TTVs are derived from short-cadence data from Kepler Q3-Q17. 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.
Figure 4.: Summed combination of Figures 1., 2., and 3. [Plot error bars = ± 3.85 min.]
Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.
31 Jan 2015
Kepler KOI-70 (Kepler-20, KIC-6850504); 7- or 8-(?)-Planet System Discussion:
KOI-70.03, the farthest-out known transiting planet in this system: After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 434.13 ± 21.26 days (436.50 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data), a plot (Figure 2.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 171.30 ± 2.42 days (LSP: 170.24 days). Similarly, a plot (Figure 3.) of the Residuals of the Residuals gave a good sinusoidal curve-fit with a periodicity of 778.18 ± 83.91 days (LSP: 777.64 days). The added combination of these three sinusoidal curves is arrayed in Figure 4. and reasonably reproduces a complex overall curvature consistent with the initial data. While the sinusoidal behaviors observed could be partially due to orbital eccentricities, it is also possible that 3 additional as yet unseen (perhaps non-transiting) planets are present in the system. No significant TTVs were noted for the other four known, closer-in planets in this system (see the 4 smaller plots following those for KOI-70.03).