TTVs are derived from Q1-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.

Figure 1.: KOI-1426.01, P = 38.87 days [Plot avg. error bars = ± 5.28 min.]
TTV_minimum: 140.97 ± 27.54 days, Amp_ttv_minimum: -37.44 ± 3.84 min.
TTV_maximum: 663.75 ± 32.98 days, Amp_ttv_maximum: 53.44 ± 3.84 min.
TTV_minimum: 1186.54 ± 42.94 days, Amp_ttv_minimum: -37.44 ± 3.84 min.
P_ttv: 1045.57 ± 29.24 days.
Amp_ttv: 90.87 ± 5.43 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1064.54 days; Power: 13.97; FAP: 2.021 x 10^-11.
Linear ephemeris (this work): Tc = [38.86852452](Tc#) + [104.31269907]


Figure 2.: KOI-1426.02, P = 74.93 days [Plot avg. error bars = ± 1.85 min. (smaller than symbols)]

TTV_minimum: 767.71 ± 294.36 days, Amp_ttv_minimum: -46.47 ± 28.38 min.
P_ttv: 1792.00 ± 484.17 days.
Amp_ttv: 117.92 ± 40.14 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1528.12 days; Power: 6.02; FAP: 6.080 x 10^-6.
Linear ephemeris (this work): Tc = [74.92773249](Tc#) + [58.00295482]


Figure 3.: Residuals of Figure 2. [Plot avg. error bars = ± 28.44 min.]

TTV_minimum: 560.28 ± 56.61 days, Amp_ttv_minimum: -10.84 ± 1.91 min.
TTV_maximum: 1000.37 ± 71.12 days, Amp_ttv_maximum: 11.67 ± 1.91 min.
P_ttv: 880.18 ± 45.72 days.
Amp_ttv: 22.51 ± 2.71 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 889.73 days; Power: 5.54; FAP: 2.479 x 10^-4.


Figure 4.: KOI-1426.03, P = 150.02 days [Plot avg. error bars = ± 2.30 min.]

TTV_maximum: 474.20 ± 31.70 days, Amp_ttv_maximum: 20.31 ± 2.49 min.
TTV_minimum: 935.56 ± 41.90 days, Amp_ttv_minimum: -23.82 ± 2.49 min.
P_ttv: 922.71 ± 31.35 days.
Amp_ttv: 44.13 ± 3.52 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 920.84 days; Power: 3.80; FAP: 3.846 x 10^-4.
Linear ephemeris (this work): Tc = [150.02020025](Tc#) + [157.68711467]


Figure 5.: Residuals of Figure 4. [Plot avg. error bars = ± 3.39 min.]

TTV_minimum: 208.36 ± 60.97 days, Amp_ttv_minimum: -3.15 ± 1.46 min.
TTV_maximum: 473.85 ± 67.39 days, Amp_ttv_maximum: 4.16 ± 1.46 min.
TTV_minimum: 739.33 ± 77.51 days, Amp_ttv_minimum: -3.15 ± 1.46 min.
TTV_maximum: 1004.82 ± 90.09 days, Amp_ttv_maximum: 4.16 ± 1.46 min.
TTV_minimum: 1270.31 ± 104.25 days, Amp_ttv_minimum: -3.15 ± 1.46 min.
P_ttv: 530.97 ± 35.83 days.
Amp_ttv: 7.31 ± 2.07 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 526.20 days; Power: 2.51; FAP: 0.146 (low credibility).


Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.

28 May 2015
      Kepler KOI-1426 (Kepler-297, KIC-11122894) 4-(or more?)-Planet System

Discussion:
KOI-1426.01 (Kepler-297b): A sinusoidal curve-fit of the [(O-C) vs. Time] data showed (Figure 1.) a periodicity (P_ttv) of 1045.57 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 1064.54 days.

KOI-1426.02 (Kepler-297c): After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 2.) a periodicity (P_ttv) of 1792.00 days (1528.12 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data), a plot (Figure 3.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 880.18 days (LSP: 889.72 days).  Here, for the primary TTV, the periodicities from both methods do not correspond closely because considerably less than one cycle of periodicity had been observed over the lifetime of the Kepler observations.

KOI-1426.03: After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 4.) a periodicity (P_ttv) of 922.71 days (920.84 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data), a plot (Figure 5.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 526.20 days (LSP: 530.97 days).

As has been typical for numerous other cases, the value of the primary TTV of KOI-1426.02 is higher than reality (as well as different for each determination) when considerably-less-than-one-sinusoidal-cycle has been observed.  Assuming this also holds for the current case, and considering that the ratios of the periods of 1426.02:1426.01 and 1426.03:1426.02 each appear to be near a 2:1 mean motion resonance value (1.928 and 2.002, respectively), where pronounced TTVs are often observed, the following is consistent with the available observations:

• 1426.01 is perturbed by 1426.02 with a TTV near 1055 days;
• 1426.02 is perturbed by both 1426.01 (TTV near 1055 days) and 1426.03 (TTV of “residuals” of ~ 885 days); and
• 1426.03 is perturbed by both 1426.02 (TTV of ~ 921 days (within experimental error (see below) of ~ 885 days) and another (“1426.04”) as yet unseen, non-transiting planetary object (TTV of “residuals” of ~ 529 days).

Exoplanet-Science.com

#############################################

#############################################

Scroll Down  to

KOI's (Blue)  or
K2 Objects (Green)