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TTVs are derived from Q0-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.

1st Figure above: KOI-518.01, Kepler-174b, P = 13.98 days [Plot avg. error bars = ± 3.44 min.]
Linear ephemeris (this work): Tc = [13.98177794 ± 0.00001373](Tc#) + [114.97594955 ± 0.00080017]

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"Figure 1": KOI-518.02, Kepler-174c, P = 44.00 days [Plot avg. error bars = ± 6.14 min.]
TTV_minimum: 189.39 ± 10.08 days, Amp_ttv_minimum: -7.04 ± 2.09 min.
TTV_maximum: 244.08 ± 10.22 days, Amp_ttv_maximum: 7.81 ± 2.09 min.
TTV_minimum: 298.77 ± 10.40 days, Amp_ttv_minimum: -7.04 ± 2.09 min.
TTV_maximum: 353.46 ± 10.60 days, Amp_ttv_maximum: 7.81 ± 2.09 min.
---(17 intervening minima + maxima)---
TTV_maximum: 1337.90 ± 17.66 days, Amp_ttv_maximum: 7.81 ± 2.09 min.
TTV_minimum: 1392.59 ± 18.16 days, Amp_ttv_minimum: -7.04 ± 2.09 min.
TTV_maximum: 1447.29 ± 18.66 days, Amp_ttv_maximum: 7.81 ± 2.09 min.
TTV_minimum: 1501.98 ± 19.18 days, Amp_ttv_minimum: -7.04 ± 2.09 min.
P_ttv: 109.38 ± 1.20 days.
Amp_ttv: 14.85 ± 2.96 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 109.25 days; Power: 6.01; FAP: 0.0113.
Linear ephemeris (this work): Tc = [44.00044151 ± 0.00011872](Tc#) + [143.76213775 ± 0.00208385]


"Figure 2": Residuals of Figure 1 [Plot avg. error bars = ± 6.49 min.]
TTV_minimum: 274.28 ± 29.97 days, Amp_ttv_minimum: -5.79 ± 1.55 min.
TTV_maximum: 476.94 ± 32.74 days, Amp_ttv_maximum: 6.18 ± 1.55 min.
TTV_minimum: 679.59 ± 36.60 days, Amp_ttv_minimum: -5.79 ± 1.55 min.
TTV_maximum: 882.25 ± 41.25 days, Amp_ttv_maximum: 6.18 ± 1.55 min.
TTV_minimum: 1084.90 ± 46.45 days, Amp_ttv_minimum: -5.79 ± 1.55 min.
TTV_maximum: 1287.56 ± 52.03 days, Amp_ttv_maximum: 6.18 ± 1.55 min.
TTV_minimum: 1490.21 ± 57.88 days, Amp_ttv_minimum: -5.79 ± 1.55 min.
P_ttv: 405.31 ± 13.70 days.
Amp_ttv: 11.98 ± 2.19 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 402.29 days; Power: 6.49; FAP: 0.00470.


"Figure 3".: Summed combination of Figures 1., 2., and 3. [Plot error bars = ± 8.93 min.]

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5th Figure above: KOI-518.03, Kepler-174d, P = 247.35 days [Plot avg. error bars = ± 4.30 min.]
TTV_maximum: 463.22 ± 30.24 days, Amp_ttv_maximum: 7.02 ± 1.33 min.
TTV_minimum: 820.14 ± 36.65 days, Amp_ttv_minimum: -9.75 ± 1.33 min.
TTV_maximum: 1177.06 ± 44.84 days, Amp_ttv_maximum: 7.02 ± 1.33 min.
P_ttv: 713.84 ± 21.84 days.
Amp_ttv: 16.77 ± 1.88 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 702.63 days; Power: 1.85; FAP: 0.0764.
Linear ephemeris (this work): Tc = [247.35397900 ± 0.00145253](Tc#) + [297.16510980 ± 0.00355795]


References:
• Numerous additional pertinent literature and major Tc#, Tc, and TTV tabulations can be found on my "Summary" webpage following the table.

14 Feb 2015

     Kepler KOI-518 (Kepler-174; KIC-8017703) 6(?)-(or more?)-Planet System

Discussion:
KOI-518.01, Kepler-174b, the closest-in of the known transiting planets, showed no credible TTVs.

KOI-518.02, Kepler-174c, the middle one of the known transiting planets, showed at least a primary and a secondary one.  After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 109.38 ± 1.20 days, a plot (Figure 2.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 405.31 ± 13.70 days.  The added combination of these two sinusoidal curves is arrayed in Figure 3. 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 2 additional as yet unseen (probably non-transiting) planets are strongly interacting with 518.02.

KOI-518.03, Kepler-174d, the farthest out known transiting planet, also showed a pronounced periodicity that might be in response to a planet that was also affecting 518.02 or, possibly, due to yet another, still further out, unseen planet: P_ttv: 713.84 ± 21.84 days.