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Starspot Jitter in Photometry, Astrometry and Radial Velocity Measurements

Analytical relations are derived for the amplitude of astrometric, photometric and radial velocity perturbations caused by a single rotating spot. The relative power of the star spot jitter is estimated and compared with the available data for $κ^1$ Ceti and HD 166435, as well as with numerical simulations for $κ^1$ Ceti and the Sun. A Sun-like star inclined at $i=90\degr$ at 10 pc is predicted to have a RMS jitter of 0.087 \uas in its astrometric position along the equator, and 0.38 m s$^{-1}$ in radial velocities. If the presence of spots due to stellar activity is the ultimate limiting factor for planet detection, the sensitivity of SIM Lite to Earth-like planets in habitable zones is about an order of magnitude higher that the sensitivity of prospective ultra-precise radial velocity observations of nearby stars.