Exoplanet-Science.com

TTVs are derived from Q4-Q17 Kepler data.  x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Normalized PDCSAP_FLUX Kepler light flux vs. time (BJD_tdb - 2454900) data.  y-axes: “(O-C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.

1st Figure above: KOI-2167.02, P = 6.96 days [Plot avg. error bars = ± 11.02 min. (smaller than symbols)]
Linear ephemeris (this work): Tc = [6.95769854 ± 0.00011587](Tc#) + [292.01299430 ± 0.01172174]
---------------------------------------------------------------------------------------------------------------------------------------------
2nd Figure above: KOI-2167.01, P = 24.34 days [Plot avg. error bars = ± 9.67 min.]

TTV_minimum: 327.71 ± 10.37 days, Amp_ttv_minimum: -16.76 ± 4.59 min.
TTV_maximum: 378.54 ± 10.55 days, Amp_ttv_maximum: 14.13 ± 4.59 min.
TTV_minimum: 429.37 ± 10.76 days, Amp_ttv_minimum: -16.76 ± 4.59 min.
TTV_maximum: 480.20 ± 10.99 days, Amp_ttv_maximum: 14.13 ± 4.59 min.
-------[16 intervening minima and maxima]-------
TTV_minimum: 1344.31 ± 17.04 days, Amp_ttv_minimum: -16.76 ± 4.59 min.
TTV_maximum: 1395.14 ± 17.47 days, Amp_ttv_maximum: 14.13 ± 4.59 min.
TTV_minimum: 1445.97 ± 17.91 days, Amp_ttv_minimum: -16.76 ± 4.59 min.
TTV_maximum: 1496.80 ± 18.36 days, Amp_ttv_maximum: 14.13 ± 4.59 min.
P_ttv: 101.66 ± 1.05 days.
Amp_ttv: 30.89 ± 6.49 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 101.44 days; Power: 5.94; FAP: 0.0293.
Linear ephemeris (this work): Tc = [24.33974702 ± 0.00014418](Tc#) + [69.05461510 ± 0.00528344]

---------------------------------------------------------------------------------------------------------------------------------------------
"Figure 1.", 3rd above: KOI-2167.03, P = 76.54 days [Plot avg. error bars = ± 13.80 min.]
TTV_maximum: 484.68 ± 83.80 days, Amp_ttv_maximum: 42.77 ± 20.12 min.
TTV_minimum: 736.31 ± 94.70 days, Amp_ttv_minimum: -48.40 ± 20.12 min.
TTV_maximum: 987.93 ± 108.23 days, Amp_ttv_maximum: 42.77 ± 20.12 min.
TTV_minimum: 1239.56 ± 123.54 days, Amp_ttv_minimum: -48.40 ± 20.12 min.
P_ttv: 503.25 ± 40.04 days.
Amp_ttv: 91.17 ± 28.46 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 506.42 days; Power: 2.92; FAP: 0.188.
Linear ephemeris (this work): Tc = [76.53465331 ± 0.00204608](Tc#) + [97.18784204 ± 0.02346311]


"Figure 2." 4th above: Residuals of Figure 1. [Plot avg. error bars = ± 24.40 min.]

TTV_maximum: 382.01 ± 24.14 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 469.37 ± 24.90 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 556.73 ± 25.80 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 644.08 ± 26.81 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 731.44 ± 27.92 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 818.79 ± 29.12 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 906.15 ± 30.40 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 993.50 ± 31.75 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 1080.86 ± 33.17 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 1168.22 ± 34.63 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 1255.57 ± 36.15 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
TTV_minimum: 1342.93 ± 37.70 days, Amp_ttv_minimum: -39.61 ± 14.22 min.
TTV_maximum: 1430.28 ± 39.30 days, Amp_ttv_maximum: 39.76 ± 14.22 min.
P_ttv: 174.71 ± 3.93 days.
Amp_ttv: 79.37 ± 20.11 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 175.05 days; Power: 3.79; FAP: 0.0505.


"Figure 3." 5th above: Residuals of Figure 2.; Residuals of Residuals of Figure 1. [Plot avg. error bars = ± 28.24 min.]

TTV_maximum: 359.86 ± 22.51 days, Amp_ttv_maximum: 34.46 ± 6.95 min.
TTV_minimum: 510.24 ± 23.80 days, Amp_ttv_minimum: -34.87 ± 6.95 min.
TTV_maximum: 660.62 ± 25.44 days, Amp_ttv_maximum: 34.46 ± 6.95 min.
TTV_minimum: 811.00 ± 27.36 days, Amp_ttv_minimum: -34.87 ± 6.95 min.
TTV_maximum: 961.39 ± 29.51 days, Amp_ttv_maximum: 34.46 ± 6.95 min.
TTV_minimum: 1111.77 ± 31.84 days, Amp_ttv_minimum: -34.87 ± 6.95 min.
TTV_maximum: 1262.15 ± 34.32 days, Amp_ttv_maximum: 34.46 ± 6.95 min.
TTV_minimum: 1412.53 ± 36.91 days, Amp_ttv_minimum: -34.87 ± 6.95 min.
P_ttv: 300.76 ± 6.44 days.
Amp_ttv: 69.33 ± 9.83 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 300.53 days; Power: 5.67; FAP: 0.000620.


"Figure 4." 6th above: Summed combination of Figures 1., 2., and 3. [Plot error bars = ± 39.79 min.]


References:
• Numerous additional pertinent literature and major Tc#, Tc, and TTV tabulations can be found on my "Summary" webpage following the table.

15 Feb 2015

              Kepler KOI-2167 (KIC-6041734) 7(?)-(or more?)-Planet System

Discussion:
KOI-2167.02, the closest-in known transiting planet in this system. showed no credible TTV.

KOI-2167.01 showed a TTV with a periodicity of 101.66 ± 1.05 days.  Since this value is substantially different than the three found (below) for 2167.03, it would appear that 2167.01 is not responsible for any of those.

KOI-2167.03, the furthest-out of the known transiting planets, showed a series of overlaid periodicities.  After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 503.25 ± 40.04 days, a plot (Figure 2.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 174.71 ± 3.93 days.  Furthermore, a plot (Figure 3.) of the Residuals of the Residuals gave a good sinusoidal curve-fit with a periodicity of 300.76 ± 6.44 days.  Lastly, the added combination of these three sinusoidal curves is arrayed in Figure 4. and reasonably reproduces a complex overall curvature consistent with the initial data.  While the sinusoidal behaviors observed could be partially due to orbital eccentricities, it is also possible that 3 additional as yet unseen (perhaps non-transiting) planets are present in the system.

Scroll Down  to

KOI's (Blue)  or
K2 Objects (Green)