Narrow-angle astrometry with the Space Interferometry Mission:: The search for extrasolar planets.: I.: Detection and characterization of single planets

A decade after the publication of the Hipparcos Catalogue, the Space Interferometry Mission (SIM) will be capable of making selected high-precision astrometric measurements about 3 orders of magnitude more accurate than the Hipparcos survey. We present results from a detailed set of end-to-end numerical simulations of SIM narrow-angle astrometric measurements and data analysis to illustrate the enormous potential that SIM has for the discovery and characterization of planets outside the solar system. Utilizing a template observing scenario, we quantify SIM sensitivity to single planets orbiting single normal nearby stars as a function of measurement errors and properties of the planet: SIM will detect over 95% of the planets with periods between a few days and the 5 yr nominal mission lifetime that produces astrometric signatures similar to2.2 times larger than the single-measurement accuracy. We provide accuracy estimates of full-orbit reconstruction and planet mass determination: at twice the discovery limit, orbital elements will be determined with a typical accuracy of 20%-30%; the astrometric signature must be 10 and 15 times the minimum signal required for detection to derive mass and inclination-angle estimates accurate to 10%. We quantify the impact of different observing strategies on the boundaries for secure detection and accurate orbit estimation: the results scale with the square root of both the number of observations and the number of reference stars. We investigate SIM discovery space, to gauge the instrument ability in detecting very low mass planets: around the nearest stars, SIM will find planets as small as Earth, if they are present. Some of these might be orbiting inside the parent star's habitable zone. Extrasolar planets figure prominently among SIM scientific goals: our results reaffirm the importance of high-precision astrometric measurements as a unique complement to spectroscopic surveys based on radial velocity. For example, establishing the existence of rocky, perhaps habitable planets would constitute both a fundamental test of theoretical models and progress toward the understanding of formation and evolution processes of planetary systems. Such discoveries would also provide the Terrestrial Planet Finder with prime targets to investigate with direct spectroscopy in terms of the potential for life.