Using Host Star Activity to Distinguish Pro & Retrograde Exoplanet Orbits

Time variation of Kepler transits induced by stellar rotating spots - a way to distinguish between prograde and retrograde motion I. Theory

Authors:

Mazeh et al

Abstract:

Some transiting planets discovered by the Kepler mission display transit timing variations (TTVs) induced by stellar spots that rotate on the visible hemisphere of their parent stars. A TTV can be derived when a planet crosses a spot, modifying the shape of the transit light curve. We present an approach that can, in principle, use the derived TTVs of a planet to distinguish between a prograde and a retrograde planetary motion with respect to the stellar rotation. Assuming a single spot darker than the stellar disc, spot crossing by the planet can induce measured positive (negative) TTV, if the crossing occurs in the first (second) half of the transit. On the other hand, the motion of the spot towards (away from) the center of the stellar visible disc causes the stellar brightness to decrease (increase). Therefore, for a planet with prograde motion, the TTV is positive when the local slope of the stellar flux at the time of transit is negative, and vice versa. Using a simplistic model we show that TTVs induced by spot crossing depend linearly on the local photometric slopes at the transit timings for most cases. The coefficient of this dependence is negative (positive) for prograde (retrograde) motion. One can identify the linear dependence even in transiting systems with Kepler long cadence data, where the obtained light curve cannot resolve individual spot-crossing events, provided the systems display transits with high enough signal-to-noise ratio and relatively large spot-induced modulation. This paper presents the concept in details and discusses its applicability to the Kepler light curves. In coming papers we present analyses of all KOIs and Kepler eclipsing binaries, following the formalism developed here.