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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-2038.01, P = 8.31 days [Plot avg. error bars = ± 8.63 min.]
TTV_minimum: 238.90 ± 66.38 days, Amp_ttv_minimum: -20.56 ± 6.05 min.
TTV_maximum: 737.47 ± 82.41 days, Amp_ttv_maximum: 31.02 ± 6.05 min.
TTV_minimum: 1236.04 ± 107.76 days, Amp_ttv_minimum: -20.56 ± 6.05 min.
P_ttv: 997.15 ± 69.80 days.
Amp_ttv: 51.58 ± 8.55 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1023.78 days; Power: 10.68; FAP: 0.0287.
Linear ephemeris (this work): Tc = [8.30551162 ± 0.00005037](Tc#) + [72.73585034 ± 0.00504183]


Figure 2.: KOI-2038.02, P = 12.51 days [Plot avg. error bars = ± 8.55 min.]
TTV_maximum: 336.28 ± 34.83 days, Amp_ttv_maximum: 47.18 ± 7.50 min.
TTV_minimum: 803.25 ± 44.70 days, Amp_ttv_minimum: -63.61 ± 7.50 min.
TTV_maximum: 1270.21 ± 58.55 days, Amp_ttv_maximum: 47.18 ± 7.50 min.
P_ttv: 933.92 ± 35.88 days.
Amp_ttv: 110.79 ± 10.61 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 912.76 days; Power: 21.02; FAP: 6.770 x 10^-7.
Linear ephemeris (this work): Tc = [12.51347851 ± 0.00012555](Tc#) + [72.41733405 ± 0.00807616]


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

31 May 2015
                 Kepler KOI-2038 (Kepler-85, KIC-8950568) 4-Planet System

Discussion:
KOI-2038.01 (Kepler-85b) showed a sinusoidal curve-fit of the [(O-C) vs. Time] data (Figure 1.) with a periodicity (P_ttv) of 997.15 ± 69.80 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a medium-credibility periodicity of 1023.78 days.

KOI-2038.02 (Kepler-85c) showed a sinusoidal curve-fit of the [(O-C) vs. Time] data (Figure 2.) with a periodicity (P_ttv) of 933.92 ± 35.88 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 912.76 days.

Importantly, the above two sinusoidal arrays were reasonably well anti-correlated, implying that they were mutually responsible for each other’s observed TTV.  The periods for these two planets were in the ratio of 1.505, i.e., in a 3/2 mean motion resonance.

Neither of the other two planets in this system, KOI-2038.03 and KOI-2038.04, showed any significant TTVs.