Simulation and analysis of sub-μas precision astrometric data for planet-finding

Abstract

We present a vector formulation of an interferometric observation of a star, including the effects of the barycentric motion of the observatory, the proper motions of the star, and the reflex motions of the star due to orbiting planets. We use this model to empirically determine the magnitude and form of the signal due to a single Earth-mass planet orbiting about a sun-mass star. Using bounding values for the known components of the model, we perform a series of expansions, comparing the residuals to this signal. We demonstrate why commonly used first order linearizations of similar measurement models are insufficient for signals of the magnitude of the one due to an Earth-mass planet, and present a consistent expansion which is linear in the unknown quantities, with residuals multiple orders of magnitude below the Earth-mass planet signal. We also discuss numerical issues that can arise when simulating or analyzing these measurements.

23 pages, 2 tables, 8 figures

References in corpus (5)

• Double-blind test program for astrometric planet detection with Gaia
• Astrometric Detection of Terrestrial Planets in the Habitable Zones of Nearby Stars with SIM PlanetQuest
• Narrow-Angle Astrometry with the Space Interferometry Mission: The Search for Extra-solar Planets. I. Detection and Characterization of Single Planets
• Narrow-Angle Astrometry with the Space Interferometry Mission: The Search for Extra-Solar Planets. II. Detection and Characterization of Planetary Systems
• On the Completeness of Reflex Astrometry on Extrasolar Planets near the Sensitivity Limit