TTVs are derived from Q1-Q17 Kepler data. x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Normalized PDCSAP_FLUX Kepler light flux vs. time (BJD_tdb - 2454900) data. y-axes: “(O – C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.
Kepler KOI-935 (Kepler-31; KIC-9347899) 4-(or more?)-Planet System
Discussion: KOI-935.01 (Kepler-31b): A sinusoidal curve-fit of the [(O-C) vs. Time] data showed (Figure 1.) a periodicity (P_ttv) of 951.65 ± 17.86 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 944.31 days. KOI-935.02 (Kepler-31c): A sinusoidal curve-fit of the [(O-C) vs. Time] data showed (Figure 2.) a periodicity (P_ttv) of 1106.30 ± 68.87 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 1126.55 days. The TTVs for the above two planets are fairly well anti-correlated suggesting they are the primary cause of each others TTVs; their periods are also in the near MMR ratio of 2.044. Further, since their Amp_ttv’s (see below) and their NEA-reported radii (935.01: Rp/R_Earth = 5.28; 935.02: Rp/R_Earth = 4.99) are very similar, their densities must also be very similar. That they are not precisely anti-correlated and that more scatter was found for 935.02 suggests that the latter may also be undergoing a significant interaction with 935.03; the period ratio for 932.03 vs. 935.02 is also a near MMR value: 2.056. KOI-935.03 (Kepler-31d) & KOI-935.04: No (or a very low) TTVs were observed.