Astrometric Microlensing of Stars

1997

Astrophys J, 2003

We outline a method by which the angular radii of giant and main-sequence stars located in the Galactic bulge can be measured to a few percent accuracy. The method combines comprehensive ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise (~10 μas) astrometric measurements of the lensed star during the event, to measure the angular radius of the source, θ*. Dense photometric coverage of one caustic crossing yields the crossing timescale Δt. Less frequent coverage of the entire event yields the Einstein timescale tE and the angle φ of source trajectory with respect to the caustic. The photometric light-curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield θE, the angular Einstein ring radius. Then the angular radius of the source is obtained by θ*=θE(Δt/tE)sinφ. We argue that the parameters tE, Δt, φ, and θE, and therefore θ*, should all be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1 m class) telescopes, combined with astrometric observations with a precision of ~10 μas to measure θE. We find that a factor of ~50 times fewer photons are required to measure θE to a given precision for binary lens events than for single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), we find that ~7 minutes of SIM time is required to measure θE to ~5% accuracy for giant sources in the bulge. For main-sequence sources, θE can be measured to ~15% accuracy in ~1.4 hr. Thus, with access to a network of 1 m class telescopes, combined with 10 hr of SIM time, it should be possible to measure θ* to 5% for ~80 giant stars, or to 15% for roughly seven main-sequence stars. We also discuss methods by which the distances and spectral types of the source stars can be measured. A by-product of such a campaign is a significant sample of precise binary lens mass measurements.

Abstract. Gravitational microlensing offers a unique opportunity to study stellar atmospheres through highly time-resolved observations carried out in response to 'alerts', usually from binary lens events.

New Astronomy Reviews, 1998

We investigate the feasibility of reconstructing the radial intensity profile of extended stellar sources by inverting their microlensed light curves. Using a simple, linear, limb darkening law as an illustration, we show that the intensity profile can be accurately determined, at least over the outer part of the stellar disc, with realistic light curve sampling and photometric errors. The principal requirement is that the impact parameter of the lens be less than or equal to the stellar radius. Thus, the analysis of microlensing events provides a powerful method for testing stellar atmosphere models.

The Astrophysical Journal, 2017

We report on the first results from a large-scale observing campaign aiming to use astrometric microlensing to detect and place limits on the mass of single objects, including stellar remnants. We used the Hubble Space Telescope to monitor stars near the Galactic Center for 3 years, and we measured the brightness and positions of ∼2 million stars at each observing epoch. In addition to this, we monitored the same pointings using the VIMOS imager on the Very Large Telescope. The stars we monitored include several bright microlensing events observed from the ground by the OGLE collaboration. In this paper, we present the analysis of our photometric and astrometric measurements for 6 of these events, and derive mass constraints for the lens in each of these. Although these constraints are limited by the photometric precision of ground-based data, and our ability to determine the lens distance, we were able to constrain the size of the Einstein ring radius thanks to our precise astrometric measurements, the first routine measurements of this type from a large-scale observing program. This demonstrates the power of astrometric microlensing as a tool to constrain the masses of stars, stellar remnants, and, in the future, of extrasolar planets, using precise ground-and space-based observations.

The Astronomical Journal, 2018

We present the analysis of microlensing event MOA-2010-BLG-117, and show that the light curve can only be explained by the gravitational lensing of a binary source star system by a star with a Jupiter mass ratio planet. It was necessary to modify standard microlensing modeling methods to find the correct light curve solution for this binarysource, binary-lens event. We are able to measure a strong microlensing parallax signal, which yields the masses of the host star, M * = 0.58 ± 0.11M , and planet m p = 0.54 ± 0.10M Jup at a projected star-planet separation of a ⊥ = 2.42±0.26 AU, corresponding to a semi-major axis of a = 2.9 +1.6 −0.6 AU. Thus, the system resembles a half-scale model of the Sun-Jupiter system with a half-Jupiter mass planet orbiting a half-solar mass star at very roughly half of Jupiter's orbital distance from the Sun. The source stars are slightly evolved, and by requiring them to lie on the same isochrone, we can constrain the source to lie in the near side of the bulge at a distance of D S = 6.9 ± 0.7 kpc, which implies a distance to the planetary lens system of D L = 3.5 ± 0.4 kpc. The ability to model unusual planetary microlensing events, like this one, will be necessary to extract precise statistical information from the planned large exoplanet microlensing surveys, such as the WFIRST microlensing survey.

2020

Gravitational microlensing is an astronomical phenomenon where the gravity of a foreground massive object bends the rays of light of a background source into images. Effectively, the background source appears to be magnified with respect to time. Since this does not require detection of light from the lens, gravitational microlensing can be used to study different populations of objects in the galaxy, even the extra-solar planets. This phenomenon was practically formulated and investigated since the last decade of 20th century by a few observing groups. Today gravitational microlensing is observed and monitored by fourth generation telescopes towards high density stellar fields like the Galactic Bulge, Large and Small Magellanic clouds. With the increased capabilities there are numerous microlensing events that are detected but not yet analysed. Analysing these events, especially formed by a binary lens is not only challenging but tedious task. However with a suitable model that exp...

2005

Using astrometry of microlensing events we study the effect of angular momentum as compared to that of the parallax. For a rotating lens it is shown that the effect of the angular momentum deviates the center of images from that in the simple standard microlensing. This effect could be observed by future astrometry missions such as GAIA and SIM for lenses with angular momentum S ×10 48 kgm 2 sec −1 . It is shown that for extreme black hole lenses the corresponding mass should be more than 10 3 M ⊙ .

Physics of Particles and Nuclei, 2008

Basics of the standard theory of microlensing are introduced. The results of microlensing observations toward Magellanic Clouds and relations with the dark matter (DM) problem in our Galaxy are described. Pixel microlensing observations and recent discoveries of planets with microlensing observations are listed.

Astronomy and Astrophysics, 2004

A small fraction of all quasars are strongly lensed and multiply imaged, with usually a galaxy acting as the main lens. Some, maybe all of these quasars are also affected by microlensing, the effects of stellar mass objects in the lensing galaxy. Stellar microlensing not only has photometric effects (the apparent magnitudes of the quasar images vary independently due to the relative motion between source, lens and observer), it also affects the observed position of the images. This astrometric effect was first explored by : the position of the quasar -i.e. the center-of-light of the many microimages -can shift by tens of microarcseconds due to the relatively sudden (dis-)appearance of a pair of microimages when a caustic is being crossed. We explore this effect quantitatively for different values of the lensing parameters κ and γ (surface mass density and external shear) covering most of the known multiple quasar systems. We show examples of microlens-induced quasar motion and the corresponding light curves for different quasar sizes. We evaluate statistically the occurrence of large shifts in angular position and their correlation with apparent brightness fluctuations. We also show statistical relations between positional offsets and time from random starting points. As the amplitude of the astrometric offset depends on the source size, astrometric microlensing signatures of quasars -combined with the photometric variations -will provide very good constraints on the size of quasars as a function of wavelength. We predict that such signatures will be detectable for realistic microlensing scenarios with near future technology in the infrared/optical (Keck-Interferometry, VLTI, SIM, GAIA). Such detections will show that not even high redshift quasars define a "fixed" coordinate system.