A Spectral Approach to Transit Timing Variations

The high planetary multiplicity revealed by Kepler implies that transit timing variations (TTVs) are intrinsically common. The usual procedure for detecting these TTVs is biased to long-period, deep transit planets, whereas most transiting planets have short periods and shallow transits. Here we introduce the Spectral Approach technique to TTVs that allows expanding the TTV catalog toward lower TTV amplitude, shorter orbital period, and shallower transit depth. In the spectral approach, we assume that a sinusoidal TTV exists in the data and then calculate the improvement to χ ² that this model allows over that of the linear-ephemeris model. This enables detection of TTVs even in cases where the transits are too shallow, so that individual transits cannot be timed. The spectral approach is more sensitive because it has fewer free parameters in its model. Using the spectral approach, we (a) detect 129 new periodic TTVs in Kepler data (an increase of ∼2/3 over a previous TTV catalog); (b) constrain the TTV periods of 34 long-period TTVs and reduce amplitude errors of known TTVs; and (c) identify cases of multi-periodic TTVs, for which absolute planetary mass determination may be possible. We further extend our analysis by using perturbation theory assuming a small TTV amplitude at the detection stage, which greatly speeds up our detection (to a level of few seconds per star). Our extended TTV sample shows no deficit of short-period or low-amplitude transits, in contrast to previous surveys, in which the detection schemes were significantly biased against such systems.