Direct imaging in the habitable zone and the problem of orbital motion

High contrast imaging searches for exoplanets have been conducted on 2.4-10 m telescopes, typically at H band (1.6 μm) and used exposure times of ∼1 hr to search for planets with semi-major axes of ≳ 10 AU. We are beginning to plan for surveys using extreme-AO systems on the next generation of 30 m class telescopes, where we hope to begin probing the habitable zones (HZs) of nearby stars. Here we highlight a heretofore ignorable problem in direct imaging: planets orbit their stars. Under the parameters of current surveys, orbital motion is negligible over the duration of a typical observation. However, this motion is not negligible when using large diameter telescopes to observe at relatively close stellar distances (1-10 pc), over the long exposure times (10-20 hr) necessary for direct detection of older planets in the HZ. We show that this motion will limit our achievable signal-to-noise ratio and degrade observational completeness. Even on current 8 m class telescopes, orbital motion will need to be accounted for in an attempt to detect HZ planets around the nearest Sun-like stars α Cen A&B, a binary system now known to harbor at least one planet. Here we derive some basic tools for analyzing this problem, and ultimately show that the prospects are good for de-orbiting a series of shorter exposures to correct for orbital motion.