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

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

Distinguishing Between Binary-Source and Planetary Microlensing Perturbations

A planetary microlensing event is characterized by a short-lived perturbation to the standard microlensing curve. Planetary perturbations typically last from a few hours to a day, have maximum amplitudes, δ_max, of ±5%-20% of the standard curve, and come in two classes: major and minor image perturbations. There exist a subset of binary-source events that can reproduce the main features of major image perturbations, which are likely to represent more than half of all planetary events, and thus masquerade as planetary events. These events require a binary source with a small flux ratio, epsilon ~ 10^-2 to 10^-4, and a small impact parameter for the fainter source, β_2 <~ ε/δmax. The detection probability of events of this type is ~β_2, and can be as high as ~30%; this is comparable to planetary detection rates. Thus a sample of planetary-like perturbations could be seriously contaminated by binary-source events, and there exists the possibility that completely meaningless physical parameters would be derived for any given major image perturbation. Here I derive analytic expressions for a binary-source event in the extreme flux-ratio limit and use these to demonstrate the basic degeneracy between binary-source and planet perturbations. I describe how the degeneracy can be broken by dense and accurate sampling of the perturbation, optical/infrared photometry, or spectroscopic measurements