Limits on the Gravity Wave Background From Microlensed Quasars

The paper previously submitted under this title is incorrect in that it drastically overestimates the cumulative deflection due to a gravitational wave (GW) background. Avi Loeb gives a simple argument that there can be no $(D\omega)^{1/2}$ enhancement: since the problem is linear in $h$, one can decompose the GWs into plane waves and for each of these there is no enhancement.Comment: This paper was incorrect in that it drastically overestimated the cumulative deflection due to a gravitational wave background. Withdraw

Microlensing and the Stellar Mass Function

Traditional approaches to measuring the stellar mass function (MF) are fundamentally limited because objects are detected based on their luminosity, not their mass. These methods are thereby restricted to luminous and relatively nearby stellar populations. Gravitational microlensing promises to revolutionize our understanding of the MF. It is already technologically feasible to measure the MFs of the Galactic disk and Galactic bulge as functions of position, although the actual execution of this program requires aggressive ground-based observations including infrared interferometry, as well as the launching of a small satellite telescope. Rapid developments in microlensing, including the new technique of ``pixel lensing'' of unresolved stars, will allow one to probe the MF and luminosity function of nearby galaxies. Such observations of M31 are already underway, and pixel-lensing observations of M87 with the {\it Hubble Space Telescope} would permit detection of dark intra-cluster objects in Virgo. Microlensing techniques can also be applied to investigate the star-formation history of the universe and to search for planets with masses as small as the Earth's. Based on an invited talk at the January 1996 AAS meeting in San Antonio. PASP (June 1996) in press, (c) ASP, reproduced with permission.Comment: 31 pages with 7 embedded figures. PASP (June 1996) in press, (c) ASP, reproduced with permissio

Self-Lensing By A Stellar Disk

I derive a general expression for the optical depth $\tau$ for gravitational lensing of stars in a disk by Massive Compact Objects (Machos) in the same disk. For the more restricted case where the disk is self-gravitating and the stars and Machos have the same distribution function, I find \tau = 2\VEV{v^2}/c^2\sec^2 i where \VEV{v^2} is the mass-weighted vertical velocity dispersion, and $i$ is the angle of inclination. This result does not depend on any assumptions about the velocity distribution. As an example, if stars within the bar of the Large Magellanic Cloud (LMC) account for the observed optical depth $\tau\sim 8\times 10^{-8}$ as has recently been suggested, then v\gsim 60\,\kms. This is substantially larger than the measured dispersions of known LMC populations.Comment: 6 pages, no figures, phyzzx macro package, or request PostScript file to [email protected], OSU-TA-13/9

A New Method to Calibrate the Stellar Color/Surface-Brightness Relation

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.Comment: Submitted to Journal of The Korean Astronomical Society; 6 pages, 1 figur

Microlens Masses from 1-D Parallaxes and Heliocentric Proper Motions

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.Comment: 4 pages, Journal of the Korean Astronomical Societ