Narrow-Angle Astrometry with the Space Interferometry Mission: The
Search for Extra-Solar Planets. II. Detection and Characterization of
Planetary Systems
(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
α/σd→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 α/σd, 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 α/σd as low as ∼5, while
α/σd≃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
α/σd≃10 or greater, quasi-coplanarity can be reliably
established with uncertainties of a few degrees, for periods in the range
0.1≤T≤15 yr; in systems where at least one component has
α/σd→1, coplanarity measurements are compromised, with typical
uncertainties on the mutual inclinations of order of 30∘−40∘. Our
findings are illustrative of the importance of the contribution SIM will make
to the fields of formation and evolution of planetary systems.Comment: 61 pages, 14 figures, 5 tables, to appear in the September 2003 Issue
of the Publications of the Astronomical Society of the Pacifi