Center of Light Curves for Whitney Fold and Cusp

The generic, qualitative, local behavior of center-of-light curves near folds and cusps are studied. The results apply to any finite number of lens planes.Comment: 2 pages, 1 figure, to appear in the ``Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity,'' eds. V. Gurzadyan, R. Jantzen, & R. Ruffini, World Scientific (Singapore

Observational Constraints on Trojans of Transiting Extrasolar Planets

Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We present a novel method of detecting Trojan companions to transiting extrasolar planets which involves comparing the time of central eclipse with the time of the stellar reflex velocity null. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. This method rules out Trojan companions to HD 209458b and HD 149026b more massive than ~13 Earth masses and \~25 Earth masses at a 99.9% confidence level. Such a Trojan would be dynamically stable, would not yet have been detected by photometric or spectroscopic monitoring, and would be unrecognizable from radial velocity observations alone. We outline the future prospects for this method, and show that the detection of a "Hot Trojan" of any mass would place a significant constraint on theories of orbital migration.Comment: 6 pages, 2 figures, 1 table, accepted to ApJL. Added references, new transiting planets to table; minor correction

The Invisible Majority? Evolution and Detection of Outer Planetary Systems without Gas Giants

We present 230 realizations of a numerical model of planet formation in systems without gas giants. These represent a scenario in which protoplanets grow in a region of a circumstellar disk where water ice condenses (the "ice line''), but fail to accrete massive gas envelopes before the gaseous disk is dispersed. Each simulation consists of a small number of gravitationally interacting oligarchs and a much larger number of small bodies that represent the natal disk of planetesimals. We investigate systems with varying initial number of oligarchs, oligarch spacing, location of the ice line, total mass in the ice line, and oligarch mean density. Systems become chaotic in ~1 Myr but settle into stable configurations in 10-100 Myr. We find: (1) runs consistently produce a 5-9 Earth mass planet at a semimajor axis of 0.25-0.6 times the position of the ice line, (2) the distribution of planets' orbital eccentricities is distinct from, and skewed toward lower values than the observed distribution of (giant) exoplanet orbits, (3) inner systems of two dominant planets (e.g., Earth and Venus) are not stable or do not form because of the gravitational influence of the innermost icy planet. The planets predicted by our model are unlikely to be detected by current Doppler observations. Microlensing is currently sensitive to the most massive planets found in our simulations. A scenario where up to 60% of stars host systems such as those we simulate is consistent with all the available data. We predict that, if this scenario holds, the NASA Kepler spacecraft will detect about 120 planets by two or more transits over the course of its 3.5 yr mission. Future microlensing surveys will detect ~130 analogs over a 5 yr survey. Finally, the Space Interferometry Mission (SIM-Lite) should be capable of detecting 96% of the innermost icy planets over the course of a 5 yr mission.Comment: 17 pages, 16 figure