Photometric Microlensing Research Articles

Astrometric Microlensing with the GAIA Satellite

The capabilities of the GAIA satellite for the detection of microlensing events are analyzed. The all-sky averaged photometric optical depth is ~7×10 -8 and there are ~4000 photometric microlensing events during the five year mission lifetime. The all-sky averaged astrometric microlensing optical depth is ~5×10 -5 and ~50 000 sources will have a significant variation of the centroid shift, together with a closest approach, during the mission lifetime. We show that GAIA is the first instrument with the capability to measure the mass locally in very faint objects like black holes and very cool white and brown dwarfs.

Detecting Galactic MACHOs with VERA through Astrometric Microlensing of Distant Radio Sources

We consider the properties of astrometric microlensing of distant radio sources (QSOs and radio galaxies) due to MACHOs, and discuss their implications for VERA (VLBI Exploration of Radio Astrometry). First, we show that in the case of astrometric microlensing of distant sources, the event duration is only a function of the lens mass and tangential velocity, but independent of the lens distance, in contrast to the well-known three-fold degeneracy for photometric microlensing. Moreover, the lens mass, $M$, is scaled by the tangential velocity, $v_\perp$, as $M\propto v_\perp$, rather than $M\propto v_\perp^2$, which is the case for photometric microlensing. Thus, in astrometric microlensing the dependence of the lens mass on the unknown parameter, $v_\perp$, is weaker, indicating that the duration of an astrometric microlensing event is a better quantity to study the mass of lensing objects than that of photometric microlensing. We also calculate the optical depth and event rate, and show that within 20${}^{\mathrm{\circ}}$ of the galactic center a typical event rate for a $10~\mu\mathrm{as}$-level shift is larger than $2.5 \times 10^{-4}$ event per year, assuming that a quarter of the halo is made up of MACHOs. This indicates that if one monitors a few hundred sources for $\sim$20 years, such an astrometric microlensing event is detectable. Since a typical event duration has been found to be fairly long (5 to 15 years), the frequency of the monitoring observation can be relatively low, i.e., once per six months, which is rather reasonable for practical observations. We discuss a practical strategy for observing astrometric microlensing with VERA, and argue that an astrometric microlensing event due to MACHOs can be detected by VERA within a few decades.

Astrometric Microlensing of Stars

Because of dramatic improvements in the precision of astrometric measurements, the observation of light centroid shifts in observed stars due to intervening massive compact objects (astrometric microlensing) will become possible in the near future. Upcoming space missions, such as SIM and GAIA, will provide measurements with an accuracy of 4-60 mu as depending on the magnitude of the observed stars, and an accuracy of similar to 1 mu as is expected to be achieved in the more distant future. There are two different ways in which astrometric microlensing signals can be used to infer information: one possibility is to perform astrometric follow-up observations on photometrically detected microlensing events, and the other is to perform a survey based on astrometric observations alone. After the predictable effects of the Sun and the planets, stars in the Galactic disk play the dominant role in astrometric microlensing. The probability that the disk stars introduce a centroid shift larger than the threshold delta(T) at a given time for a given source in the Galactic bulge toward Baade's window reaches 100% for a threshold of delta(T) = 0.7 mu as, while this probability is similar to 2% for delta(T) = 5 mu as. However, this centroid shift does not vary much during the time in which a typical photometric microlensing event differs from baseline. So astrometric follow-ups (e.g., with SIM) are not expected to be disturbed by the statistical astrometric microlensing due to disk stars, so that it is possible to infer additional information about the nature of the lens that caused the photometric event, as suggested. The probability of observing astrometric microlensing events within the Galaxy turns out to be large compared to photometric microlensing events. The probability of seeing a variation by more than 5 mu as within 1 yr and reaching the closest angular approach between lens and source is similar to 10(-4) for a bulge star toward Baade's window, while this reduces to similar to 6 x 10(-6) for a direction perpendicular to the Galactic plane. For the upcoming mission GAIA, we expect similar to 1000 of the observed stars to show a detectable astrometric microlensing signal within its 5 yr lifetime. These events can be used to determine accurate masses of the lenses, and to derive the mass and the scale parameters (length and height) of the Galactic disk.

Astrometric Microlensing as a Method of Discovering and Characterizing Extrasolar Planets

We introduce a new method of searching for and characterizing extrasolar planets. We show that by monitoring the center-of-light motion of microlensing alerts using the next generation of high-precision astrometric instruments the probability of detecting a planet orbiting the lens is high. We show that adding astrometric information to the photometric microlensing light curve greatly helps in determining the planetary mass and projected separation. We introduce astrometric maps as a new way for calcu- lating astrometric motion and planet detection probabilities. Finite source eUects are important for low- mass planets, but even Earth-mass planets can give detectable signals. Subject headings: astrometrygravitational lensingplanetary systems

Gravitational Lensing by Stars and Machos and the Orbital Motion of the Earth

We showed that it is feasible to measure the mass of a single star by observing the variation of gravitational deflection caused by the orbital motion of the Earth. When the distance of a star is less than 60 pc and some appropriate sources are within 1 arcsec. in its background, not only the distance but also the mass of the star may be determined by measuring the deflection with an accuracy of 10 μ arcsec. In the case of photometric microlensing by a MACHO, the observation of astrometric gravitational deflection is also useful. By measuring the separation between the primary image and the secondary image, the ratio of mass to distance of the MACHO will be obtained. Further, the orbital motion of the Earth modifying the light curve of the source is discussed.