I show that when the observables $(\vec π_{\rm E},t_{\rm E},θ_{\rm E},π_s,\vec μ_s)$ are well measured up to a discrete degeneracy in the microlensing parallax vector $\vec π_{\rm E}$, the relative likelihood of the different solutions can be written in closed form $P_i = K H_i B_i$, where $H_i$ is the number of stars (potential lenses) having the mass and kinematics of the inferred parameters of solution $i$ and $B_i$ is an additional factor that is formally derived from the Jacobian of the transformation from Galactic to microlensing parameters. The Jacobian term $B_i$ 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 $H_i$. Here $t_{\rm E}$ is the Einstein timescale, $θ_{\rm E}$ is the angular Einstein radius, and $(π_s,\vec μ_s)$ are the (parallax, proper motion) of the microlensed source. I also discuss how this analytic expression degrades in the presence of finite errors in the measured observables.
The impact of the free-floating planet (FFP) mass function on the event rate for the accurate microlensing parallax determination: application to Euclid and Roman parallax observation
Simultaneous observations from two spatially well-separated telescopes can lead to the measurements of the microlensing parallax parameter, an important quantity toward the determinations of the lens mass. The separation between Earth and Sun-Earth L2 point, $\sim0.01$ AU, is ideal for parallax measurements of short and ultra-short ($\sim$1\,hr to 10\,days) microlensing events, which are candidates of free-floating planet (FFP) events. In this work, we study the potential of doing so in the context of two proposed space-based missions, the Chinese Space Station Telescope (CSST) in a Leo orbit …
The event rate and the efficiency of mass estimation for free-floating planet (FFP) microlensing events were determined from the simulation of the simultaneous parallax observations by Euclid, WFIRST, and LSST. The stellar population from the Besançon Galactic model toward $(l, b)=(1^{\circ},-1.^{\circ}75)$ was applied to our 3D microlensing model, and 30,000 parallax observations were simulated for each following FFP lens masses: Jupiter-mass, Neptune-mass, and Earth-mass assuming the population of one FFP per star. The interstellar dust, unresolved stellar background, nearby star blending we…
First proposed by Paczynski in 1986, microlensing has been instrumental in the search of compact dark matter as well as discovery and characterization of exoplanets. In this article, we provide a brief history of microlensing, especially on the discoveries of compact objects and exoplanets. We then review the basics of microlensing and how astrometry can help break the degeneracy, providing a more robust determination of the nature of the microlensing events. We also outline prospects that will be made by on-going and forth-coming experiments/observatories
In this work, we use $13$ microlensing candidates with dark lenses from OGLE III catalogue \cite{2016MNRAS.458.3012W} and cross-match them with the GAIA catalogue. We identify the microlensing source stars in the GAIA catalogue by comparing the coordinate and the magnitude of stars and using the proper motion and the parallax parameters of the source stars. Combining with the microlensing light curves as well as the microlensing parallax effect, we determine the mass and the distance of lenses from Earth. We conclude that the lens for this set of microlensing events for the massive lenses are …
We introduce MulensModel, a software package for gravitational microlensing modeling. The package provides a framework for calculating microlensing model magnification curves and goodness-of-fit statistics for microlensing events with single and binary lenses as well as a variety of higher-order effects: extended sources with limb-darkening, annual microlensing parallax, satellite microlensing parallax, and binary lens orbital motion. The software could also be used for analysis of the planned microlensing survey by the NASA flag-ship WFIRST satellite. MulensModel is available at https://githu…
Aims. We study the impact of the parallax on the search for very long timescale microlensing events towards the Magellanic Clouds due to dark massive compact objects within the past MACHO and EROS, the ongoing MOA and OGLE, and the future LSST surveys. We quantify the impact of neglecting this effect on the classical event selection process and also quantify the parallax detectability without the help of follow-up observations.Methods. We define a distance between true events affected by parallax and the closest events without parallax. This distance is used to estimate the probability of miss…
I present a novel method for measuring lens masses for microlensing events. By combining a measured lens flux with the microlens parallax vector pi_E, it is possible to derive the mass of the lens system without knowing the angular size of the Einstein ring, theta_E. This enables mass and distance measurements for single, luminous lenses, as well as binary and planetary lenses without caustic crossings. I discuss applications of this method in the contexts of the Spitzer, Kepler, and WFIRST microlensing missions.
Augmenting the \emph{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, transvers…
We present limits on the lens flux of OGLE-2007-BLG-224 based on MagAO imaging taken seven years after the microlensing event. At the time of the observations, the lens should have been separated from the microlensing source by 292 mas. However, no new sources are detected with MagAO. We place an upper limit on the lens flux of $H>20.57$. This measurement supports the conclusion of Gould et al. (2009) that the lens in this event should be a brown dwarf. This is the first test of a prediction based on the terrestrial microlens parallax effect and the first AO confirmation of a sub-stellar/dark …
We report the analysis of microlensing event OGLE-2017-BLG-1038, observed by the Optical Gravitational Lensing Experiment, Korean Microlensing Telescope Network, and Spitzer telescopes. The event is caused by a giant source star in the Galactic Bulge passing over a large resonant binary lens caustic. The availability of space-based data allows the full set of physical parameters to be calculated. However, there exists an eightfold degeneracy in the parallax measurement. The four best solutions correspond to very-low-mass binaries near ($M_1 = 170^{+40}_{-50} M_J$ and $M_2 = 110^{+20}_{-30} M_J…
Microlens parallax measurements combining space-based and ground-based observatories can be used to study planetary demographics. In recent years, the Spitzer Space Telescope was used as a microlens parallax satellite. Meanwhile, \textit{Spitzer} IRAC has been employed to study short-period exoplanets and their atmospheres. As these investigations require exquisite photometry, they motivated the development of numerous self-calibration techniques now widely used in the exoplanet atmosphere community. Specifically, Pixel Level Decorrelation (PLD) was developed for starring-mode observations in …
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 robust 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 m…
