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TTVs are derived from Q1-Q15 (for 1102.03) and Q1-Q16 (for 1102.01 and 1102.02) Kepler data.  x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Kepler light flux vs. time data.  y-axes: “(O – C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.  The plots are pictured in the order of orbital periods.

Discussion:
Near-integer Mean Motion Resonances in this system:
P_1102.02/P_1102.04: 2/1.04; P_1102.01/P_1102.02: 3/1.98; P_1102.03/P_1102.01: 3/1.95.

For 1102.04, the closest-in of the planet candidates in this system (P = 4.24 days), the Lomb-Scargle periodogram showed only chance periodicities, i.e.: none due to the physical nature of the system defined by the collected light curve.

For 1102.02, the next closest-in (confirmed: Kepler-24c) exoplanet (P = 8.15 days), the major period indicated by the Lomb-Scargle periodogram of the TTV x-y data appeared at 440.49 days; it was quite strong (Power: 24.88) and the probability that it was due to chance was virtually zero (P-value: 0.00000002299).  Furthermore, correspondence with the sinusoidal-curve-determined P_ttv was excellent: 438.87 days.

For 1102.01, the third closest-in (confirmed: Kepler-24b) exoplanet (P = 12.33 days), the major period from the Lomb-Scargle periodogram of the TTV x-y data appeared at 414.61 days, was strong (Power: 18.51), and not likely due to chance (P-value: 0.000008345).  Again, correspondence with the sinusoidal-curve-determined P_ttv was exceptional: 411.18 days.

Note also from the respective TTV curves (of 1102.01 and 1102.02) the excellent anti-correlated relationship, as expected, between the TTVs for these two adjacent planets.

Lastly, for 1102.03, the furthest-out identified exoplanet candidate (P = 19.00 days) in this system, as in the case of the closest (1102.04), the Lomb-Scargle periodogram showed no non-chance periodicities, i.e.: none due to the physical nature of the system defined by the collected light curve.

1st: KOI-1102.04, P = 4.24 days
Linear ephemeris: Tc = 4.24439052(Tc#) + 70.06831758

2nd: KOI-1102.02, Kepler-24c, P = 8.15 days
TTV_minimum: 84.52 ± 17.97 days, Amp_ttv_minimum: -35.90 ± 5.50 min.
TTV_maximum: 303.95 ± 18.93 days, Amp_ttv_maximum: 41.10 ± 5.50 min.
TTV_minimum: 523.39 ± 20.81 days, Amp_ttv_minimum: -35.90 ± 5.50 min.
TTV_maximum: 742.82 ± 23.41 days, Amp_ttv_maximum: 41.10 ± 5.50 min.
TTV_minimum: 962.25 ± 26.51 days, Amp_ttv_minimum: -35.90 ± 5.50 min.
TTV_maximum: 1181.69 ± 29.95 days, Amp_ttv_maximum: 41.10 ± 5.50 min.
TTV_minimum: 1401.12 ± 33.63 days, Amp_ttv_minimum: -35.90 ± 5.50 min.
P_ttv: 438.87 ± 8.92 days.
Amp_ttv: 77.00 ± 7.78 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 440.49 days; Power: 24.88; P-value: 2.299 x 10^-8.
Linear ephemeris: Tc = 8.14512614(Tc#) + 73.56823957.
Estimated P_ttv = 1/|(nmmri_a/P_a - nmmri_b/P_b)| = 433.73 days

3rd: KOI-1102.01, Kepler-24b, P = 12.33 days
TTV_maximum: 123.69 ± 19.20 days, Amp_ttv_maximum: 36.73 ± 6.28 min.
TTV_minimum: 329.28 ± 20.19 days, Amp_ttv_minimum: -44.00 ± 6.28 min.
TTV_maximum: 534.87 ± 21.96 days, Amp_ttv_maximum: 36.73 ± 6.28 min.
TTV_minimum: 740.46 ± 24.33 days, Amp_ttv_minimum: -44.00 ± 6.28 min.
TTV_maximum: 946.05 ± 27.16 days, Amp_ttv_maximum: 36.73 ± 6.28 min.
TTV_minimum: 1151.64 ± 30.31 days, Amp_ttv_minimum: -44.00 ± 6.28 min.
TTV_maximum: 1357.23 ± 33.69 days, Amp_ttv_maximum: 36.73 ± 6.28 min.
P_ttv: 411.18 ± 8.42 days.
Amp_ttv: 80.73 ± 8.88 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 414.61 days; Power: 18.51; P-value: 8.345 x 10^-6.
Linear ephemeris: Tc = 12.33349722(Tc#) + 70.58944685.

4th: KOI-1102.03, P = 19.00 days
Linear ephemeris: Tc = 18.99891918(Tc#) + 77.71836310.

Literature:
• For Q1-Q6 TTV data of 1102.01 and 1102.02 (thru ~ 563 (BJD-2454900) days), see: Ford2012arXiv-1201.1892.
• P_ttv equation: P_ttv = 1/|(nmmri_a/P_a - nmmri_b/P_b)|…(see Fabrycky, et al., 2012, arXiv-1201.5415)

21 July 2013; updated 9 Aug 2013
KOI-1102 (Kepler-24, KIC-3231341) 4-Planets