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Discussion:
KOI-42.01 (Kepler-410Ab) is a Neptune-sized exoplanet orbiting one star (Kepler-410A) of a binary star system (see Van Eylen reference below).  This webpage summarizes its transit timing variation and several potential further implications of the observed sinusoidal variation of the TTV residuals.
After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1. below) a periodicity (P_ttv) of 965.34 ± 16.07 days (981.12 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data), a plot (Figure 2.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 283.52 ± 7.18 days (LSP: 284.70 days).  The added combination of these two sinusoidal curves is arrayed in Figure 3. and reasonably reproduces a complex overall curvature consistent with the initial data.  While the sinusoidal character of the residuals could very well be due to KOI-42.01's known eccentric orbit (see reference), it is also possible that (a) 1 or 2 additional unseen (non-transiting) planets are present in the system or (b) 1 additional such planet and the second star (Kepler-410B) are jointly responsible for the observed (O-C) results.

TTVs are derived from Short-Cadence Kepler data for one-third of Q1 and all of Q3-Q17; no data was recorded for two-thirds of Q1 nor for all of Q2.  X-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Normalized PDCSAP_FLUX Kepler light flux vs. time (BJD_tdb - 2454900) short-cadence data.  Y-axes: “(O – C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.
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Figure 1.: KOI-42.01, P = 17.83 days [Plot avg. error bars = ± 0.72 min. (smaller than symbols)]
TTV_minimum: 228.88 ± 16.61 days, Amp_ttv_minimum: -13.07 ± 0.86 min.
TTV_maximum: 711.55 ± 20.04 days, Amp_ttv_maximum: 15.68 ± 0.86 min.
TTV_minimum: 1194.22 ± 25.62 days, Amp_ttv_minimum: -13.07 ± 0.86 min.
P_ttv: 965.34 ± 16.07 days.
Amp_ttv: 28.75 ± 1.21 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 981.12 days; Power: 28.08; FAP: 4.297 x 10^-10.
Linear ephemeris (this work): Tc = [17.83362859 ± 0.00003923](Tc#) + [114.23669935 ± 0.00180787]


Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 1.12 min.]
TTV_minimum: 205.03 ± 23.83 days, Amp_ttv_minimum: -2.85 ± 0.70 min.
TTV_maximum: 346.79 ± 24.86 days, Amp_ttv_maximum: 2.55 ± 0.70 min.
TTV_minimum: 488.55 ± 26.34 days, Amp_ttv_minimum: -2.85 ± 0.70 min.
TTV_maximum: 630.31 ± 28.21 days, Amp_ttv_maximum: 2.55 ± 0.70 min.
TTV_minimum: 772.08 ± 30.39 days, Amp_ttv_minimum: -2.85 ± 0.70 min.
TTV_maximum: 913.84 ± 32.82 days, Amp_ttv_maximum: 2.55 ± 0.70 min.
TTV_minimum: 1055.60 ± 35.44 days, Amp_ttv_minimum: -2.85 ± 0.70 min.
TTV_maximum: 1197.36 ± 38.23 days, Amp_ttv_maximum: 2.55 ± 0.70 min.
TTV_minimum: 1339.13 ± 41.14 days, Amp_ttv_minimum: -2.85 ± 0.70 min.
TTV_maximum: 1480.89 �� 44.15 days, Amp_ttv_maximum: 2.55 ± 0.70 min.
P_ttv: 283.52 ± 7.18 days.
Amp_ttv: 5.40 ± 0.98 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 284.70 days; Power: 8.71; FAP: 0.105.


Figure 3.: Added combination of Figures 1. and 2. [Plot error bars = ± 1.33 min. (smaller than symbols)]
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References:
• Van Eylen, V., Lund, M. N., Aguirre, V. S., et al., arXiv: 1312.4938, 17 Dec 2013.
• Numerous other literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.
17 Nov 2014

Kepler KOI-42.01 (Kepler-410Ab; KIC-8866102 2-(or more?)-Planet System