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Data are from Q1-Q16.  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).1581.02 was run in triplicate using the Online version of EXOFAST and three different data ranges for each transit; 1581.01 was run using the Offline version.

Discussion:
While the TTVs of 1581.01 and 1581.02 are substantial (± ~ 51 and  ± ~ 84 minutes, respectively), they are completely uncorrelated in terms of their positions of maxima/minima and their P_ttv values.  This may be consistent with at least two additional unseen (non-transiting) planets in this system, one that strongly interacts with 1581.01 and another that similarly and independently affects 1581.02.

1st: KOI-1581.01, P = 29.54 days
Average sigma_Tc: 11.69 min.
TTV_maximum:  338.85 ± 95.48 days, Amp_ttv_maximum:  41.10 ± 18.15 min.
TTV_minimum:   806.87 ± 121.07 days, Amp_ttv_minimum:  -61.11 ± 18.15 min.
TTV_maximum:  1274.89 ± 157.26 days, Amp_ttv_maximum:  41.10 ± 18.15 min.
P_ttv: 936.04 ± 95.17 days.
Amp_ttv: 102.21 ± 25.67 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 930.65 days; Power: 4.62; P-value: 0.173.
Linear ephemeris: Tc = 29.54172918(Tc#) + 70.58448128 [this work].

2nd: KOI-1581.02, P = 144.56 days
Average sigma_Tc: 15.98 min.
TTV_minimum:   346.12 ± 37.29 days, Amp_ttv_minimum:  -80.82 ± 20.20 min.
TTV_maximum:  615.03 ± 42.79 days, Amp_ttv_maximum:  88.56 ± 20.20 min.
TTV_minimum:   883.93 ± 50.18 days, Amp_ttv_minimum:  -80.82 ± 20.20 min.
TTV_maximum:  1152.84 ± 58.75 days, Amp_ttv_maximum:  88.56 ± 20.20 min.
P_ttv: 537.81 ± 22.20 days.
Amp_ttv: 169.38 ± 28.57 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 538.81 days; Power: 3.35; P-value: 0.0168.
Linear ephemeris: Tc = 144.55318805(Tc#) + 198.91303291 [this work].

21 May 2013; updated 29 May 2013; updated 9 Aug 2013
Kepler KOI-1581 (KIC-7939330) 2-(or more?)-Planet System

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