Star confusion effect on SIM PlanetQuest astrometric performance

SIM PlanetQuest will measure star positions to an accuracy of a few microarcseconds using precise white light fringe measurements. One challenge for the SIM observation scenario is "star confusion," where multiple stars are present in the instrument field of view. This is especially relevant for observing dim science targets because the density of number of stars increases rapidly with star magnitude. We study the effect of star confusion on the SIM astrometric performance due to systematic fringe errors caused by the extra photons from the confusion star(s). Since star confusion from multiple stars may be analyzed as a linear superposition of the effect from single star confusion, we quantify the astrometric errors due to single star confusion surveying over many spectral types, including A0V, F0V, K5III, and M0V, and for various visual magnitude differences. To the leading order, the star confusion effect is characterized by the magnitude difference, spectral difference, and the angular separation between the target and confusion stars. Strategies for dealing with star confusion are presented. For example, since the presence of additional sources in the field of view leads to inconsistent delay estimates from different channels, with sufficient signal to noise ratio, the star confusion can be detected using chi-square statistics of fringe measurements from multiple spectral channels. An interesting result is that the star confusion can be detected even though the interferometer cannot resolve the separation between the target and confusion stars when their spectra are sufficiently different. Other strategies for mitigating the star confusion effect are also discussed.