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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.

Figure 1.: KOI-6518.01, P = 18.61 days [Plot avg. error bars = ± 0.068 min. (smaller than symbols)]
TTV_maximum: 105.16 ± 1.13 days, Amp_ttv_maximum: 1.75 ± 0.07 min.
TTV_minimum: 164.15 ± 1.15 days, Amp_ttv_minimum: -1.90 ± 0.07 min.
TTV_maximum: 223.15 ± 1.16 days, Amp_ttv_maximum: 1.75 ± 0.07 min.
TTV_minimum: 282.14 ± 1.18 days, Amp_ttv_minimum: -1.90 ± 0.07 min.
—(16 additional intervening maxima & minima)—
TTV_maximum: 1285.06 ± 1.98 days, Amp_ttv_maximum: 1.75 ± 0.07 min.
TTV_minimum: 1344.05 ± 2.04 days, Amp_ttv_minimum: -1.90 ± 0.07 min.
TTV_maximum: 1403.05 ± 2.10 days, Amp_ttv_maximum: 1.75 ± 0.07 min.
TTV_minimum: 1462.04 ± 2.17 days, Amp_ttv_minimum: -1.90 ± 0.07 min.
P_ttv: 117.99 ± 0.15 days.
Amp_ttv: 3.65 ± 0.09 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 117.85 days; Power: 32.90; FAP: 3.705 x 10^-12.
Linear ephemeris (this work): Tc = [18.61195689 ± 0.00000480](Tc#) + [66.86701692 ± 0.00021313]


Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 0.095 min.]

TTV_maximum: 103.14 ± 3.24 days, Amp_ttv_maximum: 0.33 ± 0.05 min.
TTV_minimum: 142.62 ± 3.26 days, Amp_ttv_minimum: -0.29 ± 0.05 min.
TTV_maximum: 182.11 ± 3.29 days, Amp_ttv_maximum: 0.33 ± 0.05 min.
TTV_minimum: 221.59 ± 3.32 days, Amp_ttv_minimum: -0.29 ± 0.05 min.
—(28 additional intervening maxima & minima)—
TTV_maximum: 1366.65 ± 5.95 days, Amp_ttv_maximum: 0.33 ± 0.05 min.
TTV_minimum: 1406.14 ± 6.07 days, Amp_ttv_minimum: -0.29 ± 0.05 min.
TTV_maximum: 1445.62 ± 6.20 days, Amp_ttv_maximum: 0.33 ± 0.05 min.
TTV_minimum: 1485.11 ± 6.32 days, Amp_ttv_minimum: -0.29 ± 0.05 min.
P_ttv: 78.97 ± 0.29 days.
Amp_ttv: 0.62 ± 0.07 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 79.02 days; Power: 17.04; FAP: 2.836 x 10^-5;
(Also predicting Fig. 3.: candidate P_ttv:239.98 days; Power: 11.86; FAP: 5.017 x 10^-3.)


Figure 3.: Residuals of Figure 2.; Residuals-of-the-Residuals of Figure 1. [Plot avg. error bars = ± 0.106 min.]

TTV_maximum: 172.22 ± 6.57 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 291.44 ± 6.79 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
TTV_maximum: 410.66 ± 7.13 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 529.89 ± 7.55 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
TTV_maximum: 649.11 ± 8.05 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 768.33 ± 8.61 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
TTV_maximum: 887.55 ± 9.22 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 1006.77 ± 9.88 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
TTV_maximum: 1125.99 ± 10.57 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 1245.21 ± 11.28 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
TTV_maximum: 1364.43 ± 12.02 days, Amp_ttv_maximum: 0.27 ± 0.03 min.
TTV_minimum: 1483.65 ± 12.78 days, Amp_ttv_minimum: -0.26 ± 0.03 min.
P_ttv: 238.44 ± 1.77 days.
Amp_ttv: 0.53 ± 0.04 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 237.87 days; Power: 23.76; FAP: 3.405 x 10^-8.


Figure 4.: Added combination of Figures 1., 2., and 3. [Plot error bars = ± 0.16 min.]


The following periodicities were also noted from Lomb-Scargle periodograms:
[Transit Time vs. T{FWHM}]: P_fwhm: 126.08 days; Power: 9.49; FAP: 0.0521.
[Transit Time vs. T{tau}]:  P_tau:  126.08 days; Power: 9.49; FAP: 0.0521.
[Transit Time vs. T{1,4}]:  P_dur:  126.08 days; Power: 9.50; FAP: 0.0518.


Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.

1 May 2015
                Kepler KOI-6518 (KIC-5095269) 4-(or more?)-Planet System

Discussion:
In the example of KOI-6518.01, after a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1. below) a periodicity (P_ttv) of 117.99 ± 0.15 days (117.85 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 78.97 ± 0.29 days (LSP: 79.02 days).  Similarly, the Residuals-of-the-Residuals also gave an excellent sinusoidal curve-fit (Figure 3.) with a periodicity of 238.44 ± 1.77 days (LSP: 237.87 days).  The added combination of all three sinusoidal curves, arrayed in Figure 4., produces a complex overall curvature reasonably consistent with the initial data.  While it is certainly possible (see recent work of Lithwick and others) that some of this unusual curvature obtains from eccentric orbits (and maybe even precessing eccentric orbits) of planetary objects in this system, it is also possible that at least 4 planets (with only KOI-6518.01 transiting) in near-circular orbits are mutually-interacting to give the TTV distribution observed.
KOI-6518.01 appears to be a grazing planet since the ratio of T{FWHM}:tau for every transit is 1.0000 (characteristic of an isosceles triangle).  Furthermore, the relatively small amplitudes of the TTVs (see below) could be consistent with the very large (5.573 Rp/R_jupiter) size & mass of this planet (assuming other similarly large ones are not those involved in the TTV-producing gravitational interactions).
Lastly, periodicity was also noted for T_{FWHM}, T_{tau}, and T_{1,4} (duration) of ~ 126 days, i.e., fairly close to the primary TTV of ~ 118 days.