On the Completeness of Reflex Astrometry on Extrasolar Planets near the Sensitivity Limit

We provide a preliminary estimate of the performance of reflex astrometry on Earth-like planets in the habitable zones of nearby stars. In Monte Carlo experiments, we analyze large samples of astrometric data sets with low to moderate signal-to-noise ratios. We use periodograms for discovery and least-squares fits for estimating the Keplerian parameters. We find a completeness for detection in agreement with estimates in the literature. We find mass estimation to be biased, as has been found for radial-velocity data sets, which degrades the completeness of accurate mass estimation. When we compare the true planetary position with the position predicted from the fitted parameters, at future times, we find poor completeness for an accuracy goal of 0.1 times the semimajor axis of the planet, even with no delay following the end of observations. Our findings suggest that the recommendation of the ExoPlanet Task Force (Lunine et al. 2008) for “the capability to measure convincingly wobble semi-amplitudes down to 0.2 μas integrated over the mission lifetime,” may not be adequately satisfied by a space astrometry mission characterized by astrometric accuracy σ = √ 2 μas and noise floor σfloor ≈ 0.035 μas. The most important unsolved, strategic problem in the exoplanetary science program is figuring out how to predict the future position of an Earth-like planet with accuracy sufficient to ensure the success of the science operations of a follow-on spectroscopic mission, which will search for biologically significant molecules in the atmosphere. Subject headings: astrometry, planetary systems