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 (derived using the graphically obtained linear ephemeris).
1st Figure.: KOI-806.03 TTV, P = 29.16 days [Plot avg. error bars = ± 8.91 min. (smaller than symbols)]
TTV_minimum: 359.80 ± 4.08 days, Amp_ttv_minimum: -1214.27 ± 21.64 min.
TTV_maximum: 855.80 ± 5.41 days, Amp_ttv_maximum: 1685.93 ± 21.64 min.
TTV_minimum: 1351.80 ± 7.22 days, Amp_ttv_minimum: -1214.27 ± 21.64 min.
In anticipation of KAFO observations beyond Kepler, transit timing variations (TTVs) were determined for the three confirmed planets of the KOI-806 system using Kepler data from Q1 through the first-third of Q17 (when Kepler lost its required exquisitely-stabilizing third reaction wheel). Several reports have appeared previously (see references below) describing TTVs and derived properties through either Q6 or Q12.
806.03 (Kepler-30b), the innermost planet in this system, shows a TTV periodicity (P_ttv; 1st Figure below) of 992.01 days (errors tabulated below and on the figures) and an enormous overall total amplitude (Amp_ttv) of 2900.20 minutes (or ~ 48.3 hours). This is supported by a strong, highly credible, Lomb-Scargle periodicity (LSP) of 990.49 days. The ratio of periods of the first two planets, 806.03 and 806.02, is just wide of a mean motion resonance (MMR) of 2 (actually, 2.07:1.00). The large amplitude is consistent with the huge difference in the masses of the pair (reported by Haddon & Lithwick): M_806.03_earth: 76.6 and M_806.02_earth: 1562.8. The residuals from the TTV plot showed no clear periodicity although it they do indicate a gradual drift (see 2nd Figure below), potentially resulting from orbital eccentricities and/or precessions.
806.02 (Kepler-30c)'s TTV is extremely well anti-correlated with that of 806.03 (compare 1st and 3rd Figures below), typical of strongly-interacting planets. It's P_ttv is 973.34 days (LSP: 984.25 days) which matches closely with that for 806.03. Its Amp_ttv, again as expected from the relative masses reported for 806.02 and 806.03, is considerably smaller: 65.55 minutes. The residuals from the TTV plot (4th Figure below) also show a clear "secondary P_ttv" of 388.26 days (LSP: 388.06 days) with an Amp_ttv of 8.72 minutes; this is consistent with the interaction of 806.02 with the third planet, 806.01.
806.01 (Kepler-30d) also shows a strong TTV (see 5th Figure) not perfectly anti-correlated (offset for the maxima and minima, ranging from 98-125 days, probably due to relative eccentricities) with the "secondary P_ttv" of 806.02, and with a similar P_ttv of 377.64 days (LSP: 374.89 days); its Amp_ttv is 139.15 minutes. The residuals from 806.01 (see 6th Figure) also describe a clear sinusoidal array, another "secondary P_ttv", that could be arising through the interaction with a fourth, as yet unseen (non-transiting) planet ("806.xx") having a P_ttv of 617.13 days (LSP: 613.44 days) and an Amp_ttv of 45.64 minutes.