Narrow-Angle Astrometry with the Space Interferometry Mission: The Search for Extra-Solar Planets. II. Detection and Characterization of Planetary Systems

Abstract

(Abridged) The probability of detecting additional companions is essentially unchanged with respect to the single-planet configurations, but after fitting and subtraction of orbits with astrometric signal-to-noise ratio $\alpha/\sigma_d\to 1$ the false detection rates can be enhanced by up to a factor 2; the periodogram approach results in robust multiple-planet detection for systems with periods shorter than the SIM mission length, even at low values of $\alpha/\sigma_d$, while the least squares technique combined with Fourier series expansions is arguably preferable in the long-period regime. The accuracy on multiple-planet orbit reconstruction and mass determination suffers a typical degradation of 30-40% with respect to single-planet solutions; mass and orbital inclination can be measured to better than 10% for periods as short as 0.1 yr, and for $\alpha/\sigma_d$ as low as $\sim 5$, while $\alpha/\sigma_d\simeq 100$ is required in order to measure with similar accuracy systems harboring objects with periods as long as three times the mission duration. For systems with all components producing $\alpha/\sigma_d\simeq 10$ or greater, quasi-coplanarity can be reliably established with uncertainties of a few degrees, for periods in the range $0.1\leq T\leq 15$ yr; in systems where at least one component has $\alpha/\sigma_d\to 1$, coplanarity measurements are compromised, with typical uncertainties on the mutual inclinations of order of $30^\circ-40^\circ$. Our findings are illustrative of the importance of the contribution SIM will make to the fields of formation and evolution of planetary systems.