Because Spitzer is an Earth-trailing orbit, losing about 0.1 AU/yr, it is excellently located to perform microlens parallax observations toward the Magellanic Clouds (LMC/SMC) and the Galactic bulge. These yield the so-called ``projected velocity'' of the lens, which can distinguish statistically among different populations. A few such measurements toward the LMC/SMC would reveal the nature of the lenses being detected in this direction (dark halo objects, or ordinary LMC/SMC stars). Cool Spitzer has already made one such measurement of a (rare) bright red-clump source, but warm (presumably less oversubscribed) Spitzer could devote the extra time required to obtain microlens parallaxes for the more common, but fainter, turnoff sources. Warm Spitzer could observe bulge microlenses for 38 days per year, which would permit up to 24 microlens parallaxes per year. This would yield interesting information on the disk mass function, particularly old brown dwarfs, which at present are inaccessible by other techniques. Target-of-Opportunity (TOO) observations should be divided into RTOO/DTOO, i.e., ``regular'' and ``disruptive'' TOOs, as pioneered by the Space Interferometry Mission (SIM). LMC/SMC parallax measurements would be DTOO, but bulge measurements would be RTOO, i.e., they could be scheduled in advance, without knowing exactly which star was to be observed.
We present a systematic search for parallax microlensing events among a total of 512 microlensing candidates in the OGLE II database for the 1997-1999 seasons. We fit each microlensing candidate with both the standard microlensing model and also a parallax model that accounts for the Earth's motion around the Sun. We then search for the parallax signature by comparing the chi^2 of the standard and parallax models. For the events which show a significant improvement, we further use the `duration' of the event and the signal-to-noise ratio as criteria to separate true parallax events from other …
Parallax measurements allow distances to celestial objects to be determined. Coupled with measurement of their position on the celestial sphere, it gives a full three-dimensional picture of the location of the objects relative to the observer. The distortion of the parallax value of a remote source affected by a weak microlensing is considered. This means that the weak microlensing leads to distortion of the distance scale. It is shown that the distortions to appear may change strongly the parallax values in case they amount to several microseconds of arc. In particular, at this accuracy many …
Microlensing event MACHO 97-SMC-1 is one of the rare microlensing events for which the source is a variable star, simply because most variable stars are systematically eliminated from microlensing studies. Using observational data for this event, we show that the intrinsic variability of a microlensed star is a powerful tool to constrain the nature of the lens by breaking the degeneracy between the microlens parallax and the blended light. We also present a statistical test for discriminating the location of the lens based on the χ^2 contours of the vector Λ, the inverse of the projected veloc…
Caustic-crossing binary lenses make up about 5% of all detected microlenses. The relative proper motion of a caustic-crossing binary lens can be measured with observations from a single terrestrial telescope. Thus, uniquely, binary lenses can be completely solved with only the addition of a measurement of the microlensing parallax. This solution will yield the mass, distance, and transverse velocity of the lens relative to the source. To date, only one of the $\sim 1000$ observed microlensing events has been so solved. We examine the ability of a parallax satellite combined with ground-based o…
If the microlensing events now being detected toward the Large Magellanic Cloud (LMC) are due to lenses in the Milky Way halo, then the events should typically have asymmetries of order 1% due to parallax from the reflex motion of the Earth. By contrast, if the lenses are in the LMC, the parallax effects should be negligible. A ground-based search for such parallax asymmetries would therefore clarify the location of the lenses. A modest effort (2 hours per night on a 1 m telescope) could measure 15 parallax asymmetries over 5 years and so marginally discriminate between the halo and the LMC as…
We have carried out photometry of the microlensing event MACHO-LMC-5 with Spitzer's IRAC ten years after the magnification of the LMC source star was recorded. This event is unique in the annals of gravitational microlensing: the lensing star itself has been observed using HST (once with WFPC2 and twice with ACS/HRC). Since the separation between the source and lens at the epoch of the Spitzer observations was $\sim0.24''$, the two stars cannot be resolved in the Spitzer images. However, the IRAC photometry clearly establishes that the lens is a M5 dwarf star from its infrared excess, which in…
We investigate the possibility of determining whether microlensing objects towards the Large Magellanic Cloud (LMC) are in a Galactic thick disc, or are in a Galactic halo, by using parallax measurements with an Earth-radius scale baseline. Our method makes use of EAGLE (Extremely Amplified Gravitational LEnsing) events which are microlensing events with an invisible faint source. We show that the rate of EAGLE events is as high as that of normal microlensing events, even if they are caused by dark stars in the Galactic thick disc. We explore the possibility of measuring the parallax effect in…
Perhaps as many as 30 parallax microlensing events are known, thanks to the efforts of the MACHO, OGLE, EROS and MOA experiments monitoring the bulge. Using Galactic models, we construct mock catalogues of microlensing light curves towards the bulge, allowing for the uneven sampling and observational error bars of the OGLE-II experiment. The fraction of parallax events with delta chi^2 > 50 in the OGLE-II database is around ~1%, though higher fractions are reported by some other surveys. This is in accord with expectations from standard Galactic models. The fraction of parallax events depends …
Astrometric measurements of microlensing events can in principle determine both the "parallax" \tilde r_E and the "proper motion" μof an individual event which (combined with the Einstein time scale t_E) in turn yield the mass, distance, and transverse velocity of the lens. We show, however, that the parallax measurements are generically several orders of magnitude less precise than the proper-motion measurements. Fortunately, astrometric measurements by the Space Interferometry Mission (SIM) are simultaneously **photometric** measurements, and since SIM will be in solar orbit, these allow SIM…
In recent years various models for the Galactic distribution of massive compact halo objects (MACHOs) have been proposed for the interpretation of microlensing toward the Large Magellanic Cloud (LMC). A direct way to fit the best model is by measuring the lens parameters, which can be obtained by measuring the Einstein crossing time and the parallax effect on the microlensing light curve and by astrometry of centroids of images. In this work, the theoretical distribution of these parameters is obtained for the various power-law Galactic dark halo models and MACHO mass functions (MF). For self-…
The Space Infrared Telescope Facility (SIRTF) will drift away from the Earth at about 0.1 AU/yr. Microlensing events will therefore have different characteristics as seen from the satellite and the Earth. From the difference, it is possible in principle to measure v-tilde, the transverse velocity of the lens projected onto the observer plane. Since v-tilde has very different values for different populations (disk, halo, Large Magellanic Cloud), such measurements could help identify the location, and hence the nature, of the lenses. I show that the method previously developed by Gould for measu…
We show that one can measure the effects of microlens parallax for binary microlensing events with three well-measured peaks -- two caustic crossings plus a cusp approach, and hence derive the projected Einstein radius. Since the angular Einstein radius is measurable from finite source effects for almost any well-observed caustic crossing, triple-peak events can yield the determination of the lens mass. We note that, to a certain extent, rotation of the binary can mimic the effects of parallax, but it should often be possible to disentangle parallax from rotation by making use of the late-time…
By extending the constant-acceleration analysis of Smith, Mao, & Paczynski to include jerk, I show that microlens parallax measurements are subject to a four-fold discrete degeneracy. The new degeneracy is characterized by a projected velocity \tilde v_j = -(3/4)\cscβ_\ec(\cos^2ψ\sin^2β_\ec+\sin^2ψ)^{3/2}v_earth, where β_\ec is the ecliptic latitude, ψis the phase of the Earth's orbit relative to opposition at the time of the event maximum, and v_earth=30 km/s is the speed of the Earth. The degeneracy becomes important when the lens projected velocity \tilde v is of order \tilde v_j. For event…
We analyze the Galactic bulge microlensing event MOA-2003-BLG-37. Although the Einstein timescale is relatively short, t_e=43 days, the lightcurve displays deviations consistent with parallax effects due to the Earth's accelerated motion. We show that the chi^2 surface has four distinct local minima that are induced by the ``jerk-parallax'' degeneracy, with pairs of solutions having projected Einstein radii, \tilde r_e = 1.76 AU and 1.28 AU, respectively. This is the second event displaying such a degeneracy and the first toward the Galactic bulge. For both events, the jerk-parallax formalism …
The parallax effect in ground-based microlensing (ML) observations consists of a distortion to the standard ML light curve arising from the Earth's orbital motion. In most cases, the resolution in current ML surveys is not accurate enough to observe this effect, but parallax could conceivably be detected with frequent followup observations of ML events in progress. We calculate the expected fraction of events where parallax distortions will be detected by such observations, adopting Galactic models consistent with the observed ML timescale ($t_0$) distributions. We study the dependence of the …
In gravitational lens systems with 3 or more resolved images of a quasar, the intrinsic variability may be unambiguously separated from the microlensing variability through parallax measurements from 3 observers when there is no relative motion of the lens masses (Refsdal 1993). In systems with fewer than 3 resolved images, however, this separation is not straightforward. A general approach that may be used for this purpose is presented. For simplicity, only the one-dimensional case is considered in detail: Given a well-sampled time series of the observed flux at two points in space with a kno…
We describe a unique mass determination for a microlensing event from the second phase of the Optical Gravitational Microlensing Experiment (OGLE-II). The event, sc26_2218, which is very bright (baseline magnitude I=15.10), appears to exhibit both parallax and finite source effects. The parallax effect allows us to determine the projected Einstein radius on the observer plane (approx. 3.8 AU), while the finite source effect allows us to determine the ratio of the angular source size and the angular Einstein radius. As the angular size of the star can be estimated using its color and magnitude,…
Of all planet-finding techniques, microlensing is potentially the most sensitive to Earth-mass planets. However, microlensing lightcurves generically yield only the planet-star mass ratio: the mass itself is uncertain to a factor of a few. To determine the planet mass, one must measure both the ``microlens parallax'' and source-lens relative proper motion. Here we present a new method to measure microlens masses for terrestrial planets. We show that, with only a modest adjustment to the proposed orbit of the dedicated satellite that finds the events, and combined with observations from a groun…
We combine Spitzer and ground-based observations to measure the microlens parallax of OGLE-2005-SMC-001, the first such space-based determination since S. Refsdal proposed the idea in 1966. The parallax measurement yields a projected velocity \tilde v ~ 230 km/s, the typical value expected for halo lenses, but an order of magnitude smaller than would be expected for lenses lying in the Small Magellanic Cloud (SMC) itself. The lens is a weak (i.e., non-caustic-crossing) binary, which complicates the analysis considerably but ultimately contributes additional constraints. Using a test proposed b…
We present the results from an analysis of Hubble Space Telescope High Resolution Camera data for the Large Magellanic Cloud microlensing event MACHO-LMC-5. By determining the parallax and proper motion of this object we find that the lens is an M dwarf star at a distance of 578(+65/-53)pc with a proper motion of 21.39 +/- 0.04 mas/yr. Based on the kinematics and location of this star it more likely to be part of the Galactic thick disk than thin disk population. We confirm that the microlensing event LMC-5 is a jerk-parallax event.
The uncertainty of the lens mass can be substantially reduced if it is determined from the lens proper motion obtained from astrometric measurements of the source image centroid shifts, $\vdelta\vtheta_c$, by using high precision interferometers. However, for the complete resolution of the lens parameter degeneracy it is required to determine the lens parallax by measuring the parallax-induced deviations in the centroid shifts trajectory, $\vDelta \vdelta \vtheta_c$. In this paper, we investigate the detectabilities of $\vdelta\vtheta_c$ and $\vDelta\vdelt\vtheta_c$ by determining the distribu…
We analyze PLANET photometric observations of the caustic-crossing binary-lens microlensing event, EROS BLG-2000-5, and find that modeling the observed light curve requires incorporation of the microlens parallax and the binary orbital motion. The projected Einstein radius (~r_E = 3.61 +/- 0.11 AU) is derived from the measurement of the microlens parallax, and we are also able to infer the angular Einstein radius (theta_E = 1.38 +/- 0.12 mas) from the finite source effect on the light curve, combined with an estimate of the angular size of the source given by the source position in a color-mag…
We describe a few recent microlensing results from the MACHO Collaboration. The aim of the MACHO Project was the identification and quantitative description of dark and luminous matter in the Milky Way using microlensing toward the Magellanic Clouds and Galactic bulge. We start with a discussion of the HST follow-up observations of the microlensing events toward the LMC detected in the first 5 years of the experiment. Using color-magnitude diagrams we attempt to distinguish between two possible locations of the microlensing sources: 1) in the LMC or 2) behind the LMC. We conclude that unless t…
In order to understand the nature of the lenses that generate microlensing events, one would like to measure their mass, distance, and velocity. Unfortunately, current microlensing experiments measure only one parameter of the events, the characteristic timescale, which is a combination of the underlying physical parameters. Other methods are required to extract additional information. Parallax measurements using a satellite in an Earth-like orbit yield the projected velocity of the lens: ${\bf{\tilde v}} ={\bf{v}}/(1-z)$, where ${\bf{v}}$ is the transverse velocity (speed and direction) of th…
We report on the identification of the lens responsible for microlensing event MACHO-LMC-20. As part of a \textit{Spitzer}/IRAC program conducting mid-infrared follow-up of the MACHO Large Magellanic Cloud microlensing fields, we discovered a significant flux excess at the position of the source star for this event. These data, in combination with high resolution near-infrared \textit{Magellan}/PANIC data has allowed us to classify the lens as an early M dwarf in the thick disk of the Milky Way, at a distance of $\sim 2$ kpc. This is only the second microlens to have been identified, the first…
The Einstein time scale, which is the only information obtained from current microlensing experiments, results from a complicated combination of the lens parameters that we want to determine. Of the methods for breaking the lens parameter degeneracy, the most promising and generally applicable method is to measure the lens parallax from simultaneous observations of a lensing event from the ground and a heliocentric satellite (Gould 1994). However, the elegant idea of parallax measurement, which was proposed to resolve the lens parameter degeneracy, paradoxically suffers from its own degeneracy…
We analyze the limitations imposed by photon counting statistics on extracting useful information about MACHOs from Earth-based parallax observations of microlensing events. We find that if one or more large (say $2.5\,\rm m$) telescopes are dedicated to observing a MACHO event for several nights near maximum amplification, then it is possible, in principle, to measure the velocity of the MACHO well enough to distinguish between disk and halo populations for events with $ω{A_m}\!^2 \gta 1\,\rm day^{-1}$, where $ω^{-1}$ denotes the timescale of the event and $A_m$ denotes its maximum amplificat…
