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:
No TTV was found for the first exoplanet, KOI-672.01, in this system.  However, via sinusoidal best-fits, not only does KOI-672.02 shows a significant TTV with a P_ttv of ~ 976.40 days, but the residuals of the TTV-xy plot show a second P_ttv of ~ 121.63 days.  Correspondingly, the Lomb-Scargle Periodogram of the former shows two credible periodicities of about the same strength at 983.20 and 122.11; the residuals just show one credible periodicity of 121.57 days.  This behavior is consistent with the presence of two unseen (non-transiting) exoplanets with greater semi-major axes than 672.02.

1st: KOI-672.01, P = 16.09 days [Plot error bars = ± 4.51 min.]
Linear ephemeris (this work): Tc = 16.08788073(Tc#) + 105.81335225

2nd: KOI-672.02, P = 41.75 days [Plot error bars = ± 3.38 min.]
TTV_minimum: 425.09 ± 101.93 days, Amp_ttv_minimum: -7.62 ± 3.15 min.
TTV_maximum: 913.29 ± 135.36 days, Amp_ttv_maximum: 10.31 ± 3.15 min.
TTV_minimum: 1401.49 ± 179.01 days, Amp_ttv_minimum: -7.62 ± 3.15 min.
P_ttv: 976.40 ± 107.59 days.
Amp_ttv: 17.93 ± 4.46 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 983.20 days; Power: 4.46; P-value: 0.121.
Second Lomb-Scargle periodogram, candidate P_ttv: 122.11 days; Power: 4.46; P-value: 0.121.
Linear ephemeris (this work): Tc = 41.74954156(Tc#) + 86.84512098

3rd: RESIDUALS FROM the previous KOI-672.02 TTV-xy plot [Plot error bars = ± 4.62 min.]
TTV_maximum: 113.01 ± 9.64 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 173.83 ± 9.75 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 234.64 ± 9.90 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 295.46 ± 10.10 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 356.28 ± 10.34 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 417.10 ± 10.62 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 477.91 ± 10.93 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 538.73 ± 11.27 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 599.55 ± 11.64 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 660.36 ± 12.04 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 721.18 ± 12.46 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 782.00 ± 12.90 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 842.81 ± 13.36 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 903.63 ± 13.84 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 964.45 ± 14.34 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 1025.27 ± 14.85 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 1086.08 ± 15.37 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 1146.90 ± 15.91 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 1207.72 ± 16.45 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 1268.53 ± 17.00 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 1329.35 ± 17.56 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
TTV_minimum: 1390.17 ± 18.13 days, Amp_ttv_minimum: -8.43 ± 2.51 min.
TTV_maximum: 1450.98 ± 18.71 days, Amp_ttv_maximum: 7.63 ± 2.51 min.
P_ttv: 121.63 ± 1.35 days.
Amp_ttv: 16.06 ± 3.55 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 121.57 days; Power: 5.36; P-value: 0.0343.

References:
• For Q0-Q6 TTV data of 672.01 and 672.02 (thru ~ 563 (BJD-2454900) days), see: Ford et al., 2012, arXiv-1201.1892.
• For Q0-12 TTV data of 672.01 and 672.02 (thru ~ 1116 (BJD-2454900) days), see: Mazeh et al., 2013, arXiv-1301.5499.

19 Dec 2013
KOI-672 (Kepler-209, KIC-7115785), possibly 4-Planets

Scroll Down  to

KOI's (Blue)  or
K2 Objects (Green)

Exoplanet-Science.com