Oral, Wednesday, January 8, 2003, 10:00-11:30am, 606-607

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*E. Agol, A. Farmer, K. Mandel (Caltech)*

We will prove a gravitational lensing theorem: the
magnification of a large source of uniform brightness by a
small foreground point-mass lens is
M=1+(2R_{E}^{2}-R_{L}^{2})/R_{S}^{2}, where R_{S} is the radius of the
source and R_{E} and R_{L} are the Einstein radius and size
of the lens projected into the source plane; this provides
an accurate approximation to the exact magnification for
R_{L},R_{E} << R_{S}. Remarkably, this result is independent of
the shape of the source or position of the lens (except near
the edges). We show that this formula can be generalized to
include limb-darkening of a circular source by simply
inserting the surface-brightness at the position of the
foreground object (divided by the average surface-brightness
of the star). We use this theorem to compute transit
lightcurves in binaries for which the foreground star or
planet has a size and Einstein radius much smaller than the
background star. White dwarf stars in binaries with
semi-major axes of 0.1 AU have a size comparable to their
Einstein radii. Thus, white dwarfs orbiting main-sequence
stars can show either brightening or eclipse. Since white
dwarfs are similar in size to terrestrial planets, we
predict how many white dwarf-main sequence binaries might be
found in transit searches for terrestrial type planets such
as Kepler and Eddington. We estimate that dozens of systems
may be found, although the precise number will depend on the
properties of low-level variability of the main-sequence
stars in these binaries. We also apply these results to
planetary transits (R_{E}~0), demonstrating that this
simple approximation accurately describes the exact
limb-darkened transit lightcurves. Using the HST lightcurve
of HD 209458 from Brown et al. (2001), the ratio of the
planet radius to stellar radius is measured to be
R_{p}/R_{*}=0.1207±0.0003 , marginalized over the
limb-darkening.

If you would like more information about this abstract, please follow the link to http://asc.harvard.edu/fellows/viewgraphs/2002/agol.ps. This link was provided by the author. When you follow it, you will leave the Web site for this meeting; to return, you should use the Back comand on your browser.

The author(s) of this abstract have provided an email address for comments about the abstract: agol@tapir.caltech.edu

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Bulletin of the American Astronomical Society, **34**, #4

© 2002. The American Astronomical Soceity.