TTVs are derived from Q1-Q16 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:
P_520.03/P_520.01 = 2.018 ratio, near MMR of 2/1.The gravitational interaction between KOI-520.01 and 520.03 (and simultaneous support for their presence in the same star system) is evidenced by the excellent anti-correlation observed (above) for their sinusoidal TTV curves.  In addition, reasonable agreement is found for their P_ttv's from their sinusoidal curves, their Lomb-Scargle periodograms, and from the estimate obtained with the Fabrycky equation (ref. below).

1st Plot: KOI-520.02, P = 5.43 days [Plot error bars = ± 8.77 min.]
Linear ephemeris (this work): Tc = 5.43310770(Tc#) + 71.36904024

2nd Plot: KOI-520.01, P = 12.76 days [Plot error bars = ± 5.12 min.]
TTV_minimum: 17.46 ± 98.28 days, Amp_ttv_minimum: -24.05 ± 4.16 min. (from curve, slightly outside data points).
TTV_maximum: 767.62 ± 137.91 days, Amp_ttv_maximum: 20.90 ± 4.16 min. (from curve).
TTV_minimum: 1517.77 ± 215.09 days, Amp_ttv_minimum: -24.05 ± 4.16 min. (from curve, slightly outside data points).
P_ttv: 1500.31 ± 189.14 days.
Amp_ttv: 44.95 ± 5.88 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1455.60 days; Power: 28.89; P-value: 2.68 x 10^-10.
Calc. P_ttv (given near MMR of 2/1; ref. below): 1406.26 days
Linear ephemeris (this work): Tc = 12.75936198(Tc#) + 103.32146045

3rd Plot: KOI-520.03, P = 25.75 days [Plot error bars = ± 6.62 min.]
TTV_maximum: -8.34 ± 241.00 days, Amp_ttv_maximum: 18.71 ± 8.61 min. (from curve, slightly outside data points).
TTV_minimum: 732.79 ± 338.98 days, Amp_ttv_minimum: -18.38 ± 8.61 min. (from curve).
TTV_maximum: 1473.93 ± 536.66 days, Amp_ttv_maximum: 18.71 ± 8.61 min. (from curve).
P_ttv: 1482.27 ± 482.22 days.
Amp_ttv: 37.10 ± 12.18 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1472.10 days; Power: 6.51; P-value: 0.0190.
Linear ephemeris (this work): Tc = 25.75238167(Tc#) + 69.44332084

References:
• Fabrycky et al., arXiv-1201.5415; P_ttv = 1/|(nMMRi_a/P_a - nMMRi_b/P_b)|.
• For Q0-Q6 TTV data of 520.01 and 520.03 (thru ~ 563 (BJD-2454900) days), see: Ford et al., 2012, arXiv-1201.1892.
• For Q0-12 TTV data of 520.01, 520.02, and 520.03 (thru ~ 1116 (BJD-2454900) days), see: Mazeh et al., 2013, arXiv-1301.5499.
• For Q0-12 Calc. properties from TTVs of 520.01 and 520.03, see: Hadden & Lithwick, 2013, arXiv-1310.7942.

7 Nov 2013
KOI-520 (Kepler-176, KIC-8037145) 3-(or more?)-Planets

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