Extrasolar Trojans: The Viability and Detectability of Planets in the 1:1 Resonance

Abstract

We explore the possibility that extrasolar planets might be found in the 1:1 mean-motion resonance. There are a variety of stable co-orbtial configurations, and we specifically examine three different versions of the 1:1 resonance. These include tadpole and horseshoe type orbits, as well as a more exotic configuration which occurs when one planet has a highly eccentric orbit while the other planet moves on a nearly circular orbit. We show that pairs of planets in 1:1 resonance yield characteristic radial velocity signatures which are not prone to the sin(i) degeneracy. Indeed, Keplerian fits to the radial velocities cannot reveal the presence of two planets in the 1:1 resonance. We discuss a dynamical fitting method for such systems, and illustrate its use with a simulated data set. Finally, we argue that hydrodynamical simulations and torqued three-body calculations indicate that 1:1 resonant pairs might readily form and migrate within protostellar disks.