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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-119.01, P = 49.18 days [Plot avg. error bars = ± 1.60 min.]
TTV_minimum: 85.21 ± 17.17 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 185.33 ± 17.47 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 285.44 ± 17.97 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 385.55 ± 18.67 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 485.66 ± 19.53 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 585.77 ± 20.55 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 685.88 ± 21.69 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 785.99 ± 22.94 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 886.10 ± 24.28 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 986.22 ± 25.71 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 1086.33 ± 27.19 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 1186.44 ± 28.73 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 1286.55 ± 30.32 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
TTV_maximum: 1386.66 ± 31.95 days, Amp_ttv_maximum: 3.21 ± 0.99 min.
TTV_minimum: 1486.77 ± 33.61 days, Amp_ttv_minimum: -3.10 ± 0.99 min.
P_ttv: 200.22 ± 3.90 days.
Amp_ttv: 6.31 ± 1.40 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 200.26 days; Power: 5.16; FAP: 0.0276.
Linear ephemeris (this work): Tc = 49.18393562(Tc#) + 74.91429229

Figure 2.: Residuals of Figure 1. [Plot avg. error bars = ± 1.88 min.]
TTV_maximum: 579.54 ± 100.93 days, Amp_ttv_maximum: 2.74 ± 0.81 min.
TTV_minimum: 1115.17 ± 134.04 days, Amp_ttv_minimum: -2.40 ± 0.81 min.
P_ttv: 1071.27 ± 99.17 days.
Amp_ttv: 5.14 ± 1.15 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1055.54 days; Power: 5.15; FAP: 0.0368.

Figure 3.: Residuals of Figure 2.; Residuals-of-the-Residuals of Figure 1. [Plot avg. error bars = ± 2.05 min.]
TTV_minimum: 199.39 ± 33.92 days, Amp_ttv_minimum: -1.75 ± 0.62 min.
TTV_maximum: 392.67 ± 36.29 days, Amp_ttv_maximum: 1.92 ± 0.62 min.
TTV_minimum: 585.95 ± 39.89 days, Amp_ttv_minimum: -1.75 ± 0.62 min.
TTV_maximum: 779.22 ± 44.43 days, Amp_ttv_maximum: 1.92 ± 0.62 min.
TTV_minimum: 972.50 ± 49.65 days, Amp_ttv_minimum: -1.75 ± 0.62 min.
TTV_maximum: 1165.78 ± 55.35 days, Amp_ttv_maximum: 1.92 ± 0.62 min.
TTV_minimum: 1359.06 ± 61.41 days, Amp_ttv_minimum: -1.75 ± 0.62 min.
P_ttv: 386.56 ± 14.72 days.
Amp_ttv: 3.68 ± 0.88 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 384.46 days; Power: 4.78; FAP: 0.0670.

Figure 4.: Added combination of Figures 1., 2., and 3. [Plot error bars = ± 3.21 min.]

Figure 5.: KOI-119.02, P = 190.31 days [Plot avg. error bars = ± 1.60 min.]
TTV_minimum: 555.22 ± 31.36 days, Amp_ttv_minimum: -11.27 ± 1.23 min.
TTV_maximum: 1017.91 ± 40.62 days, Amp_ttv_maximum: 12.39 ± 1.23 min.
P_ttv: 925.38 ± 28.01 days.
Amp_ttv: 23.66 ± 1.74 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 926.96 days; Power: 2.93; FAP: 0.00117.
Linear ephemeris (this work): Tc = 190.32066921(Tc#) + 245.68367593

Literature: Tc#, Tc, and TTV Major Tabulations and Other References: see my "Summary" webpage.

17 July 2014
KOI-119 (Kepler-108, KIC-9471974) 5(?)-(or more?)-Planet System

Discussion:
The two known transiting exoplanets in this system are each approximately Neptune-size:119.01: Rp_(Rearth): 3.9;119.02: Rp_(Rearth): 3.4;Neptune: Rp_(R_earth): 3.8.They show TTV's that suggest a number of additional (non-transiting, or at least not-yet-detected-transiting) planetary objects are present.  The complex TTV of 119.01 is consistent with perturbations by 3 other planets, one of which could be 119.02.  Correspondingly, the TTV of 119.02 is fairly well anti-correlated with one of those 119.01-observed perturbations.119.01:After a sinusoidal curve-fit of the (O-C) vs. Time data (Figure 1. below) showed a periodicity (P_ttv) of 200.22 ± 3.90 days (200.26 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 1071.27 ± 99.17 days (LSP: 1055.54 days).  Similarly, the Residuals-of-the-Residuals also gave a good sinusoidal curve-fit (Figure 3.) with a periodicity of 386.56 ± 14.72 days (LSP: 384.46 days).  The added combination of all three sinusoidal curves is arrayed in Figure 4. and reasonably reproduces a complex overall curvature consistent with the initial data.  While it is certainly possible (see recent work of Lithwick and others) that some of this unusual curvature obtains from eccentric orbits of planetary objects in this system, it is also possible that at least 3 other planets in near-circular orbits are mutually-interacting to give the TTV distribution observed for 119.01.119.02:A sinusoidal curve-fit of the (O-C) vs. Time data (Figure 5. below) showed a periodicity (P_ttv) of 925.38 ± 28.01 days (926.96 days was observed in the LSP of the same data.  Further, the TTV pattern is fairly well anti-correlated with the TTV-Residuals of 119.01 (compare Figure 5 with Figure 2).119.01 & 119.02:Since the sizes of 119.01 and 119.02 are fairly close, the relative amplitudes of these anti-correlated TTV signals suggest that the density of 119.01 is considerably more than that of 119.02, potentially implying that 119.01 has a larger rocky core and smaller gaseous envelope than 119.02.