DIFFRACTION EFFECTS IN MICROLENSING OF Q2237+0305

Geometrical optics provides an excellent description for quasar images crossing caustics which are formed by gravitational microlensing of objects like Q2237+0305. Within this approximation the source size can be estimated from the maximum magnification reached at caustic crossings. We evaluate the limitations imposed by diffraction on caustics using the formalism developed by Ulmer & Goodman (1995). Close to a caustic a new characteristic length, smaller that the Fresnel length, enters the problem, limiting the angular resolution to about 0.2 pico arcsecond, or equivalently about 3*10^9 cm at the source. To achieve this resolution the brightness must be monitored at time intervals of a few seconds. If a significant fraction of quasar luminosity comes from sources smaller than those limits then interference effects would make the observed intensity oscillate, in a close analogy with a two slit experiment. The characteristic period of such oscillations is expected to be about one tenth of a minute. If such oscillations are detected then photometry carried out at a single site may permit the determination of the caustic transverse velocity, and therefore may permit a direct conversion of the time units of brightness variations to the linear units at the source. Subject headings: Gravitational lensing - dark matter - quasars: structure -quasars: Q2237+0305Comment: 10 pages, plain TEX file, no figures. Submitted to ApJ postscript available at by anonymous ftp at ftp://astro.princeton.edu/library/preprint/pop615.ps.

Glass Transition in a Two-Dimensional Electron System in Silicon in a Parallel Magnetic Field

Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional electron system (2DES) in Si in the vicinity of the metal-insulator transition (MIT) persists in parallel magnetic fields B of up to 9 T. At low B, both the glass transition density $n_g$ and $n_c$, the critical density for the MIT, increase with B such that the width of the metallic glass phase ($n_c<n_s<n_g$) increases with B. At higher B, where the 2DES is spin polarized, $n_c$ and $n_g$ no longer depend on B. Our results demonstrate that charge, as opposed to spin, degrees of freedom are responsible for glassy ordering of the 2DES near the MIT.Comment: 4 pages, 5 figure

Determination of Stellar Ellipticities in Future Microlensing Surveys

We propose a method that can determine the ellipticities of source stars of microlensing events produced by binary lenses. The method is based on the fact that the products of the caustic-crossing timescale, $\Delta t$, and the cosine of the caustic incidence angle of the source trajectory, $\kappa$, of the individual caustic crossings are different for events involving an elliptical source, while the products are the same for events associated with a circular source. The product $\Delta t_\perp =\Delta t \cos\kappa$ corresponds to the caustic-crossing timescale when the incidence angle of the source trajectory is $\kappa=0$. For the unique determination of the source ellipticity, resolutions of at least three caustic crossings are required. Although this requirement is difficult to achieve under the current observational setup based on alert/follow-up mode, it will be possible with the advent of future lensing experiments that will survey wide fields continuously at high cadence. For typical Galactic bulge events, the difference in $\Delta t_\perp$ between caustic crossings is of the order of minutes depending on the source orientations and ellipticities. Considering the monitoring frequency of the future lensing surveys of $\sim 6$ times/hr and the improved photometry especially of the proposed space-based survey, we predict that ellipticity determinations by the proposed method will be possible for a significant fraction of multiple caustic-crossing binary lens events involving source stars having non-negligible ellipticities.Comment: 6 pages, 4 figures, ApJ, submitte