We complete the survey for finite-source/point-lens (FSPL) giant-source events in 2016–2019 KMTNet microlensing data. The 30 FSPL events show a clear gap in Einstein radius, 9 μas < θE < 26 μas, which is consistent with the gap in Einstein timescales near tE ∼ 0.5 days found by Mr´oz et al. (2017) in an independent sample of point-source/point-lens (PSPL) events. We demonstrate that the two surveys are consistent. We estimate that the 4 events below this gap are due to a power-law distribution of freefloating planet candidates (FFPs) dNFFP/d logM = (0.4 ± 0.2) (M/38 M⊕)−p/star, with 0.9 ≲ p ≲ 1.2. There are substantially more FFPs than known bound planets, implying that the bound planet power-law index γ = 0.6 is likely shaped by the ejection process at least as much as by formation. The mass density per decade of FFPs in the Solar neighborhood is of the same order as that of ‘Oumuamua-like objects. In particular, if we assume that ‘Oumuamua is part of the same process that ejected the FFPs to very wide or unbound orbits, the power-law index is p = 0.89 ± 0.06. If the Solar System’s endowment of Neptune-mass objects in Neptune-like orbits is typical, which is consistent with the results of Poleski et al. (2021), then these could account for a substantial fraction of the FFPs in the Neptune-mass range.

We present the analysis of a planetary microlensing event OGLE-2019-BLG-0362 with a shortduration anomaly (∼0.4 days) near the peak of the light curve, which is caused by the resonant caustic. The event has a severe degeneracy with Δχ2 = 0.9 between the close and the wide binary lens models both with planet-host mass ratio q ≃ 0.007. We measure the angular Einstein radius but not the microlens parallax, and thus we perform a Bayesian analysis to estimate the physical parameters of the lens. We find that the OGLE-2019-BLG-0362L system is a super-Jovian-mass planet Mp = 3.26+0.83 −0.58 MJ orbiting an M dwarf Mh = 0.42+0.34 −0.23 M⊙ at a distance DL = 5.83+1.04 −1.55 kpc. The projected star-planet separation is a⊥ = 2.18+0.58 −0.72 AU, which indicates that the planet lies beyond the snow line of the host star.

We report the discovery of a giant exoplanet in the microlensing event OGLE-2017-BLG-1049, with a planet―host star mass ratio of q = 9.53 ± 0.39 × 10-3 and a caustic crossing feature in Korea Microlensing Telescope Network (KMTNet) observations. The caustic crossing feature yields an angular Einstein radius of θE = 0.52 ± 0.11 mas. However, the microlens parallax is not measured because the time scale of the event, tE ≃ 29 days, is too short. Thus, we perform a Bayesian analysis to estimate physical quantities of the lens system. We find that the lens system has a star with mass Mh = 0.55+0.36 -0.29 M⊙ hosting a giant planet with Mp = 5.53+3.62 -2.87 MJup, at a distance of DL = 5.67+1.11 -1.52 kpc. The projected star{planet separation is aㅗ = 3.92+1.10 -1.32 au. This means that the planet is located beyond the snow line of the host. The relative lens{source proper motion is μrel ~ 7 mas yr-1, thus the lens and source will be separated from each other within 10 years. After this, it will be possible to measure the flux of the host star with 30 meter class telescopes and to determine its mass.

I show that when the observables (πE, tE, θE, πs, μs) are well measured up to a discrete degeneracy in the microlensing parallax vector πE, the relative likelihood of the di erent solutions can be written in closed form Pi = KHiBi, where Hi is the number of stars (potential lenses) having the mass and kinematics of the inferred parameters of solution i and Bi is an additional factor that is formally derived from the Jacobian of the transformation from Galactic to microlensing parameters. Here tE is the Einstein timescale, θE is the angular Einstein radius, and (πs;μs) are the (parallax, proper motion) of the microlensed source. The Jacobian term Bi constitutes an explicit evaluation of the \Rich Argument", i.e., that there is an extra geometric factor disfavoring large-parallax solutions in addition to the reduced frequency of lenses given by Hi. I also discuss how this analytic expression degrades in the presence of finite errors in the measured observables.

At q = 1.81 ± 0.20 × 10-5, KMT-2018-BLG-0029Lb has the lowest planet-host mass ratio q of any microlensing planet to date by more than a factor of two. Hence, it is the first planet that probes below the apparent "pile-up" at q = 5-10 ×10-5. The event was observed by Spitzer, yielding a microlens-parallax πE measurement. Combined with a measurement of the Einstein radius θE from finite-source effects during the caustic crossings, these measurements imply masses of the host Mhost = 1.14+0.10-0.12 M⊙ and planet Mplanet = 7.59+0.75-0.69 M⊕, system distance DL = 3.38+0.22-0.26 kpc and projected separation a⊥ = 4.27+0.21-0.23 AU. The blended light, which is substantially brighter than the microlensed source, is plausibly due to the lens and could be observed at high resolution immediately.

I investigate the origin of arc degeneracies in satellite microlens parallax π E measurements with only late time data, e.g., t > t 0 + t E as seen from the satellite. I show that these are due to partial overlap of a series of osculating, exactly circular, degeneracies in the π E plane, each from a single measurement. In events with somewhat earlier data, these long arcs break up into two arclets, or (with even earlier data) two points, because these earlier measurements give rise to intersecting rather than osculating circles. The two arclets (or points) then constitute one pair of degeneracies in the well-known four-fold degeneracy of space-based microlens parallax. Using this framework of intersecting circles, I show that next-generation microlens satellite experiments could yield good π E determinations with only about five measurements per event, i.e., about 30 observations per day to monitor 1500 events per year. This could plausibly be done with a small (hence cheap, in the spirit of Gould & Yee 2012) satellite telescope, e.g., 20 cm.

Like Hipparcos, Gaia is designed to give absolute parallaxes, independent of any astrophysical reference system. And indeed, Gaia’s internal zero-point error for parallaxes is likely to be smaller than any individual parallax error. Nevertheless, due in part to mechanical issues of unknown origin, there are many astrophysical questions for which the parallax zero-point error σ(π0) will be the fundamentally limiting constraint. These include the distance to the Large Magellanic Cloud and the Galactic Center. We show that by using the photometric parallax estimates for RR Lyrae stars (RRL) within 8kpc, via the ultra-precise infrared period-luminosity relation, one can independently determine a hyper-precise value for π0. Despite their paucity relative to bright quasars, we show that RRL are competitive due to their order-of-magnitude improved parallax precision for each individual object relative to bright quasars. We show that this method is mathematically robust and well-approximated by analytic formulae over a wide range of relevant distances.

Microlensing is generally thought to probe planetary systems only out to a few Einstein radii. Microlensing events generated by bound planets beyond about 10 Einstein radii generally do not yield any trace of their hosts, and so would be classified as free floating planets (FFPs). I show that it is already possible, using adaptive optics (AO), to constrain the presence of potential hosts to FFP candidates at separations comparable to the Oort Cloud. With next-generation telescopes, planets at Kuiper-Belt separations can be probed. Next generation telescopes will also permit routine vetting for all FFP candidates, simply by obtaining second epochs 4--8 years after the event.At present, the search for such hosts is restricted to within the ``confusion limit'' of θconfus ∼ 0.25 〃, but future WFIRST (Wide Field Infrared Survey Telescope) observations will allow one to probe beyond this confusion limit as well.

Augmenting the Wide Field Infrared Survey Telescope (WFIRST) microlensing campaigns with intensive observations from a ground-based network of wide-field survey telescopes would have several major advantages. First, it would enable full two-dimensional (2-D) vector microlens parallax measurements for a substantial fraction of low-mass lenses as well as planetary and binary events that show caustic crossing features. For a significant fraction of the free-floating planet (FFP) events and all caustic-crossing planetary/binary events, these 2-D parallax measurements directly lead to complete solutions (mass, distance, transverse velocity) of the lens object (or lens system). For even more events, the complementary ground-based observations will yield 1-D parallax measurements. Together with the 1-D parallaxes from WFIRST alone, they can probe the entire mass range M & M⊕. For luminous lenses, such 1-D parallax measurements can be promoted to complete solutions (mass, distance, transverse velocity) by high-resolution imaging. This would provide crucial information not only about the hosts of planets and other lenses, but also enable a much more precise Galactic model. Other benefits of such a survey include improved understanding of binaries (particularly with low mass primaries), and sensitivity to distant ice-giant and gas-giant companions of WFIRST lenses that cannot be detected by WFIRST itself due to its restricted observing windows. Existing ground-based microlensing surveys can be employed if WFIRST is pointed at lower-extinction fields than is currently envisaged. This would come at some cost to the event rate. Therefore the benefits of improved characterization of lenses must be weighed against these costs.

Euclid, which is primarily a dark-energy/cosmology mission, may have a microlensing component, consisting of perhaps four dedicated one-month campaigns aimed at the Galactic bulge. We show that such a program would yield excellent auxilliary science, including asteroseismology detections for about 100 000 giant stars, and detection of about 1000 Kuiper Belt Objects (KBOs), down to 2–2.5 mag below the observed break in the KBO luminosity function at I ∼ 26. For the 400 KBOs below the break, Euclid will measure accurate orbits, with fractional period errors . 2.5%.

WFIRST microlensing observations will return high-precision parallaxes, σ(π) . 0.3 μas, for the roughly 1 million stars with H < 14 in its 2.8 deg2 field toward the Galactic bulge. Combined with its 40,000 epochs of high precision photometry (∼ 0.7 mmag at Hvega = 14 and ∼ 0.1 mmag at H = 8), this will yield a wealth of asteroseismic data of giant stars, primarily in the Galactic bulge but including a substantial fraction of disk stars at all Galactocentric radii interior to the Sun. For brighter stars, the astrometric data will yield an external check on the radii derived from the two asteroseismic parameters, the large-frequency separation h
νnli and the frequency of maximum oscillation power νmax, while for the fainter ones, it will enable a mass measurement from the single measurable asteroseismic parameter νmax. Simulations based on Kepler data indicate that WFIRST will be capable of detecting oscillations in stars from slightly less luminous than the red clump to the tip of the red giant branch, yielding roughly 1 million detections.

I show that the WFIRST microlensing survey will enable detection and precision orbit determination of Kuiper Belt Objects (KBOs) down to Hvega = 28.2 over an effective area of ∼ 17 deg2. Typical fractional period errors will be ∼ 1.5% × 100.4(H−28.2) with similar errors in other parameters for roughly 5000 KBOs. Binary companions to detected KBOs can be detected to even fainter limits, Hvega = 29, corresponding to R ∼ 30.5 and effective diameters D ∼ 7 km. For KBOs H ∼ 23, binary companions can be found with separations down to 10 mas. This will provide an unprecedented probe of orbital resonance and KBO mass measurements. More than a thousand stellar occultations by KBOs can be combined to determine the mean size as a function of KBO magnitude down to H ∼ 25. Current ground-based microlensing surveys can make a significant start on finding and characterizing KBOs using existing and soon-to-be-acquired data.

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.

I show that the standard microlensing technique to measure the angular radius of a star using color/surface-brightness relations can be inverted, via late-time proper motion measurements, to calibrate these relations. The method is especially useful for very metal-rich stars because such stars are in short supply in the solar neighborhood where other methods are most effective, but very abundant in Galactic bulge microlensing fields. I provide a list of eight spectroscopically identified high-metallicity bulge stars with the requisite finite-source effects, seven of which will be suitable calibrators when the Giant Magellan Telescope comes on line. Many more such sources can be extracted from current and future microlensing surveys.