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.

Figure 1.: KOI-108.02, P = 179.61 days [Plot avg. error bars = ± 1.74 min. (smaller than symbols)]
TTV_minimum: 432.83 ± 117.24 days, Amp_ttv_minimum: -22.53 ± 8.27 min.
TTV_maximum: 944.32 ± 164.57 days, Amp_ttv_maximum: 22.33 ± 8.27 min.
TTV_minimum: 1455.82 ± 224.34 days, Amp_ttv_minimum: -22.53 ± 8.27 min.
P_ttv: 1022.99 ± 140.76 days.
Amp_ttv: 44.86 ± 11.69 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 1030.21 days; Power: 2.15; FAP: 0.150.
Linear ephemeris (this work): Tc = [179.60761973 ± 0.00259173](Tc#) + [228.34080328 ± 0.01073822]


Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 8.45 min.]

TTV_maximum: 338.16 ± 25.63 days, Amp_ttv_maximum: 8.39 ± 1.94 min.
TTV_minimum: 546.34 ± 27.29 days, Amp_ttv_minimum: -8.20 ± 1.94 min.
TTV_maximum: 754.53 ± 29.56 days, Amp_ttv_maximum: 8.39 ± 1.94 min.
TTV_minimum: 962.71 ± 32.31 days, Amp_ttv_minimum: -8.20 ± 1.94 min.
TTV_maximum: 1170.90 ± 35.43 days, Amp_ttv_maximum: 8.39 ± 1.94 min.
TTV_minimum: 1379.08 ± 38.84 days, Amp_ttv_minimum: -8.20 ± 1.94 min.
P_ttv: 416.37 ± 9.09 days.
Amp_ttv: 16.59 ± 2.75 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 414.46 days; Power: 2.37; FAP: 0.0240.


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

Last Figure: KOI-108.01, P = 15.97 days [Plot avg. error bars = ± 2.22 min.]
Linear ephemeris (this work): Tc = [15.96532266 ± 0.00001695](Tc#) + [75.17892964 ± 0.00086458]


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

2 Feb 2015
==============================================================================

Exoplanet-Science.com

Scroll Down  to

KOI's (Blue)  or
K2 Objects (Green)
       Kepler KOI-108 (Kepler-103; KIC-4914423) 4-(or more?)-Planet System

Discussion:
KOI-108.02 (Kepler-103c), the farthest-out known transiting planet in this system:
After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 1022.99 ± 140.76 days (1030.21 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 416.37 ± 9.09 days (LSP: 414.46 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 (non-transiting) planets are present in the system.
KOI-108.01 (Kepler-103b) showed no significant TTV at all.