Data are from Q1-Q15 (for 509.01 and 509.02) or Q1-Q16 (for 509.03).  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 (smallest first).

Discussion:
The TTV of KOI-509.03 (Amp_ttv: ± ~ 78.7 minutes) suggests the presence of another unseen (non-transiting) planet in the system.

1st: KOI-509.01, P = 4.17 days [Plot error bars (smaller than symbol) = ± 5.48 min.]
Linear ephemeris (this work, Q1-Q15): Tc = 4.16696610(Tc#) + 102.71494047.

2nd: KOI-509.02, P = 11.46 days [Plot error bars (smaller than symbol) = ± 5.61 min.]
Linear ephemeris (this work, Q1-Q15): Tc = 11.46347375(Tc#) + 70.38683379

3rd: KOI-509.03, P = 39.60 days [Plot error bars (smaller than symbol) = ± 8.30 min.]
TTV_maximum:  175.14 ± 68.64 days, Amp_ttv_maximum:   70.00 ± 17.75 min.
TTV_minimum:   677.71 ± 85.96 days, Amp_ttv_minimum: -87.49 ± 17.75 min.
TTV_maximum:  1180.28 ± 114.99 days, Amp_ttv_maximum:   70.00 ± 17.75 min.
P_ttv: 1005.14 ± 79.44 days.
Amp_ttv: 157.49 ± 25.10 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1042.75 days; Power: 7.06; P-value: 0.00120.
Linear ephemeris (this work, Q1-Q16): Tc = 39.59881111(Tc#) + 101.11848661

References:
• For Q1-Q6 TTV data of 509.01 and 509.02 (thru ~ 563 (BJD-2454900) days), see: Ford2012arXiv-1201.1892.

20 July 2013; updated 9 Aug 2013
KOI-509 (Kepler-171, KIC-6381846) 3-(or more?)-Planets

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