TTVs are derived from Q0-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-3487.01, P = 89.74 days [Plot avg. error bars = ± 0.19 min. (smaller than symbols)]
TTV_maximum: 519.20 ± 93.45 days, Amp_ttv_maximum: 1.61 ± 0.60 min.
TTV_minimum: 941.30 ± 117.04 days, Amp_ttv_minimum: -1.52 ± 0.60 min.
TTV_maximum: 1363.40 ± 146.74 days, Amp_ttv_maximum: 1.61 ± 0.60 min.
P_ttv: 844.20 ± 75.76 days.
Amp_ttv: 3.13 ± 0.84 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 840.88 days; Power: 3.07; FAP: 0.166.
Linear ephemeris (this work): Tc = 89.73974692(Tc#) + 138.26631253


Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 0.63 min.]

TTV_minimum: 200.17 ± 23.43 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 312.88 ± 24.30 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
TTV_minimum: 425.60 ± 25.48 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 538.31 ± 26.95 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
TTV_minimum: 651.02 ± 28.67 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 763.73 ± 30.58 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
TTV_minimum: 876.44 ± 32.65 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 989.15 ± 34.87 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
TTV_minimum: 1101.86 ± 37.19 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 1214.58 ± 39.60 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
TTV_minimum: 1327.29 ± 42.09 days, Amp_ttv_minimum: -0.90 ± 0.35 min.
TTV_maximum: 1440.00 ± 44.65 days, Amp_ttv_maximum: 0.87 ± 0.35 min.
P_ttv: 225.42 ± 6.01 days.
Amp_ttv: 1.78 ± 0.50 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 225.46 days; Power: 3.08; FAP: 0.117.


Figure 3.: Added combination of Figures 1. and 2. [Plot error bars = ± 0.66 min.]

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

25 Jan 2015
             Kepler KOI-3487.01 (KIC-9873760) 3-(or more?)-Planet System

Discussion:
After a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 1.) a periodicity (P_ttv) of 844.20 ± 75.76 days (840.88 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 225.42 ± 6.01 days (LSP: 225.46 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 behaviors observed could be partially due to orbital eccentricities, it is also possible that 2 additional unseen (non-transiting) planets are present in the system.

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