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-523.01, P = 49.41 days [Plot avg. error bars = ± 2.87 min.]
TTV_maximum: 742.56 ± 515.32 days;  Amp_ttv_maximum: 9.38 ± 9.90 min.
P_ttv: 1740.14 ± 851.99 days.
Amp_ttv: 23.64 ± 14.00 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1448.44 days; Power: 6.16; FAP: 0.00608.
Linear ephemeris (this work): Tc = [49.41121122 ± 0.00017282](Tc#) + [131.23995347 ± 0.00260709]


Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 10.32 min.]
TTV_minimum: 116.36 ± 9.16 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 195.60 ± 9.33 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 274.85 ± 9.57 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 354.09 ± 9.88 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 433.33 ± 10.26 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 512.58 ± 10.70 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 591.82 ± 11.18 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 671.06 ± 11.72 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 750.30 ± 12.29 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 829.55 ± 12.90 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 908.79 ± 13.53 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 988.03 ± 14.20 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 1067.28 ± 14.88 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 1146.52 ± 15.58 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 1225.76 ± 16.30 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 1305.00 ± 17.04 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
TTV_minimum: 1384.25 ± 17.79 days, Amp_ttv_minimum: -7.64 ± 1.61 min.
TTV_maximum: 1463.49 ± 18.54 days, Amp_ttv_maximum: 7.98 ± 1.61 min.
P_ttv: 158.49 ± 1.75 days.
Amp_ttv: 15.62 ± 2.28 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 158.49 days; Power: 7.76; FAP: 0.000172.


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

21 May 2015

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       Kepler KOI-523 (Kepler-177; KIC-8806123) 3-(or more?)-Planet System

Discussion:
In the example of KOI-523.01 (Kepler-177c), after a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1. below) a periodicity (P_ttv) of 1740.14 ± 851.99 days (1448.44 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 158.49 ± 1.75 days (LSP: 158.49 days).  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 3 planets in near-circular orbits are mutually-interacting to give the TTV distribution observed.