  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. An induced TTV can be observed when a planet
crosses a spot and modifies the shape of the transit light curve, even if the
time resolution of the data does not allow to detect the crossing event itself.
We present an approach that can, in some cases, 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 induced TTV is positive when the local
slope of the stellar flux at the time of transit is negative, and vice versa.
Thus, we can expect to observe a negative (positive) correlation between the
TTVs and the photometric slopes for prograde (retrograde) motion. Using a
simplistic analytical approximation, and also the publicly available SOAP-T
tool to produce light curves of transits with spot-crossing events, we show for
some cases how the induced TTVs depend on the local stellar photometric slopes
at the transit timings. Detecting this correlation in Kepler transiting systems
with high enough signal-to-noise ratio can allow us to distinguish between
prograde and retrograde planetary motions. In coming papers we present analyses
of the KOIs and Kepler eclipsing binaries, following the formalism developed
here.
