the space-based microlens parallax. However, space-based campaigns usually require “expensive” resources. Gould & Yee (2012) proposed an idea called the “cheap space-based microlens parallax” that can measure the lens-parallax using only two or three space-based observations of high-magnification events (as seen from Earth). This cost-effective observation strategy to measure microlens parallaxes could be used by space-borne telescopes to build a complete sample for studying isolated objects. This would enable a direct measurement of the mass function including both extremely low-mass objects and high-mass stellar remnants. However, to adopt this idea requires a test to check how it would work in actual situations. Thus, we present the first practical test of this idea using the high-magnification microlensing event OGLE-2016-BLG-1045, for which a subset of Spitzer observations fortuitously duplicates the prescription of Gould & Yee (2012). From the test, we confirm that the measurement of the lens-parallax adopting this idea has sufficient accuracy to determine the physical properties of the isolated lens. [ABSTRACT FROM AUTHOR]

Mass measurements of gravitational microlenses require one to determine the microlens parallax πE, but precise πE 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 πE 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-πE 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 (M1, M2) ∼ (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. [ABSTRACT FROM AUTHOR]

We report the discovery, via the microlensing method, of a new very low mass binary system. By combining measurements from Earth and from the Spitzer telescope in Earth-trailing orbit, we are able to measure the microlensing parallax of the event, and we find that the lens likely consists of a (12.0 ± 0.6)MJ + (15.7 ± 1.5)MJ super-Jupiter/brown dwarf pair. The binary is located at a distance of 3.08 ± 0.18 kpc in the Galactic plane, and the components have a projected separation of 0.43 ± 0.03 au. Two alternative solutions with much lower likelihoods are also discussed, an 8MJ and 6MJ model and a 90MJ and 70MJ model. If all photometric measurements were independent and Gaussian distributed with known variances, these alternative solutions would be formally disfavored at the 3σ and 5σ levels. We show how the more massive of these models could be tested with future direct imaging. [ABSTRACT FROM AUTHOR]

Due to the nature of the gravitational field, microlensing, in principle, provides an important tool for detecting faint and even dark brown dwarfs. However, the number of identified brown dwarfs is limited due to the difficulty of the lens mass measurement that is needed to check the substellar nature of the lensing object. In this work, we report a microlensing brown dwarf discovered from an analysis of the gravitational binary-lens event OGLE-2014-BLG-1112. We identify the brown dwarf nature of the lens companion by measuring the lens mass from the detections of both microlens-parallax and finite-source effects. We find that the companion has a mass of and it is orbiting a solar-type primary star with a mass of . The estimated projected separation between the lens components is 9.63 ± 1.33 au and the distance to the lens is 4.84 ± 0.67 kpc. We discuss the usefulness of space-based microlensing observations for detecting brown dwarfs through the channel of binary-lens events. [ABSTRACT FROM AUTHOR]

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, u0 < 0 and u0 > 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, M1 = 0.38 ± 0.04 M⊙ (0.50 ± 0.05 M⊙) and M2 = 0.38 ± 0.04 M⊙ (0.55 ± 0.06 M⊙), and the distance to the lens is DL = 2.77 ± 0.23 kpc (3.30 ± 0.29 kpc). Here the physical parameters outside and inside the parentheses are for the u0 < 0 and u0 > 0 solutions, respectively. [ABSTRACT FROM AUTHOR]

Simultaneous observations of microlensing events from multiple locations allow for the breaking of degeneracies between the physical properties of the lensing system, specifically by exploring different regions of the lens plane and by directly measuring the “microlens parallax.” We report the discovery of a 30–65MJ brown dwarf orbiting a K dwarf in the microlensing event OGLE-2015-BLG-1319. The system is located at a distance of ∼5 kpc toward the Galactic Bulge. The event was observed by several ground-based groups as well as by Spitzer and Swift, allowing a measurement of the physical properties. However, the event is still subject to an eight-fold degeneracy, in particular the well-known close-wide degeneracy, and thus the projected separation between the two lens components is either ∼0.25 au or ∼45 au. This is the first microlensing event observed by Swift, with the UVOT camera. We study the region of microlensing parameter space to which Swift is sensitive, finding that though Swift could not measure the microlens parallax with respect to ground-based observations for this event, it can be important for other events. Specifically, it is important for detecting nearby brown dwarfs and free-floating planets in high magnification events. [ABSTRACT FROM AUTHOR]

We present a combined analysis of the observations of the gravitational microlensing event OGLE-2015-BLG-0479 taken both from the ground and by the Spitzer Space Telescope. The light curves seen from the ground and from space exhibit a time offset of ∼13 days between the caustic spikes, indicating that the relative lens-source positions seen from the two places are displaced by parallax effects. From modeling the light curves, we measure the space-based microlens parallax. Combined with the angular Einstein radius measured by analyzing the caustic crossings, we determine the mass and distance of the lens. We find that the lens is a binary composed of two G-type stars with masses of ∼1.0 M⊙ and ∼0.9 M⊙ located at a distance of ∼3 kpc. In addition, we are able to constrain the complete orbital parameters of the lens thanks to the precise measurement of the microlens parallax derived from the joint analysis. In contrast to the binary event OGLE-2014-BLG-1050, which was also observed by Spitzer, we find that the interpretation of OGLE-2015-BLG-0479 does not suffer from the degeneracy between (±, ±) and (±, ∓) solutions, confirming that the four-fold parallax degeneracy in single-lens events collapses into the two-fold degeneracy for the general case of binary-lens events. The location of the blend in the color–magnitude diagram is consistent with the lens properties, suggesting that the blend is the lens itself. The blend is bright enough for spectroscopy and thus this possibility can be checked from future follow-up observations. [ABSTRACT FROM AUTHOR]

We report on the mass and distance measurements of two single-lens events from the 2015 Spitzer microlensing campaign. With both finite-source effect and microlens parallax measurements, we find that the lens of OGLE-2015-BLG-1268 is very likely a brown dwarf (BD). Assuming that the source star lies behind the same amount of dust as the Bulge red clump, we find the lens is a 45 ± 7 BD at 5.9 ± 1.0 kpc. The lens of of the second event, OGLE-2015-BLG-0763, is a 0.50 ± 0.04 star at 6.9 ± 1.0 kpc. We show that the probability to definitively measure the mass of isolated microlenses is dramatically increased once simultaneous ground- and space-based observations are conducted. [ABSTRACT FROM AUTHOR]

Motivated by the ongoing Spitzer observational campaign, and the forthcoming K2 one, we revisit, working in an heliocentric reference frame, the geometrical foundation for the analysis of the microlensing parallax, as measured with the simultaneous observation of the same microlensing event from two observers with relative distance of order au. For the case of observers at rest, we discuss the well-known fourfold microlensing parallax degeneracy and determine an equation for the degenerate directions of the lens trajectory. For the case of observers in motion, we write down an extension of the Gould relationship between the microlensing parallax and the observable quantities and, at the same time, highlight the functional dependence of these same quantities from the timescale of the underlying microlensing event. Furthermore, through a series of examples, we show the importance of taking into account themotion of the observers to correctly recover the parameters of the underlying microlensing event. In particular, we discuss the cases of the amplitude of the microlensing parallax and that of the difference of the timescales between the observed microlensing events, which are key to understand the breaking of the microlensing parallax degeneracy. Finally, we consider the case of the simultaneous observation of the same microlensing event from the ground and two satellites, a case relevant for the expected joint K2 and Spitzer observational programs in 2016. [ABSTRACT FROM AUTHOR]

The microlensing event OGLE-2015-BLG-0448 was observed by Spitzer and lay within the tidal radius of the globular cluster NGC 6558. The event had moderate magnification and was intensively observed, hence it had the potential to probe the distribution of planets in globular clusters. We measure the proper motion of NGC 6558 () as well as the source and show that the lens is not a cluster member. Even though this particular event does not probe the distribution of planets in globular clusters, other potential cluster lens events can be verified using our methodology. Additionally, we find that microlens parallax measured using Optical Gravitational Lens Experiment (OGLE) photometry is consistent with the value found based on the light curve displacement between the Earth and Spitzer. [ABSTRACT FROM AUTHOR]

Spitzer microlensing parallax observations of OGLE-2015-BLG-1212 decisively break a degeneracy between planetary and binary solutions that is somewhat ambiguous when only ground-based data are considered. Only eight viable models survive out of an initial set of 32 local minima in the parameter space. These models clearly indicate that the lens is a stellar binary system possibly located within the bulge of our Galaxy, ruling out the planetary alternative. We argue that several types of discrete degeneracies can be broken via such space-based parallax observations. [ABSTRACT FROM AUTHOR]

We report the detection of a cold Neptune mplanet = 21 ± 2 M⊕ orbiting a 0.38 M⊙ M dwarf lying 2.5–3.3 kpc toward the Galactic center as part of a campaign combining ground-based and Spitzer observations to measure the Galactic distribution of planets. This is the first time that the complex real-time protocols described by Yee et al., which aim to maximize planet sensitivity while maintaining sample integrity, have been carried out in practice. Multiple survey and follow up teams successfully combined their efforts within the framework of these protocols to detect this planet. This is the second planet in the Spitzer Galactic distribution sample. Both are in the near to mid-disk and are clearly not in the Galactic bulge. [ABSTRACT FROM AUTHOR]