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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:
At present, KOI-880.01 (Kepler-82b) and KOI-880.02 (Kepler-82c) and confirmed exoplanets while KOI-880.03 and KOI-880.04 are candidates.  The periods of the first two are in a MMR ratio of 2.000/1.026 but their TTV plots are not well anti-correlated and show somewhat different P_ttv values, suggesting that various degrees of orbital eccentricity exist for these two exoplanets.

1st Plot: KOI-880.04, P = 2.38 days [Plot error bars = ± 8.73 min.]
Linear ephemeris (this work): Tc = 2.38295404(Tc#) + 68.07986221

2nd Plot: KOI-880.03, P = 5.90 days [Plot error bars = ± 7.15 min.]
Linear ephemeris (this work): Tc = 5.90225894(Tc#) + 69.78364689

3rd Plot: KOI-880.01, P = 26.44 days [Plot error bars = ± 4.31 min.]
TTV_maximum: 99.63 ± 40.16 days, Amp_ttv_maximum: 19.80 ± 3.00 min.
TTV_minimum: 591.04 ± 47.19 days, Amp_ttv_minimum: -21.52 ± 3.00 min.
TTV_maximum: 1082.45 ± 60.95 days, Amp_ttv_maximum: 19.80 ± 3.00 min.
P_ttv: 982.83 ± 41.81 days.
Amp_ttv: 41.32 ± 4.24 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 977.52 days; Power: 13.18; P-value: 3.597 x 10^-8.
Linear ephemeris (this work): Tc = 26.44436178(Tc#) + 127.12254107

4th Plot: KOI-880.02, P = 51.54 days [Plot error bars = ± 3.05 min.]
TTV_maximum: 147.90 ± 56.78 days, Amp_ttv_maximum: 52.42 ± 6.78 min.
TTV_minimum: 754.37 ± 75.84 days, Amp_ttv_minimum: -66.46 ± 6.78 min.
TTV_maximum: 1360.84 ± 108.06 days, Amp_ttv_maximum: 52.42 ± 6.78 min.
P_ttv: 1212.94 ± 82.44 days.
Amp_ttv: 118.88 ± 9.58 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1346.98 days; Power: 8.91; P-value: 2.581 x 10^-8.
Linear ephemeris (this work): Tc = 51.53866359(Tc#) + 107.07255447

References:
• Fabrycky et al., arXiv-1201.5415; P_ttv = 1/|(nmmri_a/P_a - nmmri_b/P_b)|.
• For Q0-Q6 TTV data of 880.01, 880.02, and 880.03 (thru ~ 563 (BJD-2454900) days), see: Ford et al., 2012, arXiv-1201.1892.
• For Q0-12 TTV data of 880.01, 880.02, and 880.03 (thru ~ 1116 (BJD-2454900) days), see: Mazeh et al., 2013, arXiv-1301.5499.
• For Q0-12 Calc. properties from TTVs of 880.01 and 880.02, see: Hadden & Lithwick, 2013, arXiv-1310.7942.
• For Q0-14 TTV data, see Ji-Wei Xie's website: http://www.astro.utoronto.ca/~jwxie/TTV/TTV_Home.html

16 Dec 2013
KOI-880 (Kepler-82, KIC-7366258) 4-Planets

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