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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:
KOI-474.04, the closest-in (P = 5.04 days) known exoplanet candidate in this system, is another example for which a relatively short yet credible sinusoidal periodicity is hidden among the relatively scattered appearance of the data points.  In this case, it was first detected in its [(O-C) vs. Tc] Lomb-Scargle Periodogram (LSP) as a credible periodicity of 80.04 days.  Correspondingly, a best-fit sinusoidal curve with a periodicity of 80.05 ± 0.53 days was obtained for the same data.  The underlying cause of this observations is not known but it is reminiscent of the same (potential exomoon?) effect disclosed for 139.02, 676.02, and 774.01 (see corresponding website pages).

KOI-474.01 (P = 10.95 days) shows no sinusoidal periodicity in its (O-C) vs. Tc plot nor any credible periodicity in its LSP.

KOI-474.02 (P = 28.99 days) shows a TTV with a periodicity (P_ttv) of 571.03 ± 33.72 days, in very close agreement with the periodicity derived from an LSP, 568.40 days, of the same data.

The [O-C] vs. Tc data of KOI-474.03 (P = 94.89 days) yields a most interesting set of results.  First, a TTV with a P_ttv of 980.77 ± 135.05 days is evident, suggesting the presence of another unseen (non-transiting) exoplanet in this system.  This is backed up by a Lomb-Scargle Periodogram (LSP) periodicity of 974.85.

Next, the residuals (see "1st-Residuals of TTV" figure) of that plot also gave rise to another sinusoidal array with its own periodicity of 280.86 ± 9.86 days.  Here too the corresponding LSP periodicity is consistent: 282.86 days.  This could indicate a gravitational interaction between 474.03 and a second unseen planetary object, suggesting that the originally-obtained TTV represented a composite of two sets of interactions.

Finally, in addition, the residuals from this last plot (see "2nd-Residuals of 1st-Residuals of TTV" figure) also led to another best-fit sinusoidal array with a periodicity of 651.14 ± 44.64 days; the LSP in this case correspondingly showed a periodicity of 648.31 days.  Could it be that yet a third gravitationally interacting object has a significant influence on 474.03 (and its TTV)?

1st Plot: KOI-474.04, P = 5.04 days [Plot error bars = ± 10.90 min.]
TTV_maximum: 87.40 ± 5.79 days, Amp_ttv_maximum: 16.59 ± 4.48 min.
TTV_minimum: 127.42 ± 5.82 days, Amp_ttv_minimum: -19.19 ± 4.48 min.
TTV_maximum: 167.44 ± 5.87 days, Amp_ttv_maximum: 16.59 ± 4.48 min.
TTV_minimum: 207.46 ± 5.92 days, Amp_ttv_minimum: -19.19 ± 4.48 min.
===== (28 other minima and maxima present in the curve) =====
TTV_minimum: 1368.14 ± 10.73 days, Amp_ttv_minimum: -19.19 ± 4.48 min.
TTV_maximum: 1408.16 ± 10.95 days, Amp_ttv_maximum: 16.59 ± 4.48 min.
TTV_minimum: 1448.18 ± 11.18 days, Amp_ttv_minimum: -19.19 ± 4.48 min.
TTV_maximum: 1488.20 ± 11.40 days, Amp_ttv_maximum: 16.59 ± 4.48 min.
P_ttv: 80.05 ± 0.53 days.
Amp_ttv: 35.78 ± 6.33 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 80.04 days; Power: 10.24; P-value: 0.0370.
Linear ephemeris (this work): Tc = 5.03500550(Tc#) + 65.66327845

2nd Plot: KOI-474.01, P = 10.95 days [Plot error bars = ± 5.55 min.]
Linear ephemeris (this work): Tc = 10.94579547(Tc#) + 109.71730527

3rd Plot: KOI-474.02, P = 28.99 days [Plot error bars = ± 6.86 min.]
TTV_maximum: 307.16 ± 52.67 days, Amp_ttv_maximum: 11.17 ± 4.01 min.
TTV_minimum: 592.67 ± 60.58 days, Amp_ttv_minimum: -12.32 ± 4.01 min.
TTV_maximum: 878.19 ± 71.66 days, Amp_ttv_maximum: 11.17 ± 4.01 min.
TTV_minimum: 1163.70 ± 84.66 days, Amp_ttv_minimum: -12.32 ± 4.01 min.
TTV_maximum: 1449.22 ± 98.84 days, Amp_ttv_maximum: 11.17 ± 4.01 min.
P_ttv: 571.03 ± 33.72 days.
Amp_ttv: 23.49 ± 5.66 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 568.40 days; Power: 5.22; P-value: 0.0770.
Linear ephemeris (this work): Tc = 28.98675778(Tc#) + 67.78380579

4th Plot: KOI-474.03, P = 94.89 days [Plot error bars = ± 5.66 min.]
TTV_maximum: 365.09 ± 111.38 days, Amp_ttv_maximum: 52.04 ± 22.06 min.
TTV_minimum: 855.47 ± 154.13 days, Amp_ttv_minimum: -67.57 ± 22.06 min.
P_ttv: 980.77 ± 135.05 days.
Amp_ttv: 119.61 ± 31.20 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 974.85 days; Power: 3.13; P-value: 0.147.
Linear ephemeris (this work): Tc = 94.88861110(Tc#) + 147.82558409

5th Plot: 1st-Residuals of TTV of KOI-474.03 [Plot error bars = ± 22.78 min.]
TTV_maximum: 169.53 ± 7.78 days, Amp_ttv_maximum: 37.13 ± 11.26 min.
TTV_minimum: 309.95 ± 14.22 days, Amp_ttv_minimum: -46.46 ± 11.26 min.
TTV_maximum: 450.38 ± 20.66 days, Amp_ttv_maximum: 37.13 ± 11.26 min.
TTV_minimum: 590.81 ± 27.10 days, Amp_ttv_minimum: -46.46 ± 11.26 min.
TTV_maximum: 731.24 ± 33.54 days, Amp_ttv_maximum: 37.13 ± 11.26 min.
TTV_minimum: 871.66 ± 39.98 days, Amp_ttv_minimum: -46.46 ± 11.26 min.
TTV_maximum: 1012.09 ± 46.43 days, Amp_ttv_maximum: 37.13 ± 11.26 min.
TTV_minimum: 1152.52 ± 52.87 days, Amp_ttv_minimum: -46.46 ± 11.26 min.
TTV_maximum: 1292.95 ± 59.31 days, Amp_ttv_maximum: 37.13 ± 11.26 min.
P_ttv: 280.86 ± 9.86 days.
Amp_ttv: 83.59 ± 15.92 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 282.86 days; Power: 4.02; P-value: 0.0161.

6th Plot: 2nd-Residuals of 1st-Residuals of TTV of KOI-474.03 [Plot error bars = ± 25.41 min.]
TTV_minimum: 336.15 ± 108.55 days, Amp_ttv_minimum: -21.40 ± 5.86 min.
TTV_maximum: 661.71 ± 213.68 days, Amp_ttv_maximum: 21.90 ± 5.86 min.
TTV_minimum: 987.28 ± 318.82 days, Amp_ttv_minimum: -21.40 ± 5.86 min.
P_ttv: 651.14 ± 44.64 days.
Amp_ttv: 43.41 ± 8.29 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 648.31 days; Power: 4.03; P-value: 0.0184.

References:
• For Q0-Q6 TTV data of 474.01, 474.02, and 474.03 (thru ~ 563 (BJD-2454900) days), see: Ford et al., 2012, arXiv-1201.1892.
• For Q0-12 TTV data of 474.01, 474.02, and 474.03 (thru ~ 1116 (BJD-2454900) days), see: Mazeh et al., 2013, arXiv-1301.5499.

12 Nov 2013
KOI-474 (Kepler-164, KIC-10460984) 6(?)-(or more?)-Planets