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.
Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.
31 May 2015
Kepler KOI-2038 (Kepler-85, KIC-8950568) 4-Planet System
Discussion: KOI-2038.01 (Kepler-85b) showed a sinusoidal curve-fit of the [(O-C) vs. Time] data (Figure 1.) with a periodicity (P_ttv) of 997.15 ± 69.80 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a medium-credibility periodicity of 1023.78 days.
KOI-2038.02 (Kepler-85c) showed a sinusoidal curve-fit of the [(O-C) vs. Time] data (Figure 2.) with a periodicity (P_ttv) of 933.92 ± 35.88 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 912.76 days.
Importantly, the above two sinusoidal arrays were reasonably well anti-correlated, implying that they were mutually responsible for each other’s observed TTV. The periods for these two planets were in the ratio of 1.505, i.e., in a 3/2 mean motion resonance.
Neither of the other two planets in this system, KOI-2038.03 and KOI-2038.04, showed any significant TTVs.