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

Abstract

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 treat the idealized case of a single planet orbiting a single star, and assume there are no non-Keplerian complications or uncertainties. The real case can only be more difficult. We use periodograms for discovery and least-squares fits for estimating the Keplerian parameters. We find a completeness for detection compatible with estimates in the literature. We find mass estimation by least squares to be biased, as has been found for noisy radial-velocity data sets; this bias degrades the completeness of accurate mass estimation. When we compare the true planetary position with the position predicted from the fitted orbital parameters, at future times, we find low completeness for an accuracy goal of 0.3 times the semimajor axis of the planet, even with no delay following the end of astrometric 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 $μ$as integrated over the mission lifetime," may not be satisfied by an instrument characterized by the noise floor of the Space Interferometry Mission, $σ_\mathrm{floor}\approx0.035μ$as. An important, unsolved, strategic challenge for the exoplanetary science program is figuring out how to predict the future position of an Earth-like planet with accuracy sufficient to ensure the efficiency and success of the science operations for follow-on spectroscopy, which would search for biologically significant molecules in the atmosphere.