TTVs are derived from Q4-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.
"Figure 4." 6th above: Summed combination of Figures 1., 2., and 3. [Plot error bars = ± 39.79 min.]
References: • Numerous additional pertinent literature and major Tc#, Tc, and TTV tabulations can be found on my "Summary" webpage following the table.
15 Feb 2015
Kepler KOI-2167 (KIC-6041734) 7(?)-(or more?)-Planet System
Discussion: KOI-2167.02, the closest-in known transiting planet in this system. showed no credible TTV.
KOI-2167.01 showed a TTV with a periodicity of 101.66 ± 1.05 days. Since this value is substantially different than the three found (below) for 2167.03, it would appear that 2167.01 is not responsible for any of those.
KOI-2167.03, the furthest-out of the known transiting planets, showed a series of overlaid periodicities. After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 503.25 ± 40.04 days, a plot (Figure 2.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 174.71 ± 3.93 days. Furthermore, a plot (Figure 3.) of the Residuals of the Residuals gave a good sinusoidal curve-fit with a periodicity of 300.76 ± 6.44 days. Lastly, 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.