Kepler KOI-282 (Kepler-130, KIC-5088536) 7(?)-(or more?)-Planet System
Discussion: KOI-282.02 (Kepler-130b), the closest-in known transiting planet, shows no credible periodicity (see Figure 1.).
KOI-282.01 (Kepler-130c) shows a credible periodicity potentially due a non-transiting planet in an adjacent orbit (see Figure 2.). The P_ttv in this case is different from each of those found for the more complex KOI-282.03 (below) case (suggesting that 282.01 is not one of the perturbers of 282.03).
For KOI-282.03 (Kepler-130d, the farthest-out of the known transiting planets), after a sinusoidal curve-fit of the (O-C) vs. Time data showed (Figure 3.) a periodicity (P_ttv) of 259.36 ± 4.39 days (258.38 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data), a plot (Figure 4.) of the Residuals also gave a good sinusoidal curve-fit with a periodicity of 201.47 ± 6.21 days (LSP: 202.23 days). Similarly, a plot (Figure 5.) of the Residuals of the Residuals gave a good sinusoidal curve-fit with a periodicity of 956.13 ± 54.00 days (LSP: 970.49 days). The added combination of these three sinusoidal curves is arrayed in Figure 6. 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 3 additional as yet unseen (perhaps non-transiting) planets are present in the system.
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-282.02, P = 8.46 days [Plot avg. error bars = ± 6.36 min. (smaller than symbols)] Linear ephemeris (this work): Tc = [8.45744375 ± 0.00004119](Tc#) + [72.07012849 ± 0.00402970]