Narrow-angle astrometry with the space interferometry mission: The search for extrasolar planets. II. Detection and characterization of planetary systems

We utilize (1) detailed end-to-end numerical simulations of sample narrow-angle astrometric observing campaigns with the Space Interferometry Mission (SIM) and the subsequent data analysis process and (2) the set of extrasolar planetary systems discovered so far by radial velocity surveys as templates to provide meaningful estimates of the limiting capabilities of SIM for the detection and measurement of multiple-planet systems around solar-type stars in the solar neighborhood. We employ standard chi(2) statistics, periodograms, and Fourier analysis to evaluate SIM's ability to detect multiple planetary signatures; the probability of detecting additional companions is essentially unchanged from the single-planet configurations, but after fitting and subtraction of orbits with astrometric signal-to-noise ratio, alpha/sigma(d) --> 1, the false detection rates can be enhanced by up to a factor of 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. We explore the three-dimensional parameter space defined by astrometric signature, orbital period, and eccentricity to derive general conclusions on the capability of SIM to accurately measure the full set of orbital parameters and masses for a variety of configurations of planetary systems; the accuracy of multiple-planet orbit reconstruction and mass determination suffers a typical degradation of 30%-40% from 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 similar to5, while alpha/sigma(d) similar or equal to 100 is required in order to measure with similar accuracy systems harboring objects with periods as long as 3 times the mission duration. We gauge the potential of SIM for meaningful coplanarity measurements via determination of the true geometry of multiple-planet orbits. For systems with all components producing alpha/sigma(d) similar or equal to 10 or greater, quasi-coplanarity can be reliably established with uncertainties of a few degrees, for periods in the range 0.1 yr less than or similar to T less than or equal to 15 yr; in systems where at least one component has alpha/sigma(d) --> 1, coplanarity measurements are compromised, with typical uncertainties on the mutual inclinations on the order of 30degrees-40degrees. We quantify the improvement derived in full-orbit reconstruction and planet mass determination by constraining the multiple-planet orbital fits to SIM observations with the nominal orbital elements obtained from the radial velocity measurements; the uncertainties on orbital elements and masses can be reduced by up to an order of magnitude, especially for long-period orbits in face-on configurations and for low-amplitude orbits seen edge-on. Our findings are illustrative of the importance of the contribution SIM will make, complementing other ongoing and planned spectroscopic, astrometric, and photometric surveys, in order to fulfill the expectations for ground-breaking science in the fields of formation and evolution of planetary systems during the next decade.